wb_vm

Verification Manual for Workbench

Release 12.0ANSYS, Inc.

April 2009Southpointe

275 Technology Drive ANSYS, Inc. iscertified to ISO

9001:2008.Canonsburg, PA 15317

[email protected]

http://www.ansys.com

(T) 724-746-3304

(F) 724-514-9494

Copyright and Trademark Information

2009 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

ANSYS, ANSYS Workbench, Ansoft, AUTODYN, EKM, Engineering Knowledge Manager, CFX, FLUENT, HFSS and any and

all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks or trademarks

of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark used by ANSYS, Inc.

under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, service and feature names

or trademarks are the property of their respective owners.

Disclaimer Notice

THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFIDENTIAL

AND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS. The software products and document-

ation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreement that contains pro-

visions concerning non-disclosure, copying, length and nature of use, compliance with exporting laws, warranties,

disclaimers, limitations of liability, and remedies, and other provisions. The software products and documentation may

be used, disclosed, transferred, or copied only in accordance with the terms and conditions of that software license

agreement.

ANSYS, Inc. is certified to ISO 9001:2008.

U.S. Government Rights

For U.S. Government users, except as specifically granted by the ANSYS, Inc. software license agreement, the use, du-

plication, or disclosure by the United States Government is subject to restrictions stated in the ANSYS, Inc. software

license agreement and FAR 12.212 (for non-DOD licenses).

Third-Party Software

See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary software and

third-party software. If you are unable to access the Legal Notice, please contact ANSYS, Inc.

Published in the U.S.A.

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

I. DesignModeler Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

WBVMDM001 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

WBVMDM002 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

WBVMDM003 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

II. Mechanical Application Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

WBVMMECH001 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

WBVMMECH002 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

WBVMMECH003 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

WBVMMECH004 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

WBVMMECH005 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

WBVMMECH006 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

WBVMMECH007 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

WBVMMECH008 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

WBVMMECH009 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

WBVMMECH010 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

WBVMMECH011 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

WBVMMECH012 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

WBVMMECH013 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

WBVMMECH014 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

WBVMMECH015 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

WBVMMECH016 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

WBVMMECH017 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

WBVMMECH018 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

WBVMMECH019 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

WBVMMECH020 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

WBVMMECH021 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

WBVMMECH022 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

WBVMMECH023 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

WBVMMECH024 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

WBVMMECH025 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

WBVMMECH026 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

WBVMMECH027 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

WBVMMECH028 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

WBVMMECH029 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

WBVMMECH030 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

WBVMMECH031 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

WBVMMECH032 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

WBVMMECH033 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

WBVMMECH034 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

WBVMMECH035 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

WBVMMECH036 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

WBVMMECH037 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

WBVMMECH038 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

WBVMMECH039 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

WBVMMECH040 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

WBVMMECH041 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

WBVMMECH042 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

WBVMMECH043 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

WBVMMECH044 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

iiiRelease 12.0 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

WBVMMECH045 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

WBVMMECH046 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

WBVMMECH047 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

WBVMMECH048 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

WBVMMECH049 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

WBVMMECH050 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

WBVMMECH051 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

WBVMMECH052 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

WBVMMECH053 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

WBVMMECH054 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

WBVMMECH055 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

WBVMMECH056 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

WBVMMECH057 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

WBVMMECH058 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

WBVMMECH059 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

WBVMMECH060 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

WBVMMECH061 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

WBVMMECH062 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

WBVMMECH063 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

WBVMMECH064 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

WBVMMECH065 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

WBVMMECH066 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

WBVMMECH067 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

WBVMMECH068 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

WBVMMECH069 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

WBVMMECH070 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

WBVMMECH071 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

WBVMMECH072 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

III. Design Exploration Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

WBVMDX001 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

WBVMDX002 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

WBVMDX003 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

WBVMDX004 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

WBVMDX005 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Index .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Release 12.0 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.iv

Verification Manual for Workbench

Introduction

This manual presents a collection of test cases that demonstrate a number of the capabilities of the Workbench

analysis environment. The available tests are engineering problems that provide independent verification,

usually a closed form equation. Many of them are classical engineering problems.

The solutions for the test cases have been verified, however, certain differences may exist with regard to

the references. These differences have been examined and are considered acceptable. The workbench analyses

employ a balance between accuracy and solution time. Improved results can be obtained in some cases by

employing a more refined finite element mesh but requires longer solution times. For the tests, an error

rate of 3% or less has been the goal.

These tests were run on an Intel Xeon processor using Microsoft Windows XP Professional. These results are

reported in the test documentation. Slightly different results may be obtained when different processor

types or operating systems are used.

The tests contained in this manual are a partial subset of the full set of tests that are run by ANSYS developers

to ensure a high degree of quality for the Workbench product. The verification of the Workbench product

is conducted in accordance with the written procedures that form a part of an overall Quality Assurance

program at ANSYS, Inc.

You are encouraged to use these tests as starting points when exploring new Workbench features. Geometries,

material properties, loads, and output results can easily be changed and the solution repeated. As a result,

the tests offer a quick introduction to new features with which you may be unfamiliar.

Some test cases will require different licenses, such as DesignModeler, Emag, or Design Exploration. If you

do not have the available licenses, you may not be able to reproduce the results. The Educational version

of Workbench should be able to solve most of these tests. License limitations are not applicable to Workbench

Education version but problem size may restrict the solution of some of the tests.

The working directories for each of the Verification Manual tests are available at the Customer Portal.

Download the ANSYS Workbench Verification Manual Database Files. These databases provide all of the

necessary elements for running a test, including geometry parts, material files and workbench databases.

To open a test case in workbench, locate the working directory and double-click the Workbench database

(.wbdb).

You can use these tests to verify that your hardware is executing the ANSYS Workbench tests correctly. The

results in the databases can be cleared and the tests solved multiple times. The test results should be checked

against the verified results in the documentation for each test.

ANSYS Inc. offers the Workbench Verification and Validation package for users that must perform system

validation.

This package automates the process of test execution and report generation. If you are interested in con-

tracting for such services contact the ANSYS, Inc. Quality Assurance Group.

