Geometric Nonlinear Formulation for a Rectangular Plate with Large Deformation

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.

Geometric Nonlinear Formulation for a Rectangular Plate with Large Deformation

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.