Layout Optimization of Ill-Loaded Multiphase Bi-Modulus Materials

The optimal layouts of multiple bi-modulus materials in a continuum under ill-loaded cases are found using the scheme of fractional-norm (Q-norm and Q is in (0, 1)) weighting objective function. The major ideas of the present study are as follows. First, the bi-modulus material topology optimization is solved using material replacement approach. Second, the power-law scheme is adopted to express the equivalent stiffness of multiple materials. Third, the ill-loaded topology optimization is solved by changing the value of Q. Combining the three techniques, a feasible solution for the ill-loaded structural optimization can be found even when there are many bi-modulus materials. Numerical tests are presented to show the characters of the materials layout in the structure.