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 benefi-cial tools for designing a compliant mechanism with nonlinear elastic deformation behaviors. types of compliant mechanisms: Simple beam, Kazaguruma, Spiral, and Rhombus. Comparing the differences of the target and prediction outputs, the results show that our RBF exhibits better prediction performances than our polynomial approximation and NN. Notably, our RBF has great performance for predicting in-plane deformation behaviors of Spiral and Rhombus. To validate that our surrogate models enable us to resolve high computational costs for carrying out large-deformation analysis with the geometrical nonlinearities, we measure the computational time of the detail model and our RBF for the different sizes of Spirals. As a result, the use of our RBF for Spiral can significantly reduce computational costs. Furthermore, the average differences of coordinates of all nodes between the detail model and our RBF for Straight and Grid models are sufficiently small. The results suggest that our surrogate model can be an alternative solver for obtaining candidate in-plane deformation behaviors of a compliant mechanism.