Femap Structural - Verification Guide.pdf - banduras1

Verification Guide

Version 8.2

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Table of Contents

Proprietary and Restricted Rights Notice

Overview

Linear Statics Verification Using Theoretical Solutions

Nodal Loads on a Cantilever Beam ....................................................................................4

Axial Distributed Load on a Linear Beam ..........................................................................6

Distributed Loads on a Cantilever Beam ............................................................................9

Moment Load on a Cantilever Beam ................................................................................12

Thermal Strain, Displacement, and Stress on Heated Beam ............................................15

Uniformly Distributed Load on Linear Beam ..................................................................18

Membrane Loads on a Plate .............................................................................................21

Thin Wall Cylinder in Pure Tension .................................................................................24

Thin Shell Beam Wall in Pure Bending ...........................................................................27

Strain Energy of a Truss ...................................................................................................30

Linear Statics Verification Using Standard NAFEMS Benchmarks

Elliptic Membrane ............................................................................................................34

Cylindrical Shell Patch Test .............................................................................................39

Laminate Strip ..................................................................................................................42

Hemisphere-Point Loads ..................................................................................................44

Z–Section Cantilever ........................................................................................................47

Skew Plate Normal Pressure .............................................................................................49

Thick Plate Pressure .........................................................................................................53

Solid Cylinder/Taper/Sphere–Temperature ......................................................................58

Normal Modes/Eigenvalue Verification Using Theoretical Solutions

Undamped Free Vibration - Single Degree of Freedom ...................................................65

Two Degrees of Freedom Undamped Free Vibration - Principle Modes .........................68

Three Degrees of Freedom Torsional System ..................................................................71

Two Degrees of Freedom Vehicle Suspension System ....................................................73

Cantilever Beam Undamped Free Vibrations ...................................................................76

Natural Frequency of a Cantilevered Mass ......................................................................78

Normal Modes/Eigenvalue Verification Using Standard NAFEMS Bench-

marks

Bar Element Test Cases ....................................................................................................82

Pin-ended Cross - In-plane Vibration ........................................................................83

Pin-ended Double Cross - In-plane Vibration ...........................................................86

Free Square Frame - In-plane Vibration ....................................................................89

Cantilever with Off-Center Point Masses ................................................................. 92

Deep Simply-Supported Beam .................................................................................. 95

Circular Ring - In-plane and Out-of-plane Vibration ................................................ 98

Cantilevered Beam .................................................................................................. 101

Plate Element Test Cases ................................................................................................ 104

Thin Square Cantilevered Plate -Symmetric Modes ............................................... 105

Thin Square Cantilevered Plate - Anti-symmetric Modes ...................................... 108

Free Thin Square Plate ............................................................................................ 111

Simply-Supported Thin Square Plate ...................................................................... 114

Simply-Supported Thin Annular Plate .................................................................... 117

Clamped Thin Rhombic Plate ................................................................................. 121

Cantilevered Thin Square Plate with Distorted Mesh ............................................. 124

Simply-Supported Thick Square Plate, Test A ....................................................... 129

Simply-Supported Thick Square Plate, Test B ........................................................ 133

Clamped Thick Rhombic Plate ............................................................................... 136

Simply-Supported Thick Annular Plate .................................................................. 140

Cantilevered Square Membrane .............................................................................. 144

Cantilevered Tapered Membrane ............................................................................ 148

Free Annular Membrane ......................................................................................... 152

Cantilevered Thin Square Plate ............................................................................... 156

Cantilevered Thin Square Plate #2 .......................................................................... 161

Axisymmetric Solid and Solid Element Test Cases ....................................................... 164

Free Cylinder - Axisymmetric Vibration ................................................................ 165

Thick Hollow Sphere - Uniform Radial Vibration .................................................. 168

Simply-Supported Annular Plate -Axisymmetric Vibration ................................... 171

Deep Simply-Supported Solid Beam ...................................................................... 174

Simply-Supported Solid Square Plate ..................................................................... 178

Simply-Supported Solid Annular Plate ................................................................... 182

Cantilevered Solid Beam ......................................................................................... 186

Verification Test Cases from the Societe Francaise des Mechaniciens

Mechanical Structures - Linear Statics Analysis with Bar or Rod Elements ................. 191

Short Beam on Two Articulated Supports .............................................................. 192

Clamped Beams Linked by a Rigid Element .......................................................... 194

Transverse Bending of a Curved Pipe ..................................................................... 196

Plane Bending Load on a Thin Arc ......................................................................... 199

Nodal Load on an Articulated Rod Truss ................................................................ 201

Articulated Plane Truss ........................................................................................... 203

Beam on an Elastic Foundation ............................................................................... 206

Mechanical Structures - Linear Statics Analysis with Plate Elements ........................... 209

Plane Shear and Bending Load on a Plate ............................................................... 210

Infinite Plate with a Circular Hole .......................................................................... 212

Uniformly Distributed Load on a Circular Plate ..................................................... 215

Torque Loading on a Square Tube .......................................................................... 218

Cylindrical Shell with Internal Pressure .................................................................. 221

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