A New Compliance-function-shapeoriented Robust Approach for Volume-constrained Continuous Topology Optimization with Uncertain Loading Directions

The paper presents a new compliance-function-shape-oriented robust approach for the volume-constrained continuous topology optimization with uncertain loading directions. The pure set-based algorithm try to rearrange (take away) some amount of the material volume, originally used to minimize the nominal-compliance, to make a more balanced compliance-function-shape on the set of feasible directions which is less sensitive to the directional fluctuation. The objective is the area of the compliance function shape defined on the set of feasible directions. The area-minimal shape searching process is controlled by the maximum allowable increase of the nominal-compliance. The result will be a more robust compliance function shape which can be characterized by a higher nominal-compliance but a smaller curvature about it in any direction. Using the terminology of the classical variational problems, the proposed approach can be classified as a curve-length or surface-area minimizing inner-value problem where the inner condition, namely the maximum allowable increase of the nominal-compliance, expressed as a percentage of the original nominal compliance, the searching domain is defined implicitly as integration limits in the objective formulation and a usual equality relation is used to prescribe the allowable material volume expressed as a percentage of the total material volume. Two examples are presented to demonstrate the viability and efficiency of the proposed robust approach.