Indirect Structural Analysis by Finite Element Method

The method of indirect structural analysis by using influence lines is extended to the analysis of elastic continua plates, shells, or three dimensional solids. Effective incorporation with the finite element method is made possible by a concept similar to the Mueller-Breslau principle. The introduction of equivalent nodal forces makes it possible to find the influence surfaces for every deflection and for every internal stress in the continuum by a single inversion of the global stiffness matrix. With the influence surfaces known, critical live load positioning can then be determined to find the extreme stresses and extreme deflections. Numerical examples are given for the simply supported isotropic plate and a three-span simply supported continuous isotropic plate for accuracy and convergence check. The results are remarkably good.