Nonlinear Strain Energy Formulation of Spatially Deflected Strip Flexures

Strain energy stored in a deflected strip flexure provides an alternative way to relate its loads and deflections. When using strain energy to model kinetostatics of a compliant mechanism, it is viewed in its entirety and one can neglect the load equilibriums between its adjacent elements. This work formulates the nonlinear strain energy for spatially deflected strip flexures of large aspect ratio based on the load-displacement relation obtained in our previous work. The strain energy expressed as the product of stress and strain over the entire strip is expanded using Taylor series and further simplified by truncation of higher order terms, leading to a closed-form strain energy expression for strip flexures. The coefficient matrices in strain energy expression are validated by the load-displacement equations using the principle of virtual work. The load-displacement relations and the lateral stiffness of a compliant pivot containing multiple strip flexures are solved using the energy expression and Castigliano’s first theorem, demonstrating convenience and efficiency of the energy expression.