Analysis of a crane hook

Number Rev.

SPHK-17-0001 BDate Hash

1-Mar-2017 ba62a27Document type Pages

Technical Report 11

Author

Jeremy Theler jeremy@seamplex.comReviewed by

My Boss boss@seamplex.comReleased by

His Boss chief@seamplex.com

Project

c6500ba4d4e5a5121898a6afdc293af4

Abstract

This document is an example of a report generated online at CAEplex. It shows a mechanical analysis of acrane hook performed 100% on the cloud. The main result is that under a net load of 3 tons, the maximum VonMises stress is equal to 40% of the materials yield strength.’

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Revision history

Rev. Date AuthorB 1-Mar-2017 Jeremy Theler Minor updates in the figure captionsA 1-Mar-2017 Jeremy Theler First issue

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Contents1 Project details 4

1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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1 Project details

CAEplex¹ project settingsName Hook for PDFAuthor Jeremy ThelerUsername jeremyEmail jeremy@seamplex.comProject ID c6500ba4d4e5a5121898a6afdc293af4Type Linear structural analysisCreation date Wed, 01 Mar 2017 09:15:00 -0500 (EST)Last modification Wed, 01 Mar 2017 09:48:22 -0500 (EST)

www.caeplex.com

Figure 1: Project URL https://www.caeplex.com/project_results.php?id=2cee4116c039fa735cf95f7c2183a568

1.1 Geometry

Geometry fileName hookFormat STEPMD5 cbd6a2f1faf6d36d6b35f10544218fabOriginal size 7.78 MbLength units Millimeters

Topological entititesFaces 12Edges 34Vertices 26Wires 14Solids 1Shells 1Compounds 0Compsolids 0

Center of gravityxcog 0 mmycog 0 mmzcog 0 mm

Bounding boxxmin 0 mmxmax 72 mmymin 0 mmymax 23 mmzmin 0 mmzmax 79 mm

¹CAEplex is a web-based front-end for cloud-based open-source finite element analysis codes.

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1.2 Problem

MaterialName SteelYoung modulus E =210 GPaPoisson ratio ν =0.3Yield strength σyield =400 MPaDensity ρ = 7800 kg/m³

Volumetric forcesType None

BC #1: FixedType Displacement (Dirichlet)Condition Fixed

BC #2: LoadType Load (Neumann)Condition Force

Fx = 0 NFy = 0 N

Fz = −30 000 N

Figure 2: The magenta surface is fixed and the green surface receives a net load of 3 tons in the downward ver cal direc on.

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Figure 3: Front view o f the geometry.

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1.3 Mesh

Unstructured gridCharacteristic length ℓc 3.467 mmNodes 10,506Elements 59,214

Triangles 11,108Tetrahedra 48,106

Back-end detailsBack-end version Gmsh 2.16.02D algorithm Automatic3D algorithm Delaunay

h1(r, s) = 1− r − s

h2(r, s) = r

h3(r, s) = s

(a) Shape functions

Index Weight r s1 1/3 1/6 1/62 1/3 2/3 1/63 1/3 1/6 2/3

(b) Gauss points

(c) General coordinates

x(r, s) =

3∑j=1

hj(r, s) · xj

y(r, s) =3∑

j=1

hj(r, s) · yj

(d) Real ↔ Canonical (e) Canonical coordinates

Figure 4: Mathema cal details of the triangular isoparametric elements

h1(r, s) = 1− r − s− t

h2(r, s) = r

h3(r, s) = s

h4(r, s) = t

(a) Shape functions

Index Weight r s t1 1/4 1/6 1/6 1/62 1/4 2/3 1/6 1/63 1/4 1/6 2/3 1/64 1/4 1/6 1/6 2/3

(b) Gauss points

(c) General coordinates

x(r, s) =4∑

j=1

hj(r, s) · xj

y(r, s) =4∑

j=1

hj(r, s) · yj

(d) Real ↔ Canonical (e) Canonical coordinates

Figure 5: Mathema cal details of the tetrahedral isoparametric elements

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Figure 6: A view of the meshed model. The green square shows the characteris c length of the elements.

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1.4 Solution

Back-end detailsBack-end version Fino v0.5.37-g271e90bFormulation Variational displacement-based linear elastic problemWeighting GalerkinProblem size (unknowns) 31,518Degree of freedom ordering Node-basedPreconditioner gamgSolver cg

Figure 7: Problem s ffness matrix (31,518× 31,518). Blue (red) dots represent posi ve (nega ve) values.

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1.5 Results

DisplacementMaximum value |(u, v, w)|max =0.269 mmLocation x = 70.8 mm

y = 0.835 mmz = −87.5 mm

Von Mises stressesMaterial yield strength σyield =400 MPaMaximum Von Mises stress σmax = 158 MPaLocation x = −28.1 mm

y = −8.08 mmz = −119 mm

Mean value σmean = 31.69 MPaPeak factor fp = 4.99

Maximum load level with respect to material yield

40 % (158/400)

Mean load level with respect to material yield

8 % (32/400)

Figure 8: Von Mises stresses and exaggerated displacements (×100)

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Figure 9: Loca on of the maximum Von Mises stresses.

Figure 10: Side view of the exaggerated displacements (×100)

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