Sensitivity Study of Pseudodynamic Algorithm with Structure-Dependent Quadrature Equations

Abstract

An estimated initial stiffness matrix is generally needed to determine the coefficient matrices of quadrature equations for a structure-dependent pseudodynamic algorithm. It is shown herein that an experimentally determined initial stiffness matrix is, in general, close to the true initial stiffness matrix if an imposed displacement is small enough. This case is often encountered in practice. The case where an estimated initial stiffness is different from a true initial stiffness for employing a structure-dependent pseudodynamic algorithm is also explored. The numerical properties and error propagation properties are evaluated as a function of the initial stiffness ratio, which is the ratio of an estimated initial stiffness over a true initial stiffness. In general, accuracy and error propagation properties are insensitive to the initial stiffness ratio. It seems that the change of bifurcation point between unconditional stability and conditional stability is of worth noting. In order to avoid this stability problem, guidelines are recommended if a structure-dependent pseudodynamic algorithm is used.