Sparse Compliant Mechanism Design Problem
In this final example, the importance of the proposed methodology is explored by considering the design of hinge-free gripper mechanism (7). The design domain for this problem is shown in Fig. 4a. When a horizontal force is applied at the input port, the opposing output ports move vertically to pinch and thus grip a workpiece. The mechanism is designed with aluminum. In the first stage, the mechanism is designed utilizing a quadrilateral bilinear mesh of 5,000 elements and a material usage constraint of 12%. The resulting topology depicted in Fig.4b looks reasonable with no hinges in the resulting design; yet, such design is very stiff and very hard to use. Accordingly, a better design with higher flexibility can be achieved by using less material usage constraint; in this case, the material usage constraint is set at 3%. In order to capture a realistic performance with such a sparse system, the resulting topology is mapped onto a finer mesh of 22,500 elements and the resulting topology is shown in Fig.4c. In spite of this relatively fine mesh, it is still not capable of handling such a sparse system; therefore, it is very important to use a finer mesh. Thus, the resulting topology is then mapped onto a mesh of 90,000 elements, and the material usage constraint is kept at the same level of 3%; the resulting topology is shown in Fig. 4d. While this resulting topology looks much better and clearer than the previous one, more refinement is still needed in order to achieve a final design.
Figure 4. The gripper mechanism. a) the design domain and loading conditions; b) the resulting topology utilizing 5,000 quadrilateral bilinear elements with 12% material usage constraint; c) the resulting topology utilizing 22,500 finite elements and 3% material usage constraint; d) the resulting topology utilizing 90,000 elements and 3% material usage constraint.
In this work, a new methodology is introduced to solve large-size sparse systems in continuum topology optimization framework with relatively very low computational costs. The validity and performance of the proposed methodology has been demonstrated here in two examples involving linear and compliant mechanism design problems; however, the methodology has been successfully tested on numerous problems involving geometrical nonlinearity and buckling stability.