Finite Element Analysis of Solids and Structures

✍ Scribed by Sudip S. Bhattacharjee

• Publisher: CRC Press
• Year: 2021
• Tongue: English
• Leaves: 341
• Edition: 1
• Category: Library

✦ Synopsis

Finite Element Analysis of Solids and Structures combines the theory of elasticity (advanced analytical treatment of stress analysis problems) and finite element methods (numerical details of finite element formulations) into one academic course derived from the author’s teaching, research, and applied work in automotive product development as well as in civil structural analysis.

Features

• Gives equal weight to the theoretical details and FEA software use for problem solution by using finite element software packages
• Emphasizes understanding the deformation behavior of finite elements that directly affect the quality of actual analysis results
• Reduces the focus on hand calculation of property matrices, thus freeing up time to do more software experimentation with different FEA formulations
• Includes chapters dedicated to showing the use of FEA models in engineering assessment for strength, fatigue, and structural vibration properties
• Features an easy to follow format for guided learning and practice problems to be solved by using FEA software package, and with hand calculations for model validation

This textbook contains 12 discrete chapters that can be covered in a single semester university graduate course on finite element analysis methods. It also serves as a reference for practicing engineers working on design assessment and analysis of solids and structures.

Teaching ancillaries include a solutions manual (with data files) and lecture slides for adopting professors.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Author
Chapter 1: Introduction to Stress Analysis of Solids and Structures
Summary
1.1 Introduction – A Brief Summary of Key Historical Developments
1.2 Role of Analysis/Simulation in Product Engineering
1.3 Static Equilibrium of Structures and Analysis of Forces – Statically Determinate and Indeterminate Systems
1.4 Stiffness (Displacement) Method of Structural Analysis
1.5 Components of Stresses in a 3D Body
1.6 Variation of Stresses and Differential Equations of Equilibrium
1.7 Stress Boundary Conditions
1.8 Practice Problems on Stress Field Visualization with CAE Tools
Chapter 2: Strain–Displacement Relationship and Elasticity of Materials
Summary
2.1 Measurement of Deformation Intensity (Strain)
2.2 General Description of Deformation State in 3D Solids
2.3 Compatibility of Strain (Deformation Field) in a Body
2.4 Stress–Strain Relationships (Hooke’s Law)
2.5 Solution of Elasticity Problems Using Stress Distribution Functions
2.6 Solution of Elasticity Problems Using Displacement Variation Functions
2.7 Stiffness Method (Finite Element Method) of Structural Analysis
2.8 Stiffness Properties of 1-D Truss Element Providing Resistance to Axial Deformation Only
2.9 Higher Order Truss Element and Model Refinement
2.10 Model Preparation for Computer-Aided Analysis of Structures with Finite Element Simulation Software
2.11 Practice Problems – Stress Analysis of a Cable with Finite Element Analysis Software ABAQUS
Chapter 3: Analysis of Solids Represented by 2D Stress Fields
Summary
3.1 Plane Strain – A Special Form of Elasticity Problem
3.2 Plane Stress – A Special Form of Elasticity Problem
3.3 Stress Functions for 2D Plane Strain and Plane Stress Elasticity Problems
3.4 Example Use of Stress Function Approach to Solve Elasticity Problems
3.5 Stiffness Method Analysis of Solids Represented by 2D Stress-Deformation Fields
3.6 Iso-Parametric Definition of 2D Solid Finite Elements
3.7 Numerical Calculation of Stiffness Matrix for Iso-Parametric 2D Solid Finite Elements
3.8 Higher Order Plane-Stress/Plane-Strain Elements
3.9 Constant Stress/Strain Triangular Element
3.10 Convergence of Finite Element Model Solutions
3.11 Selection of Element Types for 2D Stress Analysis with FEA Software Packages
3.12 Description of Load Types in General Stress Analysis Problems
3.13 Refined Finite Element Model Preparation with a Pre-Processor (HyperMesh)
3.14 Practice Problems – Stress Analysis of a Plate Subjected to In-Plane Stresses
Chapter 4: FEA Model Preparation and Quality Checks
Summary
4.1 Adaptation of Finite Element Mesh to Stress Field Variations
4.2 Element Type Selection for a Given Stress Analysis Problem
4.3 Initial Geometric Design of Structural Components
4.4 FEA Model Preparation for Case-Study: Plate with Hole (by using HyperMesh)
4.4.1 CAD Data Preparation for FEA Modeling
4.4.2 Finite Element Meshing of the CAD Geometry
4.4.3 Finite Element Mesh Quality Checks
4.4.4 Material and Part Property Assignment
4.4.5 Analysis Parameters – Boundary Constraints, External Loads and Model Outputs
4.4.6 Definition of ABAQUS Analysis Step
4.4.7 Exporting the Model Input File for ABAQUS Analysis
4.5 Post-Processing of FEA Results
4.6 Practice Problems – Stress Analysis of Plate with Hole
Chapter 5: Stress Analysis of Axisymmetric and General 3D Solids
