A refined three-node triangular element based on the HW variational theorem for multilayered composite plates

Abstract

For the three-node triangular elements, the displacement parameters are linear variation within one element, so that the second and the third derivatives of displacement parameters are close to zero. Therefore, the three-node triangular element will encounter difficulty to accurately predict transverse shear stresses by integrating the three-dimensional equilibrium equation through the thickness direction. Thus, the few three-node triangular plate elements can accurately yield the transverse shear stresses of multilayered composite plates. A higher-order zig-zag model accounting for the zero transverse shear strain conditions at the top and the bottom surfaces is firstly presented in this work. Based on the proposed model, a refined three-node triangular plate element satisfying the requirement of C1 weak-continuity conditions in the inter-element is developed to accurately produce the distributions of displacements and stresses through the thickness of multilayered composite plates. To obtain the improved transverse shear stresses, the simplified three-dimensional equilibrium equation has been a priori used. It is significant that the higher-order derivatives of displacement parameters have been taken out from the expression of transverse shear stresses by employing the three-field Hu-Washizu (HW) variational principle, which is convenient for the finite element implementation. Performance of the present element is tested by comparing with three-dimensional elasticity solutions as well as the reference results evaluated using other models. A detailed study is conducted to highlight the influences of boundary condition, number of layers and aspect ratio on the static response of multilayered composite plates, and numerical results can show the accuracy and range of applicability for the proposed element.