Stiffness design of a continuum under Ill-load cases by fractional-norm objective formulation

In stiffness design with ill-load cases (ILC) by traditional method, the difficulty is to find a feasible structural component for supporting the weaker loads. This is due to significant difference between the magnitudes of the loads. A fractional-norm objective formulation is proposed to give a feasible stiffness design of a continuum under ILC. In the method, the objective function of each load case is mean structural compliance (MSC), and the multiple-load optimization is transformed into single objective design problem by using fractional-norm weighted scheme. The effect of fractional-norm on the final material distribution of structure is investigated by both theoretical and numerical analysis. Using the present method, the stiffness design with ill-load cases can be solved easily by selecting a value of norm in the interval of [0.1, 0.5].