Multiobjective optimal topology design of structures

The multiobjective topology optimization designs have been tried in this paper. The minimum compliance and the maximum fundamental eigenvalue are the two objectives pursued. The constraint is the amount of material which is allowed to use in a specified design space. The design variables are the normalized densities of the finite elements in the design space. To minimize the number of elements whose design variables have values between 0 and 1, penalties are added to those design variables to force them to be either 0 (nonexistence) or 1 (existence). The timing of adding the penalty is also studied. Topologies obtained in two dimensional design space with or without penalty and using different timing approaches are compared and discussed.