Engineering from C.H.I.P.S.

Hybrid and Incompatible Finite Element Methods
by Theodore H.H. Pian

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


  • 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


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


click here to see books videos cd-roms of related interest


Hybrid and Incompatible Finite Element Methods
by Theodore H.H. Pian
2005 400 pages $118.95 + shipping
Texas residents please add 6.75 % sales tax

Go to Top of Page

copyright © 1997-2009 Culinary and Hospitality Industry Publications Services