Summary
5.1 Axisymmetric – A Special Form of 3D Elasticity Problems
5.1.1 Equations of Equilibrium in Polar Coordinates
5.1.2 Strain–Displacement Relationships
5.1.3 Stress–Strain Relationships
5.1.4 Compatibility Condition
5.2 Stress Analysis of Axisymmetric Example – Thick Wall Cylinder
5.3 Finite Element Analysis of Axisymmetric Problems
5.4 Stress Analysis of Three-dimensional Bodies – Concentrated Loads
5.4.1 Stresses in a Semi-Infinite Solid Subjected to Concentrated Normal Force on the Boundary
5.4.2 Stresses in a Solid Beam Subjected to Concentrated Lateral Forces
5.5 Finite Elements for Stress Analysis of General 3D Solids
5.6 Three-Dimensional FEA Model Preparation and Element Quality Checks
5.7 Practice Problems – Stress Analysis of Axisymmetric and 3D Solids
Chapter 6: Deformation Analysis of Beams for Axial, Bending, Shear, and Torsional Loads
Summary
6.1 Bending Stresses in a Beam
6.2 Stresses Due to Transverse Shear
6.3 Transverse Normal Stress in a Beam
6.4 Torsional Response of a Beam
6.5 Beam Response to Combined Load Effects
6.6 Elastic Bending Deflection of Beams
6.7 Stress Analysis of Curved Beams
6.8 Stiffness Properties of Prismatic Euler–Bernoulli Beam Elements
6.9 Stiffness properties of beams including shear deformation
6.10 Analysis of Beams and Frames with FEA Software Packages
6.11 Practice Problems: Load–Deflection Analysis of Beams
Chapter 7: Analysis of 3D Thin-Wall Structures (Plates and Shells)
Summary
7.1 Bending Stresses and Strains in a Plate
7.2 Analytical Solutions for Plate Bending Deflections
7.3 In-plane Membrane Stress Resistance of a Shell
7.4 Bending Stiffness of Flat Plate Element
7.5 Flat Shell Element as a Combination of Plate Bending and Membrane Elements
7.6 Shear Deformation in Plates
7.7 Curved Shell Elements
7.8 Shell Element Mesh Quality and Integration Rules
7.9 Analysis of Shells with FEA Software
7.10 Practice Problems: Load–Deflection Analysis of Shells
Chapter 8: Multi-Component Model Assembly
Summary
8.1 Element Compatibility and Convergence of Simulation Results
8.2 Modeling of Kinematic Joints in Structural Assemblies
8.3 Deformable Joint Elements for Part-to-Part Connections
8.4 Mesh-Independent Fasteners for Part-to-Part Connections
8.5 Simulation of Part-to-Part Interface Contacts
8.6 Thin-Layer Interface Elements
8.7 Modular Organization of Data in Multi-component Model Assembly
8.8 Result Quality Checks
8.9 Practice Problems: Analysis with Multi-component Model Assemblies
Chapter 9: Interpretation of Stress Analysis Results for Strength and Durability Assessment
Summary
9.1 Engineering Properties of Materials
9.2 Stress–Strain Results from Linear Elastic Finite Element Analysis of Solids
9.3 Strength Assessment of Solids – Use of Material Failure Theories
9.4 Post-Processing of Finite Element Stress Analysis Results
9.5 Stress Analysis for Durability (Fatigue Life) Assessment of Structures
9.6 Structural Safety Assessment and Quality of FEA Stress Results
9.7 Stresses at Points of Discontinuity: Stress Intensity Factor
9.8 Practice Problems: Assessment of Structural Strength and Durability
Chapter 10: Vibration Frequency Analysis of Structures with FEA Model
Summary
10.1 Introduction – Dynamic Response of Structures
10.2 Vibration Frequency of a Single Degree of Freedom Spring-Mass System
10.3 Forced Vibration Response and Resonance of Structures
10.4 Frequency Separation and Design Targets for Structures
10.5 Vibration Mode Shape and Frequency of SDOF Structures
10.6 Vibration Frequencies of MDOF Systems
10.7 Calculation of System Mass Matrix for MDOF Systems
10.8 Numerical Calculation of Vibration Mode Shapes and Frequencies of MDOF Systems
10.9 Vibration Frequency Analysis with ABAQUS
10.10 Practice Problems: Vibration Analysis of Structures
Chapter 11: Linear Dynamic Response Analysis of Structures
Summary
11.1 Linear Elastic Response of SDOF Systems to Impulsive Loading
11.2 Response Spectrum of Linear Dynamic Systems
11.3 Time-Domain Analysis of Dynamic Structural Response
11.4 Numerical Integration Parameters for Time-Domain Analysis of Structures
11.5 Time Domain Analysis of MDOF Systems
11.6 Mode Superposition Method for Analysis of MDOF Systems
11.7 Explicit Time-Domain Analysis of MDOF Systems
11.8 Linear Dynamic Response Analysis with ABAQUS
11.9 Practice Problems: Dynamic Response Analysis of Structures
Chapter 12: Nonlinear Analysis of Structures
Summary
12.1 Simulation of Nonlinear Force-Deformation Response of Structures
12.2 Nonlinear Material Models for Finite Element Simulation of Structures
12.3 Simulation of Large Deformation Response – Nonlinear Geometric Problems
12.4 Nonlinearity Arising from Changes to Inter-Body Contacts
12.5 Nonlinear Dynamic Response Analysis of Structures
12.6 Material Failure Simulation in Nonlinear Finite Element Analysis
12.7 Computational Methods for Structural Form Simulation
12.8 Practice Problems: Nonlinear Response Analysis of Structures
References
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
R
S
T
U
V
W
Y