Application of Laminate Theory to Plate Elements Based on Absolute Nodal Coordinate Formulation

Abstract

Laminated plates have a wide range of applications in engineering, and their flexibility becomes increasingly significant with the development of lightweighting technology. The absolute nodal coordinate formulation (ANCF) has emerged as a promising approach for modeling flexible multibody dynamics. However, researches on thick laminated plates with shear deformation for multiflexible systems remain limited. To investigate the application of ANCF plate elements for laminated plates, this article introduces a new laminated plate element that considers shear deformation. We utilize the fully parameterized ANCF plate element to analyze laminated composite structures, focusing specifically on their layers in the thickness direction. By employing a structural mechanics approach, the study achieves a uniform stiffness matrix that can adapt to laminated plates with shear deformation and can be precomputed in advance. Additionally, a summary of a thin laminated plate element is provided for comparison. Both plate elements are composed by layers, and their elastic forces and Jacobian matrices are derived using first-order shear theory and Kirchhoff's theory, respectively. The effectiveness and accuracy of the proposed elements are validated through a series of benchmark problems encompassing modal, static, and dynamic investigations. The study thoroughly analyzes the results compared with the commercial finite element method software abaqus and analytical approach. The findings demonstrate that the methods effectively address laminated plates.