Homology Design for Quadratic Curves under Stiffness Constraint

Abstract

A new formulation for homology design is proposed based on the finite element sensitivity analysis. The constraint for homology design is neatly represented by a vector equation with respect to nodal displacements. Homology design to maintain a quadratic curve in a structure before and after the deformation can be efficiently carried out due to the straightforward representation of the constraint. An inequality constraint to maintain structural stiffness is added to the homology design. The inequality constraint is transformed into the equality constraint by introducing slack variables. The governing equation of the design variables is derived by the combination of these two equality constraints and solved by means of the Moore-Penrose generalized inverse. The first-order sensitivity analysis is utilized in the derivation. The validity of the proposed method is demonstrated in the numerical examples using a planar truss structure. Quadratic curves, such as the parabola and circular arc, are formed for the structure by assigning design variables to cross-sectional areas of the members. The limitation of nodal displacement is imposed as an inequality constraint to maintain the stiffness of the structure.