1Release 12.0 - 2009 SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information


Part I, DesignModeler Descriptions

WBVMDM001: Extrude, Chamfer, and Blend Features

Overview

Extrude, Chamfer, and BlendFeature:

MillimeterDrawing Units:

Test Case

Create a Model using Extrude, Chamfer, and Blend features.

A polygonal area is extruded 60 mm. A rectangular area of 30 mm x 40 mm [having a circular area of radius

6 mm subtracted] is extruded to 20 mm. Both resultant solids form one solid geometry. A rectangular area

(24 mm x 5 mm) is subtracted from the solid. Two rectangular areas (40 mm x 10 mm) are extruded 10 mm

and subtracted from solid. Two rectangular areas (25 mm x 40 mm) are extruded 40 mm and subtracted

from solid. A Chamfer (10 mm x 10 mm) is given to 4 edges on the resultant solid. Four Oval areas are extruded

and subtracted from Solid. Fillet (Radius 5 mm) is given to 4 edges using Blend Feature.

Verify Volume of the resultant geometry.

Figure: Final Model after creating Extrude, Chamfer, and Blend

Calculations

1. Volume of Solid after extruding Polygonal Area: v1 = 264000 mm3.

2. Volume of rectangular area having circular hole: v2 = 21738.05 mm3.

Net Volume = V = v1 + v2 = 285738.05 mm3.

3. Volume of rectangular (24mm x 5mm) solid extruded 30mm using Cut Material = 3600 565.5 = 3034.5

mm3.

Net volume V = 285738.05 3034.5 = 282703.5 mm3.

4. Volume of two rectangular areas each 40mm x 10mm extruded 10mm = 8000 mm3.

Net volume V = 282703.5 8000 = 274703.5 mm3.

5. Volume of two rectangular areas 25mm x 40mm extruded 40mm = 80000 mm3.



Net volume V = 274703.5 80000 = 194703.5 mm3.

6. Volume of four solids added due to Chamfer = 4 x 500 = 2000 mm3

Net volume V = 194703.5 + 2000 = 196703.5 mm3.

7. Volume of four oval areas extruded 10 mm = 7141.6 mm3.

Net volume V = 196703.5 - 7141.6 = 189561.9 mm3.

8. Volume of 4 solids subtracted due to Blend of radius 5 mm = 429.2 mm3.

Hence Net volume of final Solid body = V = 189561.9 429.2 = 189132.7 mm3.

Results Comparison

Error (%)Design-

Modeler

TargetResults

0189132.7189132.7Volume (mm3)

0.00144261.644261.29Surface Area (mm2)

05252Number of Faces

011Number of Bodies


WBVMDM001

WBVMDM002: Cylinder using Revolve, Sweep, Extrude, and Skin-Loft

Overview

Revolve, Sweep, Extrude, and Skin-LoftFeature:


Test Case

Create a Model using Revolve, Sweep, Extrude, and Skin-Loft features.

A Rectangular area (100 mm x 30 mm) is revolved about Z-Axis in 3600 to form a Cylinder. A circular area

of radius 30 mm is swept 100 mm using Sweep feature. A circular area of radius 30 mm is extruded 100

mm. A solid cylinder is created using Skin-Loft feature between two coaxial circular areas each of radius 30

mm and 100 mm apart.

Verify Volume of the resultant geometry.

Figure: Final Model after creating Revolve, Sweep, Extrude, and Skin-Loft

Calculations

1. Volume of Cylinder created after Revolving Rectangular area (100 mm x 30 mm) = v1 = 282743.3 mm3.

2. Volume of Cylinder created when a circular area (Radius 30mm) is swept 100 mm = v2 = 282743.3

mm3.

Net Volume = V = v1 + v2 = 282743.3 + 282743.3 = 565486.6 mm3.

3. Volume of Cylinder after extruding a circular area (Radius 30 mm) 100 mm = 282743.3 mm3.

Net Volume = V = 565486.6 + 282743.3 = 848229.9 mm3.

4. Volume of Cylinder created after using Skin-Loft feature between two circular areas of Radius 30 mm

and 100 mm apart. = 282743.3 mm3.

Net Volume of the final Cylinder = 848229.9 + 282743.3 = 1130973.2 mm3.



Results Comparison

Error (%)Design-

Modeler

TargetResults

01130973.31130973.3Volume (mm3)

081053.181053.1Surface Area (mm2)

033Number of Faces

011Number of Bodies


WBVMDM002

WBVMDM003: Extrude, Revolve, Skin-Loft, and Sweep

Overview

Extrude, Revolve, Skin-Loft, and SweepFeature:


Test Case

Create a Model using Extrude, Revolve, Skin-Loft, and Sweep.

A rectangular area (103 mm x 88 mm) is extruded 100 mm to form a solid box. A circular area of radius 25

mm is revolved 900 using Revolve feature and keeping Thin/Surface option to Yes and 3 mm Inward and

Outward Thickness. A solid is subtracted using Skin-Loft feature between two square areas (each of side 25

mm) and 100 mm apart. The two solid bodies are frozen using Freeze feature. A circular area of radius 25

mm is swept using Sweep feature and keeping Thin/Surface option to Yes and 3 mm Inward and Outward

Thickness. Thus a total of 4 geometries are created.

Verify the volume of the resulting geometry.

Figure: Final Model after creating Extrude, Revolve, Skin-Loft and Sweep

Calculations

1. Volume of rectangular (103 mm x 88 mm) solid extruded 100mm = 906400 mm3.

2. Volume of solid after revolving circular area of Radius 25 mm through 900 = 29639.6 mm3.

Net Volume of solid box, Va = 906400 - 29639.6 = 876760.3 mm3.

3. Volume of additional body created due to Revolve feature = Vb= 11134.15 mm3.

4. Volume of the rectangular box cut after Skin-Loft between two square areas each of side 25 mm =

62500 mm3.

Net Volume of solid box becomes Va = 876760.3 62500 = 814260.3 mm3.

5. Volume of additional two bodies created due to Sweep feature:

Vc = 47123.9 mm3 and Vd = 28352.8 mm

3.

