Structural design considering the uncertainty of load positions using the phase field design method

Ordinary topology optimization methods generate a result that is effective only for a specific load position. However, loads are often applied at many uncertain positions rather than at a specific location in most structures. For stability of the structure, it is desirable to guarantee a small amount of structural compliance despite the uncertainty of the load position. In this study, a topology optimization method is proposed to minimize the variation of compliance and its magnitude considering the uncertainty due to the wide range of load locations changes. The mean and the variance of the design objective, i.e., the compliance for each load case at various positions, are directly incorporated into a multi-objective optimization problem so that a similar degree of compliance can be obtained for the entire load case. The phase field design method is used as a topology optimization scheme in conjunction with the finite element method for structural compliance analysis. The reaction-diffusion equation combined with the double well potential functions is employed as the update scheme. Numerical examples for cantilever beam and MBB beam design are presented to demonstrate the validity of the proposed method.