Multi-scale Analysis Of Hygrothermal Buckling Of Laminated Composite Plates Using First-order Shear Deformation Theory

Composite materials are very popular in engineering application.Based on the theory of composite mechanics and the theory of plates and shells,this paper presents a comprehensively study on the structural failure of delaminated composite laminates using the first-order shear theory put forward by Reddy JN.The analysis takes into account the effects of various situations on the buckling performance of the delaminated laminates,such as the transverse shear deformation of the middle surface,the contact effect at the interface of the delamination and the hydrothermal environment.The problem dealt in this paper has the characteristics of multiscale and multi field coupling.The governing equations for the buckling of the delaminated laminates are deduced,and variations of the buckling load with respect to the delamination conditions and hydrothermal parameters are analyzed.Example studies are carried out and the solutions are compared with the finite element simulation results.The main work of this article is summarized below:Governing equations for the buckling of laminates containing a through-width delamination are derived based on first-order shear theory.The delamination divided the laminate into four sublaminates.Transverse shear deformations are considered by applying the first-order shearing theory of Reddy JN,which is ignored in classic theory for shells and plates.The transverse shear deformation consists of two parts: one is the change of the curvature of the middle plane due to out of plane deformation;another is the rotation of the cross-section with respect to middle which is described by introducing rotation functions.Using mechanics of composite materials,the constitutive relationships for each sublaminates are established.The effect of humidity and temperature are introduced into the constitutive equation of the laminate in terms of the water absorption concentration and the coefficients of wet thermal expansion.Kinematic relation between the contact force and the deflections of sublaminates above and below the delamination are found by examining the local deformation at the interface of the delamination.Governing equations for the buckling of the delaminated laminate under hydrothermal environment with interfacial contact effect is set from the classical theory for laminated plate.The governing equations are solved using separation of variable.Based on the analytical model of four sub-laminates,definite conditions required to solve the governing equation are put forward by considering the continuity conditions of the displacement and rotation,and the equilibrium conditions of the moments and shear forces at the delamination fronts.The displacement functions and rotation functions of each sub-laminate are expressed as single triangle series solutions to satisfy the simply supported boundary conditions at the edges.Using the method of separating variables,the eigen-functions to calculate the buckling modal parameters of each sublaminate are derived.Buckling loads for the delaminate laminate are computed from MATLAB programs developed by iterating.Numerical calculations and finite element analysis are conducted to examine the influence of the delamination conditions and the hydrothermal environment on the buckling load.The parameters of a particular example are selected,and the influence of different parameters on the buckling performance of the laminate is discussed.Finite element software ABAQUS was applied to analysis and simulate.Results from ABAQUS are compared with the theoretical solutions.