And total volume that gets subtracted from box due to Sweep Feature = 75476.7 mm3.



Hence Net volume of box, Va = 814260.3 - 75476.7 = 738783.6 mm3.

Sum of volumes of all four bodies = Va+Vb+Vc+Vd = 738783.6 + 11134.15 + 47123.9 +28352.8 =

825394.4 mm3.

Results Comparison

Error (%)Design-

Modeler

TargetResults

0825394.5825394.4Volume (mm3)

0101719.95101719.47Surface Area (mm2)

02222Number of Faces

044Number of Bodies


WBVMDM003

Part II, Mechanical Application Descriptions

WBVMMECH001: Statically Indeterminate Reaction Force Analysis

Overview

S.Timoshenko, Strength of Materials, Part 1, Elementary Theory

and Problems, 3rd Edition, CBS Publishers and Distributors, pg.

22 and 26

Reference:

Linear Static Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of three prismatic bars is supported at both end faces and is axially loaded with forces F1 and

F2. Force F1 is applied on the face between Parts 2 and 3 and F2 is applied on the face between Parts 1 and

2. Apply advanced mesh control with element size of 0.5.

Find reaction forces in the Y direction at the fixed supports.

Figure: Schematic

LoadingGeometric PropertiesMaterial Properties

Force F1 = -1000 (Y direc-

tion)

Cross section of all parts

= 1 x 1

E = 2.9008e7 psi

= 0.3

Force F2 = -500 (Y direc-

tion)

Length of Part 1 = 4" = 0.28383 lbm/in3

Length of Part 2 = 3"

Length of Part 3 = 3

Results Comparison

Error (%)MechanicalTargetResults

0.127901.14900Y Reaction Force at Top Fixed

Support (lbf )

-0.190598.86600Y Reaction Force at Bottom

Fixed Support (lbf )



WBVMMECH002: Rectangular Plate with Circular Hole Subjected to Tensile Loading

Overview

J. E. Shigley, Mechanical Engineering Design, McGraw-Hill, 1st Edi-

tion, 1986,Table A-23, Figure A-23-1, pg. 673

Reference:


Type(s):

SolidElement

Type(s):

Test Case

A rectangular plate with a circular hole is fixed along one of the end faces and a tensile pressure load is

applied on the opposite face. A convergence with an allowable change of 10% is applied to account for the

stress concentration near the hole. The Maximum Refinement Loops is set to 2 and the Refinement mesh

control is added on the cylindrical surfaces of the hole with Refinement = 1.

Find the Maximum Normal Stress in the x direction on the cylindrical surfaces of the hole.

Figure: Schematic


Pressure = -100 PaLength = 15 mE = 1000 Pa

Width = 5 m = 0

Thickness = 1 m

Hole radius = 0.5 m

Results Comparison


0.720314.75312.5Maximum Normal X Stress

(Pa)



WBVMMECH003: Modal Analysis of Annular Plate

Overview

R. J. Blevins, Formula for Natural Frequency and Mode Shape, Van

Nostrand Reinhold Company Inc., 1979,Table 11-2, Case 4, pg.

247

Reference:

Free Vibration AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of three annular plates has cylindrical support (fixed in the radial, tangential, and axial directions)

applied on the cylindrical surface of the hole. Sizing control with element size of 0.5 is applied to the cyl-

indrical surface of the hole.

Find the first six modes of natural frequencies.

Figure: Schematic


Inner diameter of inner

plate = 20"

E = 2.9008e7 psi

= 0.3

Inner diameter of

middle plate = 28"

= 0.28383 lbm/in3

Inner diameter of outer

plate = 34"

Outer diameter of outer

plate = 40"

Thickness of all plates =

1"



Results Comparison


1.363315.15310.9111st Frequency Mode (Hz)

0.778320.56318.0862nd Frequency Mode (Hz)

0.872320.86318.0863rd Frequency Mode (Hz)

0.108351.95351.5694th Frequency Mode (Hz)

0.214352.32351.5695th Frequency Mode (Hz)

-0.219441.48442.4516th Frequency Mode (Hz)


WBVMMECH003

WBVMMECH004: Shape Optimization of a Quarter of a Plate With Hole

Overview

Mlejnek and Schirrmacher, Comp. Meth. Appl. Mech Engg.,Vol. 106,

1993

Reference:

Shape OptimizationAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A rectangular plate (1300 x 1300 mm) with a hole is modeled with one-quarter symmetry. It has frictionless

support applied on the two flat faces along the thickness near the hole. Pressure loads are applied on the

remaining two flat faces along the thickness as shown below. Apply advanced mesh control with element

size of 29 mm to get accurate results.

Find the Optimized Mass for target reduction of 20%.

Figure: Schematic


Pressure = -0.15385 MPaQuadrant Length = 650

mm

E = 2.1e5 MPa

Pressure 2 = -0.076925

MPa

= 0.3

Quadrant Width = 650

mm

= 8e-6 kg/mm3

Thickness = 10 mm

Radius = 250 mm



Results Comparison


1.68024.323.8984Optimized Mass (kg)


WBVMMECH004

WBVMMECH005: Heat Transfer in a Composite Wall

Overview

F. Kreith, Principles of Heat Transfer, Harper and Row Publisher, 3rd

Edition, 1976, Example 2-5, pg. 39

Reference:

Linear Static Thermal AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A furnace wall consists of two layers: fire brick and insulating brick. The temperature inside the furnace is

3000F (Tf) and the inner surface convection coefficient is 3.333e-3 BTU/s ft2F (hf). The ambient temperature

is 80F (Ta) and the outer surface convection coefficient is 5.556e-4 BTU/s ft2F (ha).

Find the Temperature Distribution.

