AC 2007-1938: INTRODUCING FINITE ELEMENT ANALYSIS IN THE FIRST COURSE OF STATICS AND SOLID MECHANICS

To remain competitive companies are increasingly adopting a so called math-based strategy of virtual product development wherein Computer Aided Engineering (CAE) tools, including Finite Element Analysis (FEA) are used. Teaching FEA has thus become a necessity for the today’s undergraduate mechanical engineering programs. At Grand Valley State University (GVSU), we strive to keep our curriculum up to date, reflecting the demands of industry. We have therefore begun the process of integrating the use of FEA tools throughout the curriculum, instead of delaying it until the senior year either for senior design or elective courses. This paper describes the introduction of FEA to students in the first course of Statics and Solid Mechanics. The first priority of this course is to build the foundation for Mechanics. The challenge therefore was to determine the content without compromising the priority. Keeping this in mind, 1-D Bar elements and 2-D Truss elements are introduced in the course. These two limited topics are chosen because they are based solely on the fundamentals of the first course of Statics and Solid Mechanics. The 1-D Bar element is taught as an extension of an axially loaded member. The stiffness matrix for this element is derived using the force equilibrium at a node. Later the concept of the 1-D Bar element is extended to the 2-D Truss element with trigonometric transformation and matrix manipulations. Essentially it is a matrix method of structures with an FEA flavor. Advantage of this methodology is that the students can perform more complex analysis such as a truss design project. With FEA software tools such as ANSYS, they can quickly make design changes and complete more design iterations. They are required to analyze the final iteration using MATLAB or SCILAB. At the same time, they are also required to perform hand calculations, thus providing experience in validating the results produced by an FEA package. The inclusion of this introduction to FEA reinforces their understanding of the concepts of Statics and Solid Mechanics for the cases of axially loaded member and truss structures with increased capability of analysis. Throughout the course, the importance of understanding fundamental FEA techniques is emphasized for becoming a "well educated" engineer, as opposed to mere "well trained" user of FEA tools. Introduction The highly competitive business environment requires that the product development processes need to be faster and less expensive. To remain competitive companies are increasingly adopting a so called math-based strategy of virtual product development wherein FEA tools are used. FEA needs no introduction. With the advent of cheap computing power and proliferation of commercial softwares with strong capabilities to model complex geometries, FEA has become the de-facto method in stress analysis. It is also widely used in others areas such as vibrations, heat transfer, and fluid flow. With faster turn around rates, i.e. time required from meshing to final results, FEA is an integral part of the modern product development. To keep up with this development, teaching FEA has become a necessity for today’s undergraduate mechanical engineering programs. Also, one of the ABET criteria is familiarity with modern engineering tools, and FEA certainly fulfils that criterion. The introduction of finite element analysis (FEA) in undergraduate curriculum is not new. Traditionally many universities have an FEA course as a technical elective in senior level 1,2 . Almost all instructors use FEA for mechanical design projects 3 . Some instructors have developed case studies so that FEA software can be incorporated into engineering courses 4 . Many educators introduce FEA in lower level mechanical engineering courses, most likely in Mechanics of Materials 5, 6, 7 . Some found it beneficial for the mechanical engineering students to have exposure to FEA as frequently as possible in their engineering education 8 . Some educators even found than FEA can be introduced to students at an even earlier point in the curriculum, i.e. Statics by introducing first the deformation theory 9 or without deformation theory 10 . Obviously the approach of introducing FEA has been used in both a statics and a mechanics of materials class. However, there is a wide diversity of university backgrounds, course sequence and structure, students’ and local industry’s needs, pedagogical objectives and approaches, etc. This paper describes the introduction of FEA in the first course of statics and solid mechanics in our specific context.