A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology

Thesis (M.Eng.) - Asian Institute of Technology, 1980

The conventional guide lines for selecting shape functions of a finite element generally lead to approximate finite element solutions. An investigation is conducted on conditions. of shape Junctions, by which an exact finite element solution may be possible. Tong has earlier proved for one-dimensional problems with single dependent variable that shape functions must satisfy homogeneous Euler's equation to give exact solution. The concept is generalized in this study to one-dimensional problems with many dependent variables. It is then applied to a class of thick beam problems. Numerical results of several thick and thin beam examples show undisputedly a good agreement with the theory -. --- exact solution is obtained even with a single element model. The concept is further extended to two-dimensional plate problems. Unlike the case of one dimensional beam, several difficulties are encountered. The most important one is the over-rigid requirement imposed on the number of element degrees-of-freedom. As a result, these degrees-of freedom cannot be accommodated by either a quadrilateral or a triangular element. An attempt is therefore made to relax this requirement. Two plate elements are developed on this basis and the results seem to be satisfactory.