This e-text is a collection of three modules. The first module introduces finite elements via the Direct Stiffness Method and the Method of Weighted Residuals. The emphasis is on solving one-dimensional problems. Two-dimensional problems are solved in the second module using both Variational Techniques (Theorem of Minimum Potential Energy) and the Method of Weighted Residuals. Finally, contents of the last module include three-dimensional solid mechanics and boundary-value problems as well as modal analysis and time-dependent problems (structural dynamics and diffusion problems).
The text is designed for a graduate course in finite element analysis. The book contents are as follows.
Module 1: Review, The Six Major Steps, The Galerkin’s Method, 1D Problems, Using the 1DBVP Program, and Solving Linear Algebraic Equations.
Module 2: Variational Techniques, Basics of the Isoparametric Formulation, Problems in Solid Mechanics, Boundary Value Problems.
Module 3: Three-Dimensional Stress Analysis, Structural Dynamics, Three-Dimensional Boundary Value Problems, Diffusion Problems.
(1) 1DBVP is a Windows based computer program for solving one-dimensional boundary value problems. It is used in Module 1.
(2) Click here to download a complete set of C++ programs (Microsoft Visual Studio 2017) and library. After unraring the file you will find several projects or workspaces. One of the workspaces is call FEAT (Finite Element Analysis Template) that one can use to develop a complete finite element program. FEAT is used in Module 2.
(3) ASUTruss is a Windows based program for with an in-built toolbox for solving a number of finite element problems such as (a) torsion of non-circular sections, and (b) modal analysis and structural dynamics problems. ASUTruss program is used in Modules 2 and 3.
(4) Design3D is a comprehensive set of programs for the linear finite element analysis and design optimization. The link to download this software is coming soon.