Pian / Wu Hybrid and Incompatible Finite Element Methods

Erscheinungsjahr 2005
ISBN: 978-1-135-44220-0
Verlag: CRC Press
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 400 Seiten

Reihe: Modern Mechanics and Mathematics

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

Zielgruppe

Researchers, students, and practitioners in applied mathematics and mechanical engineering

Autoren/Hrsg.

Pian, Theodore H.H.

Wu, Chang-Chun

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Bauingenieurwesen Bauingenieurwesen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

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-• 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.