Nonlinear modeling and analysis of compliant mechanisms with circular flexure hinges based on quadrature beam elements

Linear modeling approaches for compliant mechanisms attract significant attention. However, geometrical nonlinearities require consideration generally because they may result in the modeling error. This paper presents a nonlinear quadrature beam element modeling approach for compliant mechanisms. The geometrically exact beam theory is employed as the basis for the element. Meanwhile, the element tangent stiffness matrix is obtained by using the weak form quadrature element method, which does not need shape functions any more and only performs simple algebraic operations of weighting coefficient matrices. One quadrature beam element is needed to model a flexure hinge. For validating the effectiveness of the proposed approach, typical circular flexure hinges are employed. Moreover, a typical bridge-type compliant mechanism is studied by the proposed approach. Finally, the efficiency and accuracy of the proposed approach are verified by comparing with the finite element results. Meanwhile, the results show that the shear effect can be ignored, when a single flexure hinge is investigated. Nevertheless, the nonlinear behavior of compliant mechanisms is affected at the system level. In addition, the magnification ratio of a bridge-type compliant mechanism is related to the width and material of the structure when nonlinearity is considered.