Optimal Mechanical Design by Juxtaposing Rigidity and Compliance

该补助金通过将刚性和合规性并列，为开发一种新颖的设计方法提供资金。 结构元件的刚性（刚度）和柔性（柔性）的谨慎组合对于有效的机械设计是必要的。 本研究的目的是寻求一种合理的方法来确定多少刚度/顺应性是最佳的机械设备或系统，以及在哪里。 将结构设计方法与柔顺机构综合方法相结合，建立了一个统一的理论，用于设计具有多个刚性和/或柔顺段的机械装置，这些刚性和/或柔顺段通过刚性和/或柔顺接头连接在一起。 基于动静力合成解决方案，关节（运动或顺应或固定，迄今为止尚未确定）和单个组件的可能区域被识别用于拓扑优化。 一个拓扑优化问题，占关节位置和非线性引起的大变形，然后解决。 将考虑四种类型的约束：具有可接受的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导致一种方法，使设计人员能够系统地确定一个给定的规范的最佳水平的遵守。 在这种方法中，设计人员不必指定哪些段或接头应该是刚性的或柔性的，而是优化本身将帮助设计人员做出这一决定。 拓扑优化的解决方案识别各个组件的布局以及它们之间的连接类型（运动、顺应或固定）。 在此步骤之后，设计师可以进行交互式参数研究和虚拟试用，以在虚拟环境中完善设计。 这项工作也将有助于发展有效的数值方法来计算非线性变形结构的设计灵敏度。

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.