The Improved Quadrilateral Discretization Model for the Discrete Topology Optimization of Structures

In the discrete topology optimization, material state is either solid or void and there is no topology uncertainty problem caused by intermediate material state. In this paper, the improved quadrilateral discretization model is introduced for the discrete topology optimization of structures. The design domain is discretized into quadrilateral design cells and each quadrilateral design cell is further subdivided into 16 triangular analysis cells. All kinds of dangling quadrilateral design cells and sharp-corner triangular analysis cells are removed in the improved quadrilateral discretization model to promote the material utilization. To make the designed structures safe, the local stress constraint is directly imposed on each triangular analysis cell. To circumvent the geometrical bias against the vertical design cells, the binary bit-array genetic algorithm is used to search for the optimal topology. The effectiveness of the proposed improved quadrilateral discretization model and its related discrete topology optimization method is verified by two topology optimization examples of structures.