Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures

A continuum-based design sensitivity analysis (DSA) method for geometrically nonlinear systems with nonhomogeneous boundary conditions is developed to topologically optimize the displacement-loaded nonlinear structures. In the adjoint variable method, the solution space requires just homogeneous boundary conditions even if the original system has nonhomogeneous ones. A design sensitivity expression for the instantaneous rigidity functional is derived for the displacement-loaded nonlinear topology optimization. The tangent stiffness is obtained at the end of the equilibrium iterations in the nonlinear analysis of the original system; this stiffness is used in the DSA so that no iteration would be necessary to evaluate the design sensitivity expressions. In force-loaded systems, the solution dose not converge easily because the material distributes sparsely sometimes during optimization. However, when the displacement-loaded system is used, there is no convergence difficulty. (C) 2003 Elsevier Science B.V. All rights reserved.