Isogeometric topology optimization using trimmed spline surfaces

In the present work, a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed. In the proposed approach, the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by CAD systems is employed for structural response analysis and sensitivity calculation in the topology optimization. The outer and inner boundaries of design models are represented by a spline surface and trimming curves. Design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves. New sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified. The creation of new inner fronts during optimization is allowed for the topological flexibility. An inner front merging algorithm is also presented. The proposed spline based topology optimization is used to solve some benchmarking problems. Design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization. Design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one. It is also shown that post-processing effort for converting to CAD model is eliminated by using the same spline information in numerical analysis and design optimization.