FEAP - - A Finite Element Analysis Program
Version 8.3 Theory Manual

Robert L. Taylor Department of Civil and Environmental Engineering University of California at Berkeley Berkeley, California 94720-1710 E-Mail: rlt@ce.berkeley.edu January 2009

Contents
1 Introduction 2 Introduction to Strong and Weak Forms 2.1 2.2 2.3 2.4 2.5 2.6 Strong form for problems in engineering . . . . . . . . . . . . . . . . . 1 3 3 4 5 7 8 12 16 16 17 20 21 23 26 26 28 29

Construction of a weak form . . . . . . . . . . . . . . . . . . . . . . . . Heat conduction problem: Strong form . . . . . . . . . . . . . . . . . . Heat conduction problem: Weak form . . . . . . . . . . . . . . . . . . . Approximate solutions: The finite element method . . . . . . …ver más…

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ii 31 32 32 34 37 37 40 41 45 45 50 52 56 60 62 . . . . . . . . . 62 66 67 69 69 74 74 80 80 82

7 Mixed Finite Element Methods 7.1 7.2 7.3 7.4 Solutions using the Hu-Washizu Variational Theorem . . . . . . . . . . Finite Element Solution for Mixed Formulation . . . . . . . . . . . . . Mixed Solutions for Anisotropic Linear Elastic Materials . . . . . . . . Hu-Washizu Variational Theorem: General Problems . . . . . . . . . . 7.4.1 Example: Interpolations linear for u and constant φ . . . . . . .

8 Enhanced Strain Mixed Method 8.1 8.2 8.3 8.4 8.5 Hu-Washizu Variational Theorem for Linear Elasticity

Stresses in the Enhanced Method . . . . . . . . . . . . . . . . . . . . . Construction of Enhanced Modes . . . . . . . . . . . . . . . . . . . . . Non-Linear Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution Strategy: Newton’s Method . . . . . . . . . . . . . . . . . . .

9 Linear Viscoelasticity 9.1 Isotropic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Plasticity Type Formulations 10.1 Plasticity Constitutive Equations . . . . . . . . . . . . . . . . . . . . . 10.2 Solution Algorithm for the Constitutive Equations . . . . . . . . . . . .

CONTENTS 10.3 Isotropic plasticity: J2 Model . . . . . . . . . . . . . . . . . . . . . . . 10.4 Isotropic viscoplasticity: J2 model . . . . . . . . . . . . . . . . . . . . . 11 Augmented Lagrangian Formulations 11.1 Constraint Equations - Introduction . . . . . . . . .