Stability Analysis Of Composite Laminated Reddy Plate Based On Anisotropic Modified Couple Stress Theory And Finite Element Method

The anisotropic modified couple stress theory is applicable to the analysis of microscopic anisotropic materials.Compared with Mindlin first-order shear deformation theory,the Reddy high-order theory has higher accuracy.In the premise of same unknown variables,the later satisfies the free surface conditions.Furthermore,it can calculate transverse shear stress without using shear correction factor.In this paper,a stability model of composite laminated Reddy plate is established based on the anisotropic modified couple stress theory,and the scale effect of it is analyzed by analytic method and finite element method respectively.Main work includes the following aspects:1.This paper introduces the anisotropic modified couple stress theory,and the constitutive relation of it is redefined in detail.Through the principle of virtual work,a stability model of cross-ply composite laminated Reddy plate which merely contains only one material length scale parameter is established based on the anisotropic modified couple stress theory.Moreover,a cross-ply composite laminated simple supported square plate with different angle-plies and axial loads is used to analyze the scale effect of stability,and compared with the results calculated by Mindlin and Kirchhoff theories.Numerical results show that the present model has higher prediction accuracy,and is more appropriate for analyzing the stability of thicker composite laminated plate.2.Based on the nine-parameter nonconforming element BCIZ and refined nine-parameter triangular thin plate bending element RT9,a newfangled three-node triangular plate element is proposed.The transverse displacement function of the newfangled three-node triangular plate element both satisfies the 0C continuity and 1C weak-continuity condition.To verify the applicability and accuracy of the present element,the newfangled triangular element is applied to calculate the buckling critical loads of microscopic laminated composite Reddy plate with various geometric shapes,different ply-angle and complex boundary conditions.Numerical results show that the three-node triangular plate element can capture the scale effects of critical buckling loads under different conditions.Note that the numerical results of simply supported square plate got by the present element coincide with analytical results rapidly.