Structural design sensitivity analysis with general boundary conditions: Static problem

Abstract

AbstractThis paper presents and analyses methods for design sensitivity analysis of static response for structural systems when general boundary conditions are used during the analysis phase. The design sensitivity analysis methods where the boundary conditions are used to reduce the equilibrium equation have been presented earlier. In such procedures, the reduced stiffness matrix is non‐singular. This fact is used to show differentiability of the displacement vector. When reduction procedures are not used, the global structural stiffness matrix may be singular. In such a case, differentiability of the displacement vector may be questionable. However, it is shown that the displacement vector is still differentiable. Several forms of the structural design sensitivity equations are presented. Although these equations are derived with Lagrange multiplier treatment of general boundary conditions, it is shown that they are applicable with any treatment of general boundary conditions. For example, they can also be used with co‐ordinate reduction schemes. Therefore, design sensitivity analysis can be carried out with any existing finite element analysis computer code. Moreover, the procedures presented can be used to calculate sensitivity of a force of constraint can that is desired. The formulations are kept quite general such that design dependent boundary conditions can be routinely treated. An example is used to illustrate the procedures.