Analysis of Structural Variability with Computer Algebra

Abstract

Computer algebra provides an environment of conceptual algorithmic development since the relation between the responses and inputs are maintained all along. The closed‐form algebraic formulation removes not only much tedium in lengthy derivations but also virtually all inadvertent mistakes. Furthermore, the accompanying numerical capability with indefinite precision yields consistent numerical results especially in differentiations unless sophisticated adaptive finite difference schemes are sought. In this paper a two‐bar truss with imprecise nodal position sufficiently captured the essential difficulties in numerical computations for general finite elements with stochastic system parameters. Substitutions based on algebraic pattern recognition enormously simplified the expressions for higher order derivatives of the element stiffness matrix. Thus precise numerical results of probability integrals demanded in complicated problems of system reliability analysis could be furnished without incurring intermediate round‐off errors as prevalent in conventional (FORTRAN‐type) programs.