benchmark d3

8/11/2019 Benchmark D3

http://slidepdf.com/reader/full/benchmark-d3 1/6

Verification Manual

Contains proprietary and confidential information of ANSYS, Inc.

and its subsidiaries and affiliates

Page:

!enc"mar# $% Free-Free Vibration of a Solid Beam

Overview

Reference: &. $. !le'ins, (ormulas for Natural (re)uency and ModeS"ape , Van Nostrand &ein"old Co., Ne* Yor#, NY, ++, -ables/ and /0.

AnalysisType(s):

Mode/fre)uency analysis 1 AT!"# 2 34

#lementType(s):

3/$ Structural Solid 5lements 1P6AN5734

3/$ /Node Structural Solid 5lements 1P6AN534

3/$ /Node Structural Solid 5lements 1P6AN5%4%/$ Structural Solid 5lements 1S86I$794

%/$ /Node -etra"edral Structural Solid 5lements 1S86I$+34

%/$ 3/Node Structural Solid 5lements 1S86I$+94

$np%t&istin':

'md%.dat

Test ase

A free/free solid beam is analy;ed to determine t"e first a<ial and bending mode n



Verification Manual



Page: 3

fre)uencies. (or t"e a<ial mode case use =ouse"older eigen'alue e<traction and fbending mode case use !loc# 6anc;os eigen'alue e<traction to e<tract t"e re)uireeigen'alues. 5<amine t"e influence of rectangular, trape;oidal, and parallelogramelement s"ape models on t"e eigen'alue calculations.

Fi'%re *+, Free-Free Solid Beam "roblem Setc.

/aterial"roperties

0eometric "roperties &oadin' and Bo%ndaryonditions

5 2 3 < +

N>m3

? 2 .%

@ 2 #g>m%

6 2 3 m

d 2 . m

t 2 .3 m

"arameter efinitions 2 5lement $istortion Angle

At B 2 6>3 B 2

At D 2 D 2

At Y 2 Y 2 1A<ial mode4



Verification Manual



Page: %

Representative /es. Options

Tar'et Sol%tion and Res%lts omparison

-arget Solution:

(re) 2 3.%%% =; 1A<ial Mode4

(re) 2 .% =; 1!ending Mode4



Verification Manual



Page: 7

Res%lts omparison:

,st at%ral Fre1%ency Ratio

A2ial /ode

S"ape Angle P6AN573 P6AN53 P6AN5% S86I$79 S86I$+3 S86

&ectangular .7 . . .9 . .

-rape;oidal 9 .7 . . .9 . .

-rape;oidal % .7 . . .9 . .

-rape;oidal 79 .9 . . .0 . .

Parallelogram 9 .7 . . .9 . .

Parallelogram % .7 . . .9 . .

Parallelogram 79 .7 . . .9 . .

Bendin' /ode

&ectangular . .+++ .+++ . .7 .

-rape;oidal 9 .90 . . .9+ .9 .

-rape;oidal % .+% .% .% 3.9 . .

-rape;oidal 79 3.3 .3 .3 3.397 .3 .9

Parallelogram 9 .7 .+++ .+++ .7% .9 .

Parallelogram % .+ .+++ .+++ .+ .+ .

Parallelogram 79 .+ .+++ .+++ .3 .3 .



Verification Manual



Page: 9

Ass%mptions3 /odelin' otes3 and Sol%tion

omments. -"e problem tests t"e influence of irregular element s"apes on eigen'alue

calculations. Alt"oug" t"e problem appears rat"er simplistic in nature, it isse'ere test for linear irregular s"aped elements *"ere accurate bendingfre)uencies are re)uired.

3. Since t"e beam is free of any constraints, only one/"alf of t"e beam is re)for modeling. Symmetry constraints are applied at t"e mid/lengt" of t"emodels. -o obtain t"e desired bending mode 1in t"e BY plane4 all nodes a

are constrained in t"e D direction. Additionally, for t"e a<ial mode only,nodes at Y 2 are constrained in t"e Y direction.

%. (or t"e a<ial mode case, =ouse"older e<traction is used *it" all B degrefreedom c"osen as M$8(s. (or t"e bending mode case, e<traction is useds"ifted !loc# 6anc;os to circum'ent ;ero energy modes.

7. All load cases s"o* good agreement in t"e prediction of t"e first a<ial natfre)uency. -"is mode is simply linearly/'arying longitudinal motion *"ic" ieasily "andled by bot" linear and )uadratic elements. Irregular element s"a'e only a minor effect on solution accuracy since a<ial motion is

predominant.9. (or t"e linear elements 1P6AN573, S86I$794, prediction of t"e first bendi

mode is significantly affected by irregularly s"aped elements. 6inear elem"a'e an in"erent inability to properly account for s"ear energy in bendingmodes resulting in e<cessi'e stiffness *it"in t"e element. -"e inclusion ofs"ape functions in t"e element formulation "elp in correcting t"e s"ear enprediction, but are only suitable to rectangular element s"apes. =ence,rectangular element results for P6AN573 and S86I$79 are in good agree=o*e'er, as t"e elements are distorted, t"e stiffness of t"e element incre

"ence o'erpredicting t"e bending mode natural fre)uency.0. (or t"e )uadratic elements 1P6AN53, P6AN5% , S86I$+3, S86I$+94,

prediction of t"e first bending mode is 'ery good. Irregular element s"ape)uadratic elements "a'e little effect on t"e solution accuracy.



Verification Manual



Page: 0

&elease %.: / E 3:: SAS IP, Inc. All rig"ts reser'ed.

benchmark d3

Documents