Optimal Mechanical Design by Juxtaposing Rigidity and Compliance

这笔赠款通过将刚性和合规性并列在一起，为开发一种新的设计方法提供资金。结构元件的刚性(刚性)和柔顺性(柔性)的谨慎组合对于有效的机械设计是必要的。这项研究的目的是寻求一种合理的方法来确定机械设备或系统中多大程度的刚性/柔度是最佳的，以及在哪里。通过将结构设计和柔顺机构综合的方法相结合，将为多个刚性和/或柔性段通过刚性和/或柔性关节连接在一起的机械装置的设计开发出统一的理论。基于运动-静力综合解，为拓扑优化识别关节(运动学的、柔顺的或固定的、迄今尚未确定的)和单个组件的可能区域。然后，解决了考虑节点位置和大变形引起的非线性的拓扑优化问题。将考虑四种类型的约束：具有可接受误差包络的期望路径、体积约束、连接数量约束和应力约束。这项研究的成功完成将产生一种方法，使设计人员能够系统地确定给定规范的最佳遵从性水平。在这种方法中，设计者不必指定哪些管段或连接应该是刚性的或柔顺的，而是优化本身将帮助设计者做出这一决定。拓扑优化的解决方案确定各个零部件的布局以及它们之间的连接类型(运动型、柔顺型或固定型)。在这一步之后，设计师可以进行交互式参数研究和虚拟试用，以在虚拟环境中优化设计。这项工作还将有助于开发有效的数值方法来计算经历非线性变形的结构的设计灵敏度。

This grant provides funding for the development of a novel design methodology by juxtaposing rigidity and compliance. A prudent combination of rigidity (stiffness) and compliance (flexibility) of structural elements is necessary for efficient mechanical design. The objective of this research is to seek a rational approach to determination of how much rigidity/compliance is optimal in a mechanical device or a system, and where. By combining the methods of structural design and compliant mechanism synthesis, a unified theory will be developed for design of mechanical devices with multiple rigid and/or compliant segments connected together with rigid and/or compliant joints. Based on the kinetostatic synthesis solution, possible regions for joints (kinematic or compliant or fixed, hitherto undetermined) and individual components are identified for the topology optimization. A topology optimization problem that accounts for joint locations and the nonlinearity incurred due to large deformations, is then solved. Four types of constraints will be considered: desired path with an acceptable error envelope, volume constraints, constraint on the number of connections, and stress constraints. The successful completion of this research will lead to a method that will enable designers to systematically determine the optimal level of compliance for a given specification. In this method, the designer doesn't have to specify which segments or joints ought to be rigid or compliant, rather the optimization itself will assist the designer to make this decision. The solution of the topology optimization identifies the layout of individual components as well as the type of connections (kinematic, compliant, or fixed) among them. Following this step, the designer can do an interactive parametric study and a virtual tryout to refine the design in a virtual environment. This work will also contribute to the development of efficient numerical methods to compute the design sensitivities of structures undergoing nonlinear deformations.