Surrogate model of elastic large-deformation behaviors of compliant mechanism using co-rotational beam element

We propose a surrogate model for predicting in-plane nonlinear structural deformations of a compliant mechanism. Our model utilizing a 2-dimensional co-rotational beam element extracts the essential deformation degrees-of-freedoms (DOFs) of bending flexible beams. The total number of DOFs of nodes at both ends of a 2-dimensional beam is six, while the number of deformation DOFs is three, i.e., axial extension, symmetric bending, and anti-symmetric bending. Therefore, it enables us to reduce the computational cost, from six to three, associated with the models by using the essential deformation DOFs of the co-rotational beam element. Moreover, it is difficult to predict the nonlinear responses of forces derived from displacements of a compliant mechanism due to bifurcation of the deformation-path. To overcome the problem, we generate the datasets by applying external forces and use the inverse response for constructing the surrogate models. In the numerical example, large-deformation behaviors of several types of compliant mechanisms are predicted by our surrogate models constructed by three typical learning algorithms: polynomial approximation, radial basis function, and neural network. The prediction performances and computational costs are investigated for verifying that they can be beneficial tools for designing a compliant mechanism with nonlinear elastic deformation behaviors.