Finite Element Analysis: Thermomechanics of Solids

Finite element modeling has developed into one of the most important tools at an engineer's disposal, especially in applications involving nonlinearity. While engineers coping with such applications may have access to powerful computers and finite element codes, too often they lack the strong foundation in finite element analysis (FEA) that nonlinear problems require. Finite Element Analysis: Thermomechanics of Solids builds that foundation. It offers a comprehensive, unified presentation of FEA applied to coupled mechanical and thermal, static and dynamic, and linear and nonlinear responses of solids and structures. The treatment first establishes the mathematical background, then moves from the basics of continuum thermomechanics through the finite element method for linear media to nonlinear problems based on a unified set of incremental variational principles. As the use of FEA in advanced materials and applications continues to grow and with the integration of FEA with CAD, rapid prototyping, and visualization technology, it becomes increasingly important that engineers fully understand the principles and techniques of FEA. This book offers the opportunity to gain that understanding through a treatment that is concise yet comprehensive, detailed, and practical.

Table of Contents:
MATHEMATICAL FOUNDATIONS: VECTORS AND MATRICES Introduction Vectors Matrices MATHEMATICAL FOUNDATIONS: TENSORS Tensors Divergence, Curl, Gradient, and Laplacian of a Tensor Invariants Positive Definiteness Polar Decomposition Theorem Kronecker Products on Tensors INTRODUCTION TO VARIATIONAL AND NUMERICAL METHODS Introduction to Variational Methods Newton Iteration and Arc-Length Methods KINEMATICS OF DEFORMATION Kinematics Strain Differential Volume Element Differential Surface Element Rotation Tensor Compatibility Conditions for E(L) and D Sample Problems MECHANICAL EQUILIBRIUM AND THE PRINCIPLE OF VIRTUAL WORK Traction and Stress Stress Flux Balance of Mass, Linear Momentum and Angular Momentum Principle of Virtual Work Sample Problems STRESS-STRAIN RELATIONS AND THE TANGENT-MODULUS TENSOR Stress-Strain Relations: Classical Linear Elasticity Isothermal Tangent Modulus Tensor Incompressibile and Near-Incompressible Hyperelastic Materials Nonlinear Materials at Large Deformation THERMAL AND THERMOMECHANICAL RESPONSE Balance of Energy and Production of Entropy Classical Coupled Linear Thermoelasticity Thermal and Thermomechanical Analogs of the Principle of Virtual Work INTRODUCTION TO THE FINITE ELEMENT METHOD Introduction Overview of the Finite Element Method Mesh Development ELEMENT FIELDS IN LINEAR PROBLEMS Interpolation Models Strain-Displacement Relations and Thermal Analogs Stress-Strain Temperature Relations in Linear Thermoelasticity ELEMENT AND GLOBAL STIFFNESS AND MASS MATRICES Application of the Principle of Virtual Work Thermal Counterpart of the Principle of Virtual Work Assemblage and Imposition of Constraints SOLUTION METHODS FOR LINEAR PROBLEMS Numerical Methods in FEA Time Integration: Stability and Accuracy Newmark's Method Integral Evaluation by Gaussian Quadrature Modal Analysis by FEA ROTATING AND UNCONSTRAINED ELASTIC BODIES Finite Elements in Rotation Finite Element Analysis for Unconstrained Elastic Bodies THERMAL, THERMOELASTIC AND INCOMPRESSIBLE MEDIA Transient Conductive Heat Transfer Coupled Linear Thermoelasticity Compressible Elastic Media Incompressible Elastic Media TORSION AND BUCKLING Torsion of Prismatic Bars Buckling of Beams and Plates INTRODUCTION TO CONTACT PROBLEMS Introduction: The Gap Point-to-Point Contact Point-to-Surface Contact INTRODUCTION TO NONLINEAR FEA Overview Types of Nonlinearity Combined Incremental and Iterative Methods Finite Stretching of a Rubber Rod Under Gravity Illustration of Newton Iteration INCREMENTAL PRINCIPLE OF VIRTUAL WORK Incremental Kinematics Incremental Stresses Incremental Equilibrium Equation Incremental Principle of Virtual Work Incremental Finite Element Equation Incremental Contributions from Nonlinear Boundary Conditions Effect of Variable Contact Interpretation as Newton Iteration Buckling TANGENT-MODULUS TENSORS FOR THERMOMECHANICAL RESPONSE OF ELASTOMERS Introduction Compressible Elastomers Incompressible and Near-Incompressible Elastomers Stretch-Ratio Based Models: Isothermal Conditions Extension to Thermohyperelastic Materials Thermomechanics of Damped Elastomers Constitutive Model: Potential Functions Variational Principles INELASTIC AND THERMOINELASTIC MATERIALS Plasticity Thermoplasticity Thermoinelastic Tangent-Modulus Tensor Tangent Modulus Tensor in Viscoplasticity Continuum Damage Mechanics ADVANCED NUMERICAL METHODS Iterative Triangularization of Perturbed Matrices Ozawa's Method for Incompressible Materials REFERENCES INDEX Each chapter also contains exercises.