Topology optimization design of continuum structures under stress and displacement constraints

Topolopy optimization design of continuum structures that can rake account of stress and displacement constraints simultaneously is difficult to solve at present. The main obstacle lies in that, the explicit function expressi ons between topological variables and stress or displacement constraints ca n nor be obtained using homogenization method or variable density method. F urthermore, large quantities of design variables in the problem make it har d to deal with by the formal mathematical programming approach. In this pap er, a smooth model of topology optimization for continuum structures is est ablished which has weight objective considering stress and displacement con straints based on the independent-continuous topological variable concept a nd mapping transformation method proposed by Sui Yunkang and Yang Deqing. M oreover, the approximate explicit expressions are given between topological variables and stress or displacement constraints. The problem is well solv ed by using dual programming approach, and the proposed element deletion cr iterion implements the inversion of topology variables from the discrete to the continuous. Numerical examples verify the validity of proposed method.