The Research On The Level Set-based Parameterization Method For Topology Optimization Using CS-RBF

Topology optimization aims at finding the optimum distribution of materials within thedesign domain under given loads, boundaries and constraints to improve the materialutilization and the performance of the structures for lightweight design. Compared withthe traditional topology and shape optimization method, the structural boundary in thelevel set method is implicitly embedded, which can maintain a smooth boundary anddescribe the topology and shape change simultaneously. But there exists some problems inthe standard level set method, which affect the performance of the method. This paperdeeply analyzed the research status both in home and abroad. To deal with theshortcomings of the existing research, this paper proposed a parametric level setmethod based on the implicit boundary description, to overcome the application defects oftraditional level set method. Finally, this method is applied into the real-world engineeringproblems.First, we study the basic form of continuum topology optimization, and analysis theadvantages and disadvantages of standard level set method (Level Set Method). Then, weproposed the parametric level set method using the radial basis functions. The method usesan implicit level set function to describe the structural boundary, and introduces the C4compactly supported radial basis function (Compactly Supported Radial Basis Functions(CS-RBF)) to interpolate the values of level set function on discrete knots. Thus, ittransforms the complex Hamilton-Jacobi partial differential equation (PDE) into arelatively easy ordinary partial differential equation (ODE). By combining with theoptimization criteria method (OC), the efficiency and practicality of the solution strategyis greatly improved, and the shortcomings in standard level set-based topologyoptimization methods are overcome. Finally, numerical examples illustrate theeffectiveness and superiority of this method.Secondly, a number of topology optimization problems under multiple loading casesare studied. Linear weighted averaging method is employed to construct the objectivefunction. The optimization model for C4CS-RBF based parametric level set topologyoptimization under multiple loading cases is formulated and several numerical examples in2D are studied. Through the comparative analysis of the results, we verify theeffectiveness of the proposed method for solving the topology optimization problem undermultiple loading conditions.Finally, the optimization model for the topology optimization problems consideringsymmetry constraint is constructed via the C4CS-RBF based parametric level set method.By the investigation of the example regarding the beam under asymmetric loads, we verifythe validity of the method on the manufacturability problems.