A Shape Optimization Approach Based on Natural Design Variables and Shape Functions

在许多工程产品中，设计的形状对性能有相当大的影响。水坝、输电塔、圆角、飞机和汽车的性能都受其几何形状的影响。形状优化设计可以应用于任何存在数学模型的结构。形状优化设计的基本方法是选择一组设计变量来确定结构的形状。几何结构的变化可以通过有限元网格的变化与设计变量的变化联系起来。主要研究人员提出了一种结构形状优化的新方法。设计变量将表示为结构上的虚拟载荷。将这些虚拟荷载产生的位移加到有限元网格中，得到新的形状。这种新方法在计算上优于标准方法，并允许对一类问题的最优性准则进行物理解释的可能性。本研究是与亚利桑那州立大学的Subramaniam Rajan的联合研究项目，由DMC-8614205号拨款单独资助。

In many engineering products, the shape of a design can have considerable affect on performance. The performance of dams, transmission towers, fillets, aircraft, and automobiles are all affected by their geometric shape. Shape optimal design can be applied to any structures for which a mathematical model exists. The basic approach in shape optimal design is to choose a set of design variables that defines the shape of the structure. Changes in the geometric structure can then be related via changes in the finite-element mesh to changes in the design variables. The Principal Investigators propose to develop a new approach for shape optimization of structures. The design variables will be represented as fictitious loads on the structure. The displacements produced by these fictitious loads are added to the finite-element mesh to obtain a new shape. This new approach is computationally superior to the standard approaches and allows the possibility of physical interpretation of optimality criteria for a class of problems. This research is a joint research project with Subramaniam Rajan at Arizona State University who is being funded separately under grant DMC-8614205.