Figure: Schematic


Cross-section = 1" x 1"Fire brick wall: k = 2.222e-4

BTU/s ft F Fire brick wall thickness

= 9"Insulating wall: k = 2.778e-5

BTU/s ft F Insulating wall thickness

= 5"

Results Comparison


0.205336.69336Minimum Temperature (F)

0.0072957.22957Maximum Temperature (F)



WBVMMECH006: Heater with Nonlinear Conductivity

Overview

Vedat S. Arpaci, Conduction Heat Transfer, Addison-Wesley Book

Series, 1966, pg. 130

Reference:

Nonlinear Static Thermal AnalysisAnalysis Type(s):

SolidElement Type(s):

Test Case

A liquid is boiled using the front face of a flat electric heater plate. The boiling temperature of the liquid is

212F. The rear face of the heater is insulated. The internal energy generated electrically may be assumed

to be uniform and is applied as internal heat generation.

Find the maximum temperature and maximum total heat flux.

Figure: Schematic


Front face temperature

= 212F

k = [0.01375 * (1 + 0.001 T)]

BTU/s inF

Radius = 3.937

Thickness = 1

Internal heat generation

= 10 BTU/s in3

Conductiv-

ity (BTU/s

inF)

Temperat-

ure (F)

1.419e-00232

2.75e-0021000

Results Comparison


0.960480.57476Maximum Temperature (F)

-0.0039.999710Maximum Total Heat Flux

(BTU/s in2)



WBVMMECH007: Thermal Stress in a Bar with Temperature Dependent

Conductivity

Overview

Any basic Heat Transfer bookReference:

Nonlinear Thermal Stress AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A long bar has thermal conductivity that varies with temperature. The bar is constrained at both ends by

frictionless surfaces. A temperature of TC is applied at one end of the bar (End A). The reference temperature

is 5C. At the other end, a constant convection of h W/m2C is applied. The ambient temperature is 5C.

Advanced mesh control with element size of 2 m is applied.

Find the following:

Minimum temperature

Maximum thermal strain in z direction (on the two end faces)

Maximum deformation in z direction

Maximum heat flux in z direction at z = 20 m

Figure: Schematic


Rear face temperature T

= 100C

Length = 20 mE = 2e11 Pa

Width = 2 m = 0

Film Coefficient h =

0.005 W/m2C

Breadth = 2 m = 1.5e-05 / C

k = 0.038*(1 + 0.00582*T)

W/m C Ambient temperature =

5CConductiv-

ity (W/m C)

Temperat-

ure (C) Reference temperature

= 5C3.91e-0025

0.215800



Analysis

Temperature at a distance "z" from rear face is given by:

T x zz = + 171 82 73886 82 1492 13. . . ( )

Thermal strain in the z direction in the bar is given by:

zT zT= 1 5 10 55. ( )

Deformation in the z direction is given by:

u T dzz z

z

= ( . ( ))1 425 10 550

Heat flux in the z direction is given by:

q Tz= 0 005 5. ( )

Results Comparison


-0.01638.01438.02Minimum Temperature (C)

0.0420.000495210.000495Maximum Thermal strain (z

= 20) (m/m)

0.0000.0014250.001425Maximum Thermal strain (z

= 0) (m/m)

0.9050.0023410.00232Maximum Z Deformation (m)

0.0420.165070.165Maximum Z Heat Flux (z = 20)

(W/m2)


WBVMMECH007

WBVMMECH008: Heat Transfer from a Cooling Spine

Overview

Kreith, F., Principles of Heat Transfer, Harper and Row, 3rd Edition,

1976, Equation 2-44a, pg. 59, Equation 245, pg. 60

Reference:

Linear Static Thermal AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A steel cooling spine of cross-sectional area A and length L extend from a wall that is maintained at temper-

ature Tw. The surface convection coefficient between the spine and the surrounding air is h, the air temper

is Ta, and the tip of the spine is insulated. Apply advanced mesh control with element size of 0.025'.

Find the heat conducted by the spine and the temperature of the tip.

Figure: Schematic



Tw = 100FCross section = 1.2 x

1.2

E = 4.177e9 psf

Ta = 0F = 0.3

h = 2.778e-4 BTU/s ft2 FL = 8Thermal conductivity k =

9.71e-3 BTU/s ft F

Results Comparison


0.05579.07879.0344Temperature of the Tip (F)

-0.0416.3614e-36.364e-3Heat Conducted by the Spine

(Heat Reaction) (BTU/s)



WBVMMECH009: Stress Tool for Long Bar with Compressive Load

Overview

Any basic Strength of Materials bookReference:


Type(s):

SolidElement

Type(s):

Test Case

A multibody of four bars connected end to end has one of the end faces fixed and a pressure is applied to

the opposite face as given below. The multibody is used to nullify the numerical noise near the contact re-

gions.

Find the maximum equivalent stress for the whole multibody and the safety factor for each part using the

maximum equivalent stress theory with tensile yield limit.

Figure: Schematic

Material Properties

Tensile Yield (Pa)E (Pa)Material

2.07e801.93e11Part 1

2.8e807.1e10Part 2

2.5e802e11Part 3

2.8e801.1e11Part 4

LoadingGeometric Properties

Pressure = 2.5e8 PaPart 1: 2 m x 2 m x 3 m

Part 2: 2 m x 2 m x 10

m

Part 3: 2 m x 2 m x 5 m

Part 4: 2 m x 2 m x 2 m



Results Comparison


0.0002.5e82.5e8Maximum Equivalent Stress

(Pa)

0.0000.8280.828Safety Factor for Part 1


0.00011Safety Factor for Part 3



WBVMMECH009

WBVMMECH010: Modal Analysis of a Rectangular Plate

Overview

Blevins, Formula for Natural Frequency and Mode Shape, Van Nos-

trand Reinhold Company Inc., 1979,Table 11-4, Case 11, pg. 256

Reference:

Free Vibration AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A rectangular plate is simply supported on both the smaller edges and fixed on one of the longer edges as

shown below. Sizing mesh control with element size of 6.5 mm is applied on all the edges to get accurate

results.

Find the first five modes of natural frequency.

