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.