Finite Element Analysis for Engineers - Basics and Practical Applications with Z88Aurora

Finite Element Analysis for Engineers

Preface

1 Introduction

2 The Basic Procedure

3 Some Elasticity Theory

3.1 Displacements and Strains

3.1.1 For the Truss

3.1.2 For Plane Stress

3.1.3 In Space

3.1.4 For the Plate

3.2 Stress-Strain Relations

3.3 Basics of Thermomechanical Loading

3.4 Basic Principles of Natural Vibration

3.5 Basic Principles of Non-linear Calculations

4 Finite Elements and Element Matrices

4.1 Basics of Element Stiffness Matrices

4.2 Constitutive Matrices

4.3 B Matrix

4.4 Shape Functions

4.5 Integration

4.6 The Application of Loads, Load Vectors

4.6.1 The Basic Procedure

4.6.2 Plate Elements

4.6.3 Volume Elements

4.6.4 Plane and Axial-Symmetrical State of Stress

4.6.5 Distributed Loads for Beams

4.6.6 Gerber Joints for Beams

4.7 A complete Element Stiffness Routine

4.8 Some Remarks on Modelling

4.8.1 Choice of Element Types

4.8.2 Polymers and Material Laws

4.8.3 Structural Optimization

4.9 Some Remarks on Shells

4.10 Element Matrices for Heat Transfer

4.11 Element Matrices for Vibration

4.12 Element Matrices of the Non-linear Finite Element Analysis

5 Compilation, Storage Schemes and Boundary Conditions

5.1 Compilation

5.2 Storage Schemes

5.2.1 Band Width Storage Scheme

5.2.2 The Skyline Storage Scheme

5.2.3 The Jennings Storage Scheme

5.2.4 The Non-Zero Storage Scheme

5.2.5 Summary of the Storage Schemes

5.3 Boundary Conditions

5.3.1 Single Forces and Single Displacements

5.3.2 Distributed Loads with Plates

5.3.3 Fixture of plates

5.3.4 Boundary Conditions in Temperature Analyses

5.3.5 Boundary Conditions with Vibration

5.3.6 Boundary Conditions in the Non-linear Finite Element Analysis

6 Solvers

6.1 Direct Solvers

6.1.1 The Cholesky Solver

6.2 Condition and Scaling

6.3 Iterative Solvers

6.3.1 The Jacobi Method

6.3.2 The Gauss-Seidel Method

6.3.3 The SOR Method and the JOR Method

6.3.4 The basic CG Solver

6.3.5 The CG Solver with Pre-conditioning

6.4 Solver for Thermomechanical Problems

6.5 Solver for Vibration Problems

6.6 Solver for the Non-linear Finite Element Analysis

7 Stresses and Nodal Forces

7.1 Stresses

7.2 Reduced Stresses

7.3 Nodal Forces

8 Mesh Generation of Curvilinear Finite Elements

8.1 Basis Considerations of the Procedure

8.2 Mathematical Foundations

8.3 Description of a Simple Mapped Mesher

9 Z88: The Basics

9.1 General Information

9.1.1 Summary of the Z88 Element Library

9.2 The Open Source FE Program Z88

9.2.1 Overview of the Z88 Program Modules

9.2.2 Dynamic Memory Z88

9.2.3 The Input and Output of Z88:

9.3 The Freeware FE Program Z88Aurora

9.3.1 Overview of the Z88Aurora Modules

9.3.2 Memory Requirement in Z88Aurora

9.3.3 The Input and Output of Z88Aurora

10 Z88: The Modules

10.1 The Linear Solver Z88R

10.1.1 Z88R: The Cholesky Solver

10.1.2 Z88R: The Sparse Matrix Solvers SICCG and SORCG

10.1.3 Z88R: The Sparse Matrix multi-core Solver PARDISO

10.1.4 Which Solver to choose?

10.1.5 Explanations for Stress Calculations

10.1.6 Explanations for Nodal Force Calculations

10.2 The Mapped Mesher Z88N

10.3 The Advanced Mapped Mesher in Z88Aurora

10.3.1 The Use of Z88N in Z88Aurora

10.3.2 Tetrahedron Refiner Z88MTV

10.3.3 The 2D Shell Thickener Z88MVS

10.4 The OpenGL Plot Program Z88O in Z88 V14 OS or the Post-Processor of Z88Aurora

10.5 The DXF Converter Z88X

10.6 The 3D Converter Z88G

10.7 The Ansys Converter Z88ASY in Z88Aurora

10.8The Abaqus Converter Z88INP in Z88Aurora

10.9 Das Cuthill-McKee Program Z88H

10.10 The STEP Import Z88GEOCON (STEP) in Z88Aurora

10.11 The STL Converter Z88GEOCON (STL) in Z88Aurora

10.12 The Tetrahedron Mesher in Z88Aurora

10.13 The Picking Module of Z88Aurora

10.14 The Material Data Base of Z88Aurora

10.15 Applying Boundary Conditions in Z88Aurora

10.16 The User Support with Spider in Z88Aurora

10.17 The Thermomechanical Solver in Z88Aurora

