Pian / Wu Hybrid and Incompatible Finite Element Methods

Erscheinungsjahr 2005
ISBN: 978-1-135-44220-0
Verlag: Taylor & Francis
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

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

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.