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Abstract

This paper outlines an efficient approach to introducing the finite element method to undergraduate mechanical engineering students. This approach requires that the students have prior experience with MATLAB and a fundamental understanding of solid mechanics. Only two-dimensional beam element problems are considered, to simplify the development. The approach emphasizes an orderly solution procedure and involves important finite element concepts, such as the stiffness matrix, element and global coordinates, force equilibrium, and constraints. Two important and challenging engineering problems — a statically indeterminate beam structure and a stepped shaft — are analyzed with the systematic solution procedure and a MATLAB program. The ability of MATLAB to manipulate matrices and solve matrix equations makes the computer solution concise and easy to follow. The flexibility associated with the computer implementation allows example problems to be easily modified into design projects.

Keywords

finite element method beam elements MATLAB

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An Introduction to the Finite Element Method Using MATLAB

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