Concept of Equivalent Load for Stiffness and Its Application

This paper proposes the concept of “equivalent load for stiffness” (ELS) and presents the applicability of this concept to a variety of structural problems. ELS is a set of additional forces applied to an original structure to produce the same response as that of a modified structure. That is, ELS is equivalent to the changes of stiffness in the original structure. The novelty of the proposed algorithm is that it requires computational operations of an order of $qmn$ , as compared to the full analysis requiring $m^{2}n$ , where $m=\text{half}$ -bandwidth of the global stiffness matrix; $q=\text{number}$ of degrees of freedom (DOF) associated with the modified members, and $n=\text{number}$ of DOFs. Therefore, the proposed algorithm is particularly efficient for such situations as a limited number of members are modified. In addition, the algorithm involves a clear physical concept based on static condensation and is applicable to a variety of problems, including sensitivity analysis, nonlinear analysis, dynamic analysis, and so forth.