Basis for Derivation of Matrices for the Direct Stiffness Method

Previous developments in the direct stiffness method are reviewed. The advantages of extending the definitions to make the method a variational approach are cited. The finite element formulation of the method of minimum potential energy is given. Explicit requirements of potential energy displacements are presented, and a criterion insuring monotonic convergence is developed. Illustrative displacements yielding matrices resulting in monotonic convergence are included. Available matrices are reviewed with respect to the extended developments.