Internal forces expressed as ratios of polynomials in the unimodal stiffnesses

Abstract

The analytical solution of the linear structural problem is applied to generate approximate analysis models. As the exact expression is too long to be employed efficiently, its construct is used to develop explicit models for the internal forces. Two alternatives are presented. In both cases the models are exact along all the univariate lines radiating from the current point. A first model is created by using subsets of the exact expression. Although this approach gives excellent results it is plagued by linear dependency problems in selecting appropriate subsets. A second model can be viewed as a ratio of two linear Taylor series. After enforcing scaling invariance this model is equally efficient. The two methods are visualized by numerical examples of truss and frame design.