Figure: Schematic


Length = 0.25 mE = 2e11 Pa

Width = 0.1 m = 0.3

Thickness = 0.005 m = 7850 kg/m3

Results Comparison


-0.952590.03595.71st Frequency Mode (Hz)

-0.9871118.41129.552nd Frequency Mode (Hz)

-0.6672038.12051.793rd Frequency Mode (Hz)

-0.9942879.32906.734th Frequency Mode (Hz)

-0.48933503366.485th Frequency Mode (Hz)



WBVMMECH011: Large Deflection of a Circular Plate with Uniform Pressure

Overview

Timoshenko S.P.,Woinowsky-Krieger S.,Theory of Plates and Shells,

McGraw-Hill, 2nd Edition, Article 97, equation 232, pg. 401

Reference:

Nonlinear Structural Analysis (Large Deformation On)Analysis

Type(s):

ShellElement

Type(s):

Test Case

A circular plate is subjected to a uniform pressure on its flat surface. The circular edge of the plate is fixed.

To get accurate results, apply sizing control with element size of 5 mm on the circular edge.

Find the total deformation at the center of the plate.

Figure: Schematic


Pressure = 6585.18 PaRadius = 0.25 mE = 2e11 Pa

Thickness = 0.0025 m = 0.3

Results Comparison


-0.960.0012380.00125Total deformation (m)



WBVMMECH012: Buckling of a Stepped Rod

Overview

Warren C.Young, Roark's Formulas for Stress & Strains, McGraw

Hill, 6th Edition,Table 34, Case 2a, pg. 672

Reference:

Buckling AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A stepped rod is fixed at one end face. It is axially loaded by two forces: a tensile load at the free end and

a compressive load on the flat step face at the junction of the two cross sections. To get accurate results,

apply sizing control with element size of 6.5 mm.

Find the Load Multiplier for the First Buckling Mode.

Figure: Schematic


Force at free end = 1000

N

Larger diameter =

0.011982 m

E = 2e11 Pa

= 0.3

Force at the flat step

face = -2000 N

Smaller diameter =

0.010 m

Both forces are in the z

direction

Length of larger diamet-

er = 0.2 m

Length of smaller dia-

meter = 0.1 m

Results Comparison


1.64922.87122.5Load Multiplier



WBVMMECH013: Buckling of a Circular Arch

Overview

Warren C.Young, Roark's Formulas for Stress Strains, McGraw Hill,

6th Edition,Table 34, Case 10, pg. 679

Reference:


Type(s):

ShellElement

Type(s):

Test Case

A circular arch of a rectangular cross section (details given below) is subjected to a pressure load as shown

below. Both the straight edges of the arch are fixed.

Find the Load Multiplier for the first buckling mode.

Figure: Schematic


Pressure = 1 MPaArch cross-section = 5

mm x 50 mm

E = 2e5 MPa

= 0

Mean radius of arch =

50 mm

Included angle = 90

Results Comparison


0.357545.94544Load Multiplier



WBVMMECH014: Harmonic Response of a Single Degree of Freedom System

Overview

Any basic Vibration Analysis bookReference:

Harmonic AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly where four cylinders represent massless springs in series and a point mass simulates a spring

mass system. The flat end face of the cylinder (Shaft 1) is fixed. Harmonic force is applied on the end face

of another cylinder (Shaft 4) as shown below.

Find the z directional Deformation Frequency Response of the system on the face to which force is applied

for the frequency range of 0 to 500 Hz for the following scenarios using Mode Superposition. Solution intervals

= 20.

Scenario 1: Damping ratio = 0

Scenario 2: Damping ratio = 0.05

Figure: Schematic

Material Properties

(kg/m3

)E (Pa)Material

1e-80.341.1e11Shaft 1

1e-80.341.1e11Shaft 2

1e-80.354.5e10Shaft 3

1e-80.354.5e10Shaft 4


Force = 1e7 N (Z-direction)Each cylinder:

Point Mass = 3.1044 KgDiameter = 20 mm

Length = 50 mm



Results Comparison


0.5910.141230.1404Maximum Amplitude without

damping (m)

0.000180180Phase angle without damp-

ing (degrees)

0.5770.14080.14Maximum Amplitude with

damping (m)

0.000175.58175.6Phase angle with damping

(degrees)


WBVMMECH014

WBVMMECH015: Harmonic Response of Two Storied Building under Transverse

Loading

Overview

W.T.Thomson, Theory of Vibration with Applications, 3rd Edition,

1999, Example 6.4-1, pg. 166

Reference:


Type(s):

SolidElement

Type(s):

Test Case

A two-story building has two columns (2K and K) constituting stiffness elements and two slabs (2M and M)

constituting mass elements. The material of the columns is assigned negligible density so as to make them

as massless springs. The slabs are allowed to move only in the y direction by applying frictionless supports

on all the faces of the slabs in the y direction. The end face of the column (2K) is fixed and a harmonic force

is applied on the face of the slab (M) as shown in the figure below.

Find the y directional Deformation Frequency Response of the system at 70 Hz on each of the vertices as

shown below for the frequency range of 0 to 500 Hz using Mode Superposition. Use Solution intervals = 50.

Figure: Schematic

Material Properties

(kg/m3

)E (Pa)Material

78500.32e18Block 2

1e-80.354.5e10Shaft 2

157000.32e18Block 1

1e-80.359e10Shaft 1


Force = -1e5 N (y direction)Block 1 and 2:



40 mm x 40 mm x 40 mm

Shaft 1 and 2:

20 mm x 20 mm x 200 mm

Results Comparison


0.8630.210330.20853Maximum Amplitude for ver-

tex A (m)

0.7610.075470.074902Maximum Amplitude for ver-

tex B (m)


WBVMMECH015

WBVMMECH016: Fatigue Tool with Non-Proportional Loading for Normal Stress

Overview

Any basic Machine Design bookReference:

Fatigue AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A bar of rectangular cross section has the following loading scenarios.

Scenario 1: One of the end faces is fixed and a force is applied on the opposite face as shown below

in Figure : Scenario 1 (p. 43).

Scenario 2: Frictionless support is applied to all the faces of the three standard planes (faces not seen

in Figure : Scenario 2 (p. 43)) and a pressure load is applied on the opposite faces in positive y- and z-

directions.

Find the life, damage, and safety factor for the normal stresses in the x, y, and z directions for non-propor-

tional fatigue using the Soderberg theory. Use a design life of 1e6 cycles, a fatigue strength factor or 1, a

scale factor of 1, and 1 for coefficients of both the environments under Solution Combination.

