Apply Principle of Minimum Potential Energy to Obtain Finite Element Formulation

Procedure to find implicit finite element formulation for a system with given potential energy form is introduced (Rayleigh-Ritz Method). This is a general scheme for many systems when their potential energy can be derived easily or readily found from textbooks. A rope element is used as an example. To better understand the process, brief reviews on related concepts such as quadratic form of matrix, Principle of minimum potential energy, and shape functions for 1D elements were included. Symbolic MATLAB derivation was also included. Acknowledgement: This is the solution to a homework problem assigned to ME313 class at WSU Everett. It was adapted from an assignment when the author was taking AAE320 (Finite Element Method) course with Prof. P.H. Geubelle at University of Illinois.