Optimal Mechanical Design by Juxtaposing Rigidity and Compliance

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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.