Analytical Trial Function Method I — Membrane and Plate Bending Elements
This chapter introduces a novel finite element method, namely, the analytical trial function method. A detailed discussion on the features of the analytical trial function method is firstly given in Sect. 14.1. Then, in the next five sections, the basic analytical solutions of plane problem, thick plate problem and thin plate problem are derived and taken as the trial functions for the corresponding finite element models. It can be seen that those resulting models exhibit excellent performance. Some challenging problems, such as the trapezoidal locking and shear locking, can be avoided naturally.
Keywordsfinite element analytical trial function method membrane element plate bending element
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