Figure: Scenario 1

Figure: Scenario 2

Material Properties

E = 2e11 Pa

= 0.3



Material Properties

Ultimate Tensile Strength = 4.6e8 Pa

Yield Tensile Strength = 3.5e8 Pa

Endurance Strength = 2.2998e6 Pa

Alternating Stress (Pa)Number of Cycles

4.6e81000

2.2998e61e6


Scenario 1: Force = 2e6 N

(y-direction)

Bar: 20 m x 1 m x 1m

Scenario 2: Pressure = -1e8

Pa

Analysis

Non-proportional fatigue uses the corresponding results from the two scenarios as the maximum and min-

imum stresses for fatigue calculations. The fatigue calculations use standard formulae for the Soderberg

theory.

Results Comparison


-0.1563329.93335.1049LifeStress Component - Component X

0.157300.31299.8406Damage

0.1320.0190250.019Safety Factor

-0.7641465314765.7874LifeStress Component - Component Y

0.77268.24767.724Damage

-0.6830.0453780.04569Safety Factor

0.0011476614765.7874LifeStress Component - Component Z

0.00167.72567.724Damage

0.0130.0456960.04569Safety Factor


WBVMMECH016

WBVMMECH017:Thermal Stress Analysis with Remote Force and Thermal Loading

Overview


Linear Thermal Stress AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A cylindrical rod assembly of four cylinders connected end to end has frictionless support applied on all the

cylindrical surfaces and both the flat end faces are fixed. Other thermal and structural loads are as shown

below.

Find the Deformation in the x direction of the contact surface on which the remote force is applied. To get

accurate results apply a global element size of 1.5 m.

Figure: Schematic


Given temperature (End A)

= 1000C

Diameter = 2 mE = 2e11 Pa

Lengths of cylinders in

order from End A: 2 m,

5 m, 10 m, and 3 m.

= 0

Given temperature (End B)

= 0C

= 1.2e-5/C

Remote force = 1e10 N ap-

plied on the contact surface

at a distance 7 m from end

A.

Location of remote force =

(7,0,0) m

Results Comparison


-1.6250.100160.101815Maximum X Deformation (m)



WBVMMECH018: A Bar Subjected to Tensile Load with Inertia Relief

Overview


Linear Static Structural Analysis (Inertia Relief On)Analysis

Type(s):

SolidElement

Type(s):

Test Case

A long bar assembly is fixed at one end and subjected to a tensile force at the other end as shown below.

Turn on Inertia Relief.

Find the deformation in the z direction

Figure: Schematic


Force P = 2e5 N (positive z

direction)

Cross-Section = 2 m x 2

m

E = 2e11 Pa

= 0.3

Lengths of bars in order

from End A: 2 m, 5 m,

10 m, and 3 m.

= 7850 kg/m3

Analysis

zPL

AE

PL

mE=

2

2

where:

L = total length of bar

A = cross-section

m = mass



Results Comparison


0.1522.5038e-62.5e-6Maximum Z Deformation (m)


WBVMMECH018

WBVMMECH019: Mixed Model Subjected to Bending Loads with Solution

Combination

Overview



Type(s):

Beam and ShellElement

Type(s):

Test Case

A mixed model (shell and beam) has one shell edge fixed as shown below. Bending loads are applied on

the free vertex of the beam as given below. Apply a global element size of 80 mm to get accurate results.

Scenario 1: Only a force load.

Scenario 2: Only a moment load.

Find the deformation in the y direction under Solution Combination with the coefficients for both the envir-

onments set to 1.

Figure: Scenario 1

Figure: Scenario 2


Force F = -10 N (y direction)Shell = 160 mm x 500

mm x 10 mm

E = 2e5 Pa

Moment M = -4035 Nmm

@ z-axis

= 0



Beam rectangular cross

section = 10 mm x 10

mm

Beam length = 500 mm

Analysis

yF

EI

M

EI= +

23

384

19

128

3 2l l

where:

I = total bending length of the mixed model

I = moment of inertia of the beam cross-section

Results Comparison


0.929-7.2542-7.18742Maximum Y-Deformation

(mm)


WBVMMECH019

WBVMMECH020: Modal Analysis for Beams

Overview


Modal AnalysisAnalysis

Type(s):

BeamElement

Type(s):

Test Case

Two collinear beams form a spring mass system. The density of the longer beam is kept very low so that it

acts as a massless spring and the smaller beam acts as a mass. The end vertex of the longer beam (acting

as a spring) is fixed. The cross section details are as shown below.

Find the natural frequency of the axial mode.

Figure: Cross Section Details for Both Beams

Figure: Schematic

Material Properties

(kg/m3)E (Pa)Material

1e-80.341.1e11Spring

7.85e502e11Mass




Spring beam length = 500 mm

Mass beam length = 5 mm

Results Comparison


0.1601190.51188.6Natural Frequency of Axial

Mode (Hz)


WBVMMECH020

WBVMMECH021: Buckling Analysis of Beams

Overview

Warren C.Young, Roark's Formulas for Stress and Strains, McGraw

Hill, 6th Edition,Table 34, Case 3a, pg. 675

Reference:


Type(s):

BeamElement

Type(s):

Test Case

A beam fixed at one end and is subjected to two compressive forces. One of the forces is applied on a

portion of the beam of length 50 mm (L1) from the fixed end and the other is applied on the free vertex,

as shown below.

Find the load multiplier for the first buckling mode.

Figure: Schematic


Force on L1 = -1000 N (x

direction)

L1 = 50 mmE = 2e11 Pa

Total length = 200 mm = 0.3

Force on free vertex = -

1000 N (x direction)

Rectangular cross sec-

tion = 10 mm x 10 mm

Results Comparison


-0.40710.19810.2397Load Multiplier



WBVMMECH022: Structural Analysis with Advanced Contact Options

Overview

Any basic Strength of Material bookReference:

Nonlinear Static Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

An assembly of two parts with a gap has a Frictionless Contact defined between the two parts. The end

faces of both the parts are fixed and a given displacement is applied on the contact surface of Part 1 as

shown below.

