Design Change to Realize Homologous Deformation

Abstract

A formulation based on the finite element sensitivity analysis is proposed for homology design, the primary aim of which is the shape control of a structure. The shape of a structure can be passively controlled by realizing homologous deformation, in which a prescribed geometrical property is maintained for the structure before and after the deformation. The stiffness equation is partitioned and separated into two modified stiffness equations by introducing the constraint of homologous deformation. The governing equation for the design change is derived by utilizing the sensitivity analysis related to the modified stiffness equations. The Moore-Penrose generalized inverse is employed to solve the governing equation with a rectangular coefficient matrix. The proposed method is verified to be valid and versatile by numerical examples using a planar frame structure, for which a center rib subjected to a concentrated load is kept straight by homology design in which the diameter or the length of beam members is changed.