MATLAB Guide to Finite Elements

This is a book for people who love finite elements and MATLAB I . We will use the popular computer package MATLAB as a matrix calculator for doing finite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulationsespecially when applying the boundary conditions. In particular the steps ofthe finite element method are emphasized in this book. The reader will not find ready-made MATLAB programsfor use as blackboxes. Insteadstep-by-stepsolutionsoffiniteelementprob- lems are examined in detail using MATLAB. Problems from linearelastic structural mechanics are used throughout the book. The emphasis is not on mass computation or programming, but rather on leaming the finite element method computations and understanding of the underlying concepts. In addition to MATLAB, the MATLAB Symbolic Math 'Ioolbox? is used in Chapters 12, 13, and 14. Many types of finite elements are studied in this book including the spring ele- ment, the bar element, two-dimensional and three-dimensional truss elements, plane and space beam and frame elements, two-dimensional elasticity elements for plane stress and plane strain problems,and one three-dimensional solid element. Each chap- ter deals with only one type ofelement. Also each chapter starts with a summary of the basic equations for the elementfollowed by a numberofexamples demonstrating the use of the element using the provided MATLAB functions. Special MATLAB functions for finite elements are provided as M-files on the accompanying CD-ROM to be used in the examples.