Hybrid and Incompatible Finite Element Methods

, by Pian, Theodore H. H.; Wu, Chang-Chun

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ISBN: 9780203487693 | 0203487699
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Copyright: 11/4/2005

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Hybrid and Incompatible Finite Element Methods reduces theory and abstract mathematics into practical tools. Beginning with an introduction to the variational formulation of finite element methods in solid mechanics, the authors introduce recent advances in the theory and applications of incompatible and multivariable finite element methods. They present a discussion of fundamental theories, laying the theoretical foundation for incompatible elements and their application in plasticity theory and introducing new ideas in the development of hybrid finite elements. The final chapters explore applications to fracture problems and demonstrate the implementation of a finite element analysis program.

Variational Formulation of Finite Element Methods in Solid Mechanics
Introduction
Equations for 3-D Elasticity
Conventional Variational Principles in Solid Mechanics
Modified Variational Principles for Relaxed Continuity or Equilibrium Conditions Along Interelement Boundaries
Assumed-Displacement Finite Elements
Assumed-Stress Hybrid-Finite Elements
Hybrid-Strain Finite Elements
Hybrid Finite Elements by the HuâÇôWashizu Principle
Hybrid-Displacement Finite Elements
Foundation of Incompatible Analysis
Introduction
Energy Inequality and Elliptic Conditions
Weak Connection Condition of Incompatible Elements
Numerical Stability of Incompatible Elements
Consistency and Patch Test Condition (PTC)
Generation of Incompatible Functions: General Formulation
Relaxation of PTC by the Revise-Stiffness Approach
The PTC in Curvilinear Coordinates
Equivalent Nodal Load and Calculation of Stresses
Elements for the Theory of Elasticity
Introduction
Four-Node Plane-Incompatible Elements: NQ6
P2-Linked Incompatible Methods with the Fewest Degrees of Freedom (DOF)
Eight-Node 3-D Solid Incompatible Element
Axisymmetric Incompatible Elements
Hermite Type Incompatible Plate Elements
Bending Model Under Reasonable w-âÇó Constraint
Foundation in Mechanics of Hybrid Stress Elements
Introduction
Energy Consistency Analysis for Incompatible Hybrid Elements
Patch Test and Element Optimization Condition (OPC)
Optimization Method for Hybrid-Stress Finite Elements
Matching Multivariable Parameters
Optimization of Hybrid-Stress Finite Elements
Four-Node Plane Hybrid Element
Penalty Equilibrium Hybrid Element P-S(a)
Three-Dimensional Body 18b-Optimization Hybrid Element
Axisymmetric 8b-Optimization Hybrid Element
Model Optimization of Hybrid-Stress General-Shell Element
Appendix
Numerical Stability: Zero Energy Mode Analysis
Introduction
Definition of ZEM
Rank Conditions for Two-Field Hybrid-Mixed Elements
Determination of the Zero Energy Modes
Control of the Zero-Energy Displacement Modes
Control of the Zero Energy Stress Modes
Patch Stability Test
Examples
Plastic Analysis of Structures
Introduction
Form of Incompressible Elements and Analysis of
Plane-Stress Plastic Analysis
Incompatible Elements in Plasticity Analysis
Deviatoric Hybrid Model for the Incompressible Medium
Computational Fracture
Introduction
Dual Path-Independent Integral and Bound Theorem
Numerical Strategy and Error Measure
Numerical Tests of Crack Estimation
Incompatible Numerical Simulation of an Axisymmetric Cracked Body
Extension of J to Dynamic the Fracture of a Functional Graded Material
Evaluation of Electro-Mechanical Crack Systems
Computational Materials
Hybrid Element Analysis of Composite Laminated Plates
Bimaterial Interface Hybrid Element for Piezoelectric Laminated Analysis
Numerical Solutions on Fractures of Piezoelectric Materials
Homogenization-based Hybrid Element for Torsion of Composite Shafts
A Study of 3-D Braided Piezoceramic Composites
Finite Element Implementation
Overview
Description of Variables and Subroutines
Instructions for Input Data
Examples
Each chapter also contains a complete section of References
Table of Contents provided by Publisher. All Rights Reserved.

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Hybrid and Incompatible Finite Element Methods

Summary

Table of Contents

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