Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear strain and transverse normal strain are taken into account. Different from the previous absolute nodal coordinate formulation, the absolute nodal coordinates, which describe the displacement and slope of the element nodes, are separated into three parts: the absolute nodal coordinates in X, Y and Z directions, respectively, so that the dimension of the mass, stiffness and force matrices is reduced. Furthermore, by using constant matrices, which can be calculated and saved before simulation, the nonlinear stiffness matrices can be calculated by matrix multiplication for each time step, so that the computational efficiency can be improved. Finally, simulation example of a rectangular plate with large deformation was used to verify the accuracy and efficiency of the present formulation.
The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain- displacement relation, equations of motion for flexible multi-body system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation （ANCF） verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models.
