Shape design sensitivity analysis and optimization using meshless methods

The shape design sensitivity and optimization procedures using a meshless method are presented. A connection with a CAD tool is established for seamless integration of modeling, analysis, and design optimization. The approach proposed is applied to 2D and 3D linear elastic problems, as well as to large deformation hyperelastic problems.; The meshless model for analysis is created using the built-in capabilities of the CAD tool, for consistency between the CAD and CAE models. The discretized model is separated into a particle model and an integration model. The meshless shape functions are associated to the particles and are constructed based on the distance between particles and the supports for window functions. Non-convex boundaries of the physical domain generate difficulties in establishing the connectivity between the particles. Procedures that use the visibility criterion are implemented, and their advantages and disadvantages are discussed. A background mesh created by the CAD tool is used to compute the integrals that appear in the Galerkin method. The pressure projection method is used to overcome the difficulties generated by the nearly-incompressible material. The Lagrange multiplier method is employed to impose the essential boundary conditions.; The design sensitivity analysis (DSA) for hyperelastic materials is developed using the continuum approach. The material property and shape design sensitivity coefficients are determined accurately and efficiently, in the framework provided by the meshless method.; A new CAD-based method for design velocity field computation is proposed and implemented. The method is general and is applicable to the meshless method, in addition to the finite element method. The shape design parameters can be chosen among the geometric parameters defined in the CAD model, which is very important for a concurrent engineering environment.; A new CAD-based method for updating the discretized model is proposed and implemented to support shape design optimization. The meshless model is updated automatically at each design iteration, in a continuous and consistent way. The method is demonstrated to be effective for optimization using a 2D engine mount and a 3D elastic beam.