Generalized variational principles in the finite-element method.

The application of a generalized finite-element method to the static and dynamic analysis of plate and shell structures is presented. The displacement formulation of the finite-element method is used. A particular form of generalized variational principle is used which admits completely arbitrary displacement functions for an element. The form of the matrix equations is presented; the method of solution and the problem of dependent algebraic equations are discussed. Numerical results for a variety of polynomial displacement forms and continuity requirements are given and discussed. Limitations of the method are pointed out.