Perimeter control with variational upper-bound based on nodal independent continuous mapping method

In order to overcome numerical instabilities such as checkerboards, mesh-dependence and gray regions in the topological optimization of continuum structures, a perimeter-constrained version of the nodal independent continuous mapping method with variational upper-bound is proposed. In order to avoid the determination of value of the perimeter constraint by experiments, an upper-bound perimeter is determined automatically in every optimization iteration. A topological optimization model with nodal variables of continuum structure is developed in independent continuous mapping. According to calculations for the partial derivative of compound function, derivatives of perimeter are deduced. Perimeter constraint is approximately formulated based on first-order Taylor expansion. Numerical examples show that good convergent solution and clear topological configuration can be obtained by the proposed method.