Hybrid and Incompatible Finite Element Methods introduces the theory of incompatible and multivariable finite element methods.

Features:

• Reduces the theory and abstract mathematics into practical tools
• Explores applications to problems in elasticity, plasticity, and fracture analysis
• Develops a finite element program in Fortran 90 for the linear elastic static analysis of plane stress, plane strain, axisymmetric, and 3-D solid problems., including plane problems with piezoelectricity

Contents

Variational Formulation of Finite Element Methods in Solid Mechanics

• 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

• 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

• 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

• 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

Numerical Stability: Zero Energy Mode Analysis

• 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

Plastic Analysis of Structures

• 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

• 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 Elements Implementation

• Description of Variables and Subroutines
• Instructions for Input Data

Index

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