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Hybrid and Incompatible Finite Element Methods

Theodore H. H. Pian and Chang-Chun Wu
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2006
Number of Pages: 
369
Format: 
Hardcover
Series: 
Modern Mechanics and Mathematics 4
Price: 
99.95
ISBN: 
1-58488-276-X
Category: 
Monograph
We do not plan to review this book.

 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 Hu-Washizu 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-o 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.

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