A Module For Teaching Fundamentals Of Finite Element Theory And Practice Using Elementary Mechanics Of Materials

This paper presents a study module that is incorporated into a formal introductory undergraduate level course on finite element theory and practice. The module consists of an Integrative Project and Homework Exercises based upon sophomore level education in mechanics of materials. The objective of the module is to support the teaching of the finite element method and to emphasize assumptions and limitations in the application of the technique. The Project centers on a simply supported beam with geometric discontinuities. This beam is investigated using a commercial finite element code in five different phases. Each phase uses a different solution model consisting of a hand calculation, beam, twodimensional area, and three-dimensional solid elements. The solution from each phase is compared to the solution from traditional mechanics of materials beam theory in terms of the following: weight and center of gravity, deflection, and stress. Static failure theories, stress concentrations and a redesign are also considered. The approach of a comparative solution to a problem using different element types has not been considered in any finite element textbook to date and very few books consider stress concentrations and failure theories. The Homework Exercises involve solving similar, yet smaller problems using commercial software and verifying the finite element solutions with the mechanics of materials solutions. The five homework exercises considered here include: a truss, an Lbracket with re-entrant corner, a plate with a notch, a thick-walled pressure vessel, and a pin joint connection. The project and some of the homework exercises reinforce the following: an understanding of finite element theory, an understanding of mechanics of materials theory, a knowledge about the physical behavior and usage of each element type, the ability to select a suitable element for a given problem, and the ability to interpret and evaluate finite element solution quality. Emphasis is strongly placed on the importance of verification. The project and several of the homework exercises also illustrate common major conceptual mistakes made by students and, often, by practitioners using commercial software. P ge 874.2