Corner Elimination in Discrete Topology Optimization of Compliant Mechanisms

Abstract

In discrete topology optimization, material state is either solid or void and there is no topology uncertainty caused by intermediate material state. A common problem of the current discrete topology optimization is that boundaries are unsmooth. Unsmooth boundaries are caused by the corners in topology solutions. Although outer corner cutting and inner corner filling strategy can mitigate corners, it cannot eliminate them. 90-degree corners are usually mitigated to 135-degree corners under the corner handling strategy. The existence of corners in topology solutions is because of the subdivision model. If regular triangles are used to subdivide a design domain, corners are inevitable in topology solutions. To eradicate corner from any topology solution, an innovative subdivision model is introduced in this paper for discrete topology optimization of compliant mechanisms. A design domain is discretized into quadrilateral design cells and every quadrilateral design cell is further subdivided into special triangular analysis cells that have a curved hypotenuse. With the presented subdivision model, all boundaries are smooth in any topology solution. Two discrete topology optimization examples of compliant mechanisms are solved based on the proposed subdivision approach.