ICM method for topology optimization of multimaterial continuum structure with displacement constraint

A new topology optimization method is formulated for lightweight design of multimaterial structures, using the independent continuous mapping (ICM) method to minimize the weight with a prescribed nodal displacement constraint. Two types of independent topological variable are used to identify the presence of elements and select the material for each phase, to realize the interpolations of the element stiffness matrix and total weight. Furthermore, an explicit expression for the optimized formulation is derived, using approximations of the displacement and weight given by first- and second-order Taylor expansions. The optimization problem is thereby transformed into a standard quadratic programming problem that can be solved using a sequential quadratic programming approach. The feasibility and effectiveness of the proposed multimaterial topology optimization method are demonstrated by determining the best load transfer path for four numerical examples. The results reveal that the topologically optimized configuration of the multimaterial structure varies with the material properties, load conditions, and constraint. Firstly, the weight of the optimized multimaterial structure is found to be lower than that composed of a single material. Secondly, under the precondition of a displacement constraint, the weight of the topologically optimized multimaterial structure decreases as the displacement constraint value is increased. Finally, the topologically optimized multimaterial structures differ depending on the elastic modulus of the materials. Besides, the established optimization formulation is more reliable and suitable for use in practical engineering applications with structural performance parameters as constraint.