10.18 The free Vibration Solver in Z88Aurora

10.19 The Non-linear Solver Z88NL of Z88Aurora

11 Generating Input Files

11.1 General Information

11.2 General Structure Data File Z88I1.TXT

11.3 Boundary Condition File Z88I2.TXT

11.4 Surface and Pressure Loads File Z88I5.TXT

11.5 Material Parameters File Z88MAT.TXT

11.6 Material Data File *.TXT

11.7 Element Parameters File Z88ELP.TXT

11.8 Integration Order File Z88INT.TXT

11.9 Mapped Mesher Input File Z88NI.TXT

11.10 Solver Parameters File Z88MAN.TXT

11.11 Comparison of the different Z88 Data File Formats

12 The Finite Elements of Z88 and Z88Aurora

12.1 Hexahedron No..1 with 8 Nodes

12.2 Beam No..2 with 2 Nodes in Space

12.3 Plane Stress Element No..3 with 6 Nodes

12.4 Truss No..4 in Space

12.5 Shaft No..5 with 2 Nodes

12.6 Torus No..6 with 3 Nodes

12.7 Plane Stress Element No..7 with 8 Nodes

12.8 Torus No..8 with 8 Nodes

12.9 Truss No. 9 in the Plane

12.10 Hexahedron No..10 with 20 Nodes

12.11 Plane Stress Element No..11 with 12 Nodes

12.12 Torus No..12 with 12 Nodes

12.13 Beam No..13 in the Plane

12.14 Plane Stress Element No..14 with 6 Nodes

12.15 Torus No..15 with 6 Nodes

12.16 Tetrahedron No.16 with 10 Nodes

12.17 Tetrahedron No..17 with 4 Nodes

12.18 Plate No..18 with 6 Nodes

12.19 Plate No..19 with 16 Nodes

12.20 Plate No..20 with 8 Nodes

12.21 Shell No..21 with 16 Nodes

12.22 Shell No..22 with 12 Nodes

12.23 Shell No..23 with 8 Nodes

12.24 Shell No..24 with 6 Nodes

12.25 Element/Solver Overview Z88Aurora V2

13

460

13.1 Flat Wrench (Plate No..7)

13.1.1 With Z88 V14

13.1.2With Z88Aurora V2

13.2 Crane Girder made of Trusses No..4

13.2.1 With Z88 V14

13.2.2 With Z88Aurora V2

13.3 Gear Shaft with Shaft No..5

13.3.1 With Z88 V14

13.3.2 With Z88Aurora V2

13.4 Bending Girder with Beam No..13

13.4.1 With Z88 V14

13.4.2 With Z88Aurora V2

13.5 Plate Segment of Hexahedrons No..1 and No..10

13.5.1 With Z88 V14

13.5.2 With Z88Aurora V2

13.6 Pipe under Internal Pressure, Plain Stress Element No..7

13.6.1 With Z88 V14

13.6.2 With Z88Aurora V2

13.7 Pipe under Internal Pressure, Torus No..8

13.7.1 With Z88 V14

13.7.2 With Z88Aurora V2

13.8 Two-Stroke Engine Piston

13.8.1 With Z88 V14

13.8.2 With Z88Aurora V2

13.9 RINGSPANN Spring and Belleville Spring

13.9.1 With Z88 V14

13.9.2 With Z88Aurora V2

13.10 Liquid Gas Tank

13.10.1 With Z88 V14

13.10.2 With Z88Aurora V2

13.11 Motorcycle Crankshaft

13.11.1 With Z88 V14

13.11.2 With Z88Aurora V2

13.12 Torque-measuring hub

13.12.1 With Z88 V14

13.12.2 With Z88Aurora V2

13.13 Plane Frameworks

13.13.1 With Z88 V14

13.13.2 With Z88Aurora V2

13.14 Gearwheel

13.14.1 With Z88 V14

13.14.2 With Z88AuroraV2

13.15 3D Wrench

13.15.1 With Z88 V14

13.15.2 with Z88Aurora V2

13.16 Force Measuring Element, Plane Stress Elements No..7

13.16.1 With Z88 V14

13.16.2 With Z88Aurora V2

13.17 Circular Plate, Plates No..20

13.17.1 With Z88 V14

13.17.2 With Z88Aurora V2

13.18 Rectangular Plate with 16 Nodes Plates No..19

13.18.1 With Z88 V14

13.18.2 With Z88Aurora V2

13.19 Four-stroke Engine Pistons with Tetrahedrons No..16

13.19.1 With Z88 V14

13.19.2 With Z88Aurora V2

13.20 Motorcar Fan Wheel

13.20.1 With Z88 V14

13.20.2 With Z88Aurora V2

13.21 Diesel Piston

13.21.1 With Z88 V14

13.21.2 With Z88Aurora V2

13.22 Calculation of a Stress Concentration Factor

13.22.1 With Z88 V14

13.22.2 With Z88Aurora V2

13.23 Gear Root Stress

13.23.1 With Z88 V14

13.23.2 With Z88Aurora V2

13.24 Square Pipe, Shell No..24

13.24.1 With Z88 V14

13.24.2 With Z88Aurora V2

13.25 Submarine made of Shells No..22

13.26 Gear Wheel out of Tetrahedrons No..17

13.27 Oscillating Drum

13.28 Modal Analysis Crankshaft

13.29 Thermo-mechanical Analysis of a Spoon

13.30 Thermal Analysis of a four-stroke Engine Piston

13.31 Non-linear Calculation of a Belleville Spring

13.32 Non-linear Calculation of a Hinge

References and further reading

Index