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.
Additional Resources
(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 the FEAT (Finite Element Analysis Template) C++ program (Microsoft Visual Studio 2022). FEAT is discussed extensively in Module 2. Click here to download the library files linked to the FEAT program. You will have to change the path in the FEAT workspace to access the library files.
(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, (b) modal analysis and structural dynamics problems, and (c) displaying the FE model used with the FEAT-program related projects. ASUTruss program is used in Modules 2 and 3.