Parametric unification of matrix structural analysis: classical formulation and d-connected mixed elements

Abstract

Concepts and techniques from the field of Parametrized Variational Principles (PVPs) are extended to Matrix Structural Analysis (MSA). Free parameters are used as weighting factors of governing discrete equations. Combining this idea with matrix manipulation techniques yields a continuous spectrum of supermatrix equations. Setting parameters to numerical values provides specific solution methods, some of which are well known whereas others are not. The approach is applied to the classical MSA of truss and framework structures as well as to displacement-connected FE models generated by a parametrized mixed functional. The main advantage of this “top down” derivation of solution schemes is the unification of seemingly disjoint methods for instructional and classification purposes. In addition, the question of duality between range-space and null-space representations is clarified.