Advanced Finite Elements Methods

Description

This book covers advanced techniques for the analysis of linear elastic structures by the Finite Element Method (FEM). It has been constructed from Notes prepared for the course Advanced to Finite Element Methods or AFEM. This course has been taught at the Department of Aerospace Engineering Sciences, University of Colorado at Boulder since 1990. It is offered every 2 or 3 years. AFEM is a continuation of Introduction to Finite Element Methods, or IFEM. 1 Overview 2 Decomposition of Poisson Problems Homework Exercises for Chapter 2 Solutions 3 Weak and Variational Forms of the Poisson’s Equation Homework Exercises for Chapter 3 Solutions 4 The Bernoulli-Euler Beam Homework Exercises for Chapter 4 Solutions 5 Three-Dimensional Linear Elastostatics Homework Exercises for Chapter 5 Solutions 6 The HR Variational Principle of Elastostatics Homework Exercises for Chapter 6 Solutions 7 The Three-Field Mixed Principle of Elastostatics Homework Exercises for Chapter 7 Solutions 8 Hybrid Variational Principles of Elastostatics Homework Exercises for Chapter 8 Solutions 9 Structures of Revolution 10 Axisymmetric Iso-P Elements Homework Exercises for Chapter 10 Solutions 11 Iso-P Quadrilateral Ring Elements 12 A Complete Axisymmetric FEM Program 14 Solid Elements 16 The Ten Node Tetrahedron 17 A Compendium of FEM Integration Rules for CAS Work 18 Hexahedron Elements 21 Variational Crimes and the Patch Test 22 Recent Advances in Finite Element Templates 23 Optimal Membrane Triangles with Drlling Freedoms 24 Kirchhoff Plates: Field Equations 25 Kirchhoff Plates: BCs and Variational Forms 26 Thin Plate Elements: Overview 27 Triangular Plate Displacement Elements 28 Templates and Morphing 29 Shell Structures: Basic Concepts 30 A Solid Shell Element