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FINITE ELEMENTS METHODS
Contents
Preface
1Computational modeling
Introduction
Physical problems in engineering
Computational modeling using the FEM
Simulation
Visualization
2 Introduction to mechanics for solids and structures
Introduction
Equations for three-dimensional solids
Equations for two-dimensional solids
Equations for truss members
Equations for beams
Equations for plates
Remarks
3 Fundamentals for finite element method
Introduction
Strong and weak forms
Hamilton’s principle
FEM procedure
Static analysis
Analysis of free vibration Eigen value analysis
Transient response
Remarks
Review questions
4 FEM for trusses
Introduction
FEM equation
Worked examples
High order one-dimensional elements
Review questions
5 FEM for beams
Introduction
FEM equations
Remarks
Worked examples
Case study: resonant frequencies of micro resonant transducer
Review questions
6 FEM for frames
Introduction
FEM equations for planar frames
FEM equations for space frames
Remarks
Case study: finite element analysis of a bicycle frame
Review questions
7 FEM for two-dimensional solids
Introduction
Linear triangular elements
Linear rectangular elements
Linear quadrilateral elements
Higher order elements
Elements with curved edges
Comments on gauss integration
Case study: side frive micro-motor
Review questions
8 FEM for plates and shells
Introduction
Plate elements
Shell elements
Remarks
Case study: natural frequencies of micro-motor
Case study: transient analysis of a micro-motor
Review questions
9 FEM for 3D solids
Introduction
Tetrahedron element
Hexahedron element
Higher order elements
Elements with curved surfaces
Case study: stress and strain analysis of a quantum dot
Heterostructure
Review questions
10 Special purpose elements
Introduction
Crack tip elements
Methods for infinite domains
Finite strip elements
Strip element method (SEM)
11 Modeling techniques
Introduction
CPU time estimation
Geometry modeling
Meshing
Mesh compatibility
Use of symmetry
Modeling of offsets
Modelling of supports
Modelling of joints
Other applications of MPC equations
Implementation of MPC equations
Review questions
12 FEM for heat transfer problems
Field problems
Weighted residual approach for FEM
ID heat transfer problem
2D heat transfer problem
Summary
Case study: temperature distribution of heated road surface
Review questions
13 Using ABAQUS
Introduction
Basic building block: keywords and data lines
Using sets
ABAQUS input syntax rules
Defining a finite element model in ABAQUS
General procedures
References
Index