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Zusatztext "? is useful for graduate students in computational mechanics." ? Mathematical Reviews! Issue 2006m. Informationen zum Autor Pian\! Theodore H.H.; Wu\! Chang-Chun Klappentext " is useful for graduate students in computational mechanics." ? Mathematical Reviews! Issue 2006m. Many engineers and mathematicians consider the uniqueness of multivariable elements too abstract and impractical. Beginning with an introduction to the variational formulation of finite element methods in solid mechanics! this book introduces the advancement of the theory and applications of incompatible and multivariable finite element methods. A discussion of fundamental theories follows! laying the theoretical foundation for incompatible elements and their application in plasticity theory! and introducing new ideas in the development of hybrid finite elements. They conclude with applications in fracture problems and implementation of the methods in a finite element analysis program. Zusammenfassung Presents an introduction to the variational formulation of finite element methods in solid mechanics. This book also introduces advances in the theory and applications of incompatible and multivariable finite element methods. 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...
