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
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
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
Strong and weak forms
Hamilton’s principle
FEM procedure
Static analysis
Analysis of free vibration Eigen value analysis
Transient response
Review questions
4 FEM for trusses
FEM equation
Worked examples
High order one-dimensional elements
5 FEM for beams
FEM equations
Case study: resonant frequencies of micro resonant transducer
6 FEM for frames
FEM equations for planar frames
FEM equations for space frames
Case study: finite element analysis of a bicycle frame
7 FEM for two-dimensional solids
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
8 FEM for plates and shells
Plate elements
Shell elements
Case study: natural frequencies of micro-motor
Case study: transient analysis of a micro-motor
9 FEM for 3D solids
Tetrahedron element
Hexahedron element
Elements with curved surfaces
Case study: stress and strain analysis of a quantum dot
Heterostructure
10 Special purpose elements
Crack tip elements
Methods for infinite domains
Finite strip elements
Strip element method (SEM)
11 Modeling techniques
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
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
13 Using ABAQUS
Basic building block: keywords and data lines
Using sets
ABAQUS input syntax rules
Defining a finite element model in ABAQUS
General procedures
References
Index
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