Thermal Response Analysis Of Composite Laminated Structures

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 three-dimensional equilibrium equation through the thickness direction.In order to obtain accurately 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.An effective high-order zig-zag model is developed in this paper.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.The finite element formula of composite laminates under external load is derived,analyzing the bending problem of composite multilayer plates.In order to avoid the difficulties caused by the C¹type continuity of the plates element,the C⁰ type three node triangular plate element is developed to analyze the bending of sandwich thick plates.The higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu-Washizu variational principle before the finite element procedure is implement.Then,performance of the proposed C⁰ type three-node triangular element is effective evaluated by analyzing multilayered sandwich plates with different loading conditions,lamination sequences,material constants and boundary conditions.The transient temperature field can be obtained by using the method of separation variables.And based on the higher-order global-local model（GLHT-52）proposed by Wu and Chen,the transient thermal response of laminated beam is analyzed.The trait of the proposed model is that it can a priori satisfy the interlaminar continuity conditions of transverse shear stresses.Based on the Navier’s technique,the analytical solution for laminated beam subjected to transient temperature field has been presented.Numerical results show that transient temperature field has an important impact on displacements and stresses of laminated beams.