Find the Normal stress and Directional deformation - both in the z direction for each part for the following

scenarios:

Scenario 1: Interface treatment - adjust to touch.

Scenario 2: Interface treatment - add offset. Offset = 0 m.

Scenario 3: Interface treatment - add offset. Offset = 0.001 m.

Scenario 4: Interface treatment - add offset. Offset = -0.001 m.

Validate all of the above scenarios for Augmented Lagrange and Pure Penalty formulations.

Figure: Schematic


Given displacement = (0, 0,

0.0006) m

Gap = 0.0005 mE = 2e11 Pa

Dimensions for each

part: 0.1 m x 0.1 m x

0.5m

= 0

Results Comparison

The same results are obtained for both Augmented Lagrange and Pure Penalty formulations.



Er-

ror

(%)

Mechan-

ical

Tar-

get

Results

0.0006e-46e-4Maximum directional z de-

formation Part 1 (m)

Adjust To Touch

-0.3575.9786e-

4

6e-4Maximum directional z de-


0.0002.4e82.4e8Maximum normal z stress

Part 1 (Pa)

-0.354-2.3915e8-2.4e8Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset = 0 m

-0.3560.99644e-

4

1e-4Maximum directional z de-



Part 1 (Pa)

-0.355-3.9858e7-4e7Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset = 0.001

m

-0.3551.0961e-

3

1.1e-

3

Maximum directional z de-



Part 1 (Pa)

-0.357-4.3843e8-4.4e8Maximum normal z stress

Part 2 (Pa)



Add Offset. Offset = -

0.001 m

0.00000Maximum directional z de-



Part 1 (Pa)

000Maximum normal z stress

Part 2 (Pa)


WBVMMECH022

WBVMMECH023: Curved Beam Assembly with Multiple Loads

Overview



Type(s):

BeamElement

Type(s):

Test Case

An assembly of two curved beams, each having an included angle of 45, has a square cross-section. It is

fixed at one end and at the free end a Force F and a Moment M are applied. Also, a UDL of "w " N / mm is

applied on both the beams. Use a global element size of 30 mm to get accurate results. See the figure below

for details.

Find the deformation of the free end in the y direction.

Figure: Schematic

Equivalent Loading:


Force F = -1000 N (y direc-

tion)

For each beam:Beam 1:

Cross-section = 10 mm

x 10 mm

E1 = 1.1e5 MPa

Moment M = -10000 Nmm

(about z-axis)

1 = 0

Radius r = 105 mm1 = 8.3e-6 kg/mm3




UDL w = -5 N/mm (y direc-

tion) on both beams

Included angle = 45Beam 2:

E2 = 2e5 MPa

This UDL is applied as an

edge force on each beam

2 = 0

2 = 7.85e-6 kg/mm3

with magnitude = -5 (2 x

3.14 x 105) / 8 = -412.334

N

Analysis

The deflection in the y direction is in the direction of the applied force F and is given by:

=

+ +

+

10 142699 0 29289 0 039232

1

1

3 2 4

2

3

E IFr Mr r

E IFr

[ ( . ) ( . ) ( . )]

[ (( . ) ( . ( . )]0 642699 0 707 0 2935642472 4+ +

Mr r

where:

= deflection at free end in the y direction

I = moment of inertia of the cross-section of both beams

Results Comparison


0.619-8.4688-8.416664Minimum Y Deformation

(mm)


WBVMMECH023

WBVMMECH024: Harmonic Response of a Single Degree of Freedom System for

Beams

Overview



Type(s):

BeamElement

Type(s):

Test Case

Two collinear beams form a spring-mass system. The density of the longer beam is kept very low so that it

acts as a massless spring and the smaller beam acts as a mass. The end vertex of the longer beam (acting

as a spring) is fixed. A Harmonic force F is applied on the free vertex of the shorter beam in z direction. Both

beams have hollow circular cross-sections, as indicated below.

Scenario 1: Damping ratio = 0

Scenario 2: Damping ratio = 0.05

Find the z directional deformation of the vertex where force is applied at frequency F = 500 Hz for the above

scenarios with solution intervals = 25 and a frequency range of 0 to 2000 Hz. Use both Mode Superposition

and Full Method.

Figure: Schematic

Material Properties

(kg/m3)E (Pa)Material

1e-80.341.1e11Spring

7.85e502e11Mass


Harmonic force F = 1 e6 N

(z-direction)

Cross-section of each

beam:

Outer radius = 10 mm

Inner radius = 5 mm

Length of longer beam

= 100 mm



Length of shorter beam

= 5 mm

Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

-0.8594.078e-34.11332e-

3

Maximum z directional deforma-

tion without damping (m)

Mode Superposi-

tion

-0.8764.0765e-

3

4.11252e-

3


tion with damping (m)

-0.0034.1132e-

3

4.11332e-

3


tion without damping (m)

Full Method

-1.0464.0695e-

3

4.11252e-

3


tion with damping (m)


WBVMMECH024

WBVMMECH025: Stresses Due to Shrink Fit Between Two Cylinders

Overview

Stephen P.Timoshenko, Strength of Materials, Part 2 - Advanced

Theory and Problems, 3rd Edition, pg. 208-214

Reference:


Type(s):

SolidElement

Type(s):

Test Case

One hollow cylinder is shrink fitted inside another. Both cylinders have length L and both the flat faces of

each cylinder are constrained in the axial direction. They are free to move in radial and tangential directions.

An internal pressure of P is applied on the inner surface of the inner cylinder. To get accurate results, apply

a global element size of 0.8 inches.

Find the maximum tangential stresses in both cylinders.

Note

Tangential stresses can be obtained in the Mechanical application using a cylindrical coordinate

system.

To simulate interference, set Contact Type to Rough with interface treatment set to add offset

with Offset = 0.

Figure: Schematic


P = 30000 psiInner Cylinder:Both cylinders are made

of the same material ri = 4

E = 3e7psi ro = 6.005

= 0 Ri = 6

= 0.28383 lbm/in3

Ro = 8



Length of both cylinders

= 5

Results Comparison


0.9593573635396.67Maximum normal y stress, inner cylin-

der (psi)

0.0024228242281.09Maximum normal y stress, outer cyl-

inder (psi)

Note

Here y corresponds to direction of a cylindrical coordinate system.


WBVMMECH025

WBVMMECH026: Fatigue Analysis of a Rectangular Plate Subjected to Edge

Moment

Overview

Any standard Machine Design and Strength of Materials bookReference:

Fatigue AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A plate of length L, width W, and thickness T is fixed along the width on one edge and a moment M is applied

on the opposite edge about the z-axis.

Find the maximum Bending Stress (Normal X Stress) and maximum Total Deformation of the plate. Also find

the part life and the factor of safety using Goodman, Soderberg, & Gerber criteria. Use the x-stress component.

Consider load type as fully reversed and a Design Life of 1e6 cycles, Fatigue Strength factor of 1, and Scale

factor of 1.

Figure: Schematic

Material Properties

E = 2e11 Pa

= 0.0

Ultimate tensile strength = 1.29e9 Pa

Endurance strength = 1.38e8 Pa

Yield Strenth = 2.5e8 Pa

Alternating Stresses (Pa)No. of Cycles

1.08e91000

1.38e81e6


Moment M = 0.15 Nm

(counterclockwise @ z-axis)

Length L = 12e-3 m

Width W = 1e-3 m

Thickness T = 1 e-3 m



Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

0.0009e89e8Maximum normal x-stress (Pa)

0.3116.5002e-

4

6.48e-4Maximum total deformation (m)

0.0200.153330.1533Safety factorSN-Goodman

0.0051844.41844.3Life

0.0200.153330.1533Safety factorSN-Soderberg

0.0051844.41844.3Life

0.0200.153330.1533Safety FactorSN-Gerber

0.0051844.41844.3Life


WBVMMECH026

WBVMMECH027: Thermal Analysis for Shells with Heat Flow and Given

Temperature

Overview

Any standard Thermal Analysis bookReference:

Thermal Stress AnalysisAnalysis

Type(s):

ShellElement

Type(s):

Test Case

A plate of length (L), width (W), and thickness (T) is fixed along the width on one edge and heat flow (Q) is

applied on the same edge. The opposite edge is subjected to a temperature of 20 C. Ambient temperature

is 20 C. To get accurate results, apply a sizing control with element size = 2.5e-2 m.

Find the maximum temperature, maximum total heat flux, maximum total deformation, and heat reaction

at the given temperature.

Figure: Schematic


Heat flow Q = 5 WLength L = 0.2 mE = 2e11 Pa

Given Temperature = 20CWidth W = 0.05 m = 0.0

Thickness T = 0.005 mCoefficient of thermal

expansion = 1.2e-5/C

Thermal conductivity k

= 60.5 W/mC

Analysis

Heat Reaction = -(Total heat generated)

Heat flow due to conduction is given by:

Q kAT T

lh l=

( )

where:



Th = maximum temperature

T1 = given temperature

Total heat flux is:

qQ

A=

Temperature at a variable distance z from the fixed support is given by:

T TT T z

lz h

h=

( )1

Thermal deformation in the z-direction is given by:

z zl

T T dz= ( )10

Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

0.00086.11686.1157Maximum Temperature (C)

0.0002e42e4Maximum Total Heat Flux (W/m2)

0.7817.9958e-

5

7.93386e-

5

Maximum Total Deformation (m)

0.000-5-5Heat Reaction (W)


WBVMMECH027

WBVMMECH028: Bolt Pretension Load Applied on a Semi-Cylindrical Face

Overview

Any standard Strength of Materials bookReference:

Static Structural AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A semi-cylinder is fixed at both the end faces. The longitudinal faces have frictionless support. A bolt preten-

sion load is applied on the semi-cylindrical face. To get accurate results, apply sizing control with element

size of 0.01 m.

Find the Z directional deformation and the adjustment reaction due to the bolt pretension load.

Figure: Schematic


Pretension as preload =

19.635 N (equal to adjust-

ment of 1e-7 m)

Length L = 1 mE = 2e11 Pa

Diameter D = 0.05 m = 0.0

Analysis

The bolt pretension load applied as a preload is distributed equally to both halves of the bar. Therefore the

z-directional deformation due to pretension is given by:

PretensionPretension Load

=L

AE

/ 2

Adjustment Pretension= 2



Results Comparison

Er-

ror

(%)

Mechan-

ical

TargetResults

0.004-0.50002e-

7

-0.5e-7Minimum z-directional deformation

(m)

0.0001e-71e-7Adjustment Reaction (m)


WBVMMECH028

WBVMMECH029: Elasto-Plastic Analysis of a Rectangular Beam

Overview

Timoshenko S., Strength of Materials, Part II, Advanced Theory and

Problems,Third Edition, Article 64, pp. 349

Reference:

Static Plastic AnalysisAnalysis

Type(s):

SolidElement

Type(s):

Test Case

A rectangular beam is loaded in pure bending. For an elastic-perfectly-plastic stress-strain behavior, show

that the beam remains elastic at M = Myp = ypbh2 / 6 and becomes completely plastic at M = Mult = 1.5

Myp. To get accurate results, set the advanced mesh control element size to 0.5 inches.

Figure: Stress-Strain Curve

Figure: Schematic


M = 1.0 Myp to 1.5 MypLength L = 10E = 3e7 psi

(Myp = 24000 lbf - in)Width b = 1 = 0.0

Height h = 2yp = 36000 psi



Analysis

The load is applied in three increments: M1 = 24000 lbf-in, M2 = 30000 lbf-in, and M3 = 36000 lbf-in.

Results Comparison

Error

(%)

MechanicalTargetM/Myp

Equivalent Stress

(psi)

StateEquivalent Stress

(psi)

State

0.16436059fully

elastic

36000fully

elastic

1

0.80036288elastic-

plastic

36000elastic-

plastic

1.25

-solution not con-

verged

plasticsolution not con-

verged

plastic1.5


WBVMMECH029

WBVMMECH030: Bending of Long Plate Subjected to Moment - Plane Strain

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