Scale Effects Of Buckling Analysis Of Laminated Composite Mindlin Plate Model Based On New Modified Couple-Stress Theory By Finite Element Method

A model of buckling analysis for composite laminated Mindlin plate based on new modified couple stress theory is developted. On the basis of the modified couple stress theory for isotropic material, the new modified couple stress theory for anisotropic material is suggested and the constitutive relations for the theory are proposed in the paper. In the modified couple stress theory, the rotation variables are known as curvatures. Compared with the classical couple stress theory, the curvature tensors are symmetric. Differing from composite laminated Kirchhoff plates based on modified couple stress theory, the Mindlin laminated plates considering the transverse shear deformation.Due to complicated geometric shapes and boundary conditions of laminated plates, it is difficult to find analytical solutions of modified couple stress laminated plates. It severely restricts theoretical research and practical application of engineering. A finite element method based on new modified couple stress theory is presented firstly to extend the study of buckling analysis scale effect for various boundary conditions and geometric shapes on composite laminated Mindlin plates.In order to study the buckling analysis scale effect of Mindlin laminated plates, a assembled element: an nine-parameter nonconforming triangular element BCIZ and a refined nine-parameter triangular thin plate bending element RT9 is adopted in this paper. And C1weak-continuity condition and C0 continuity condition also can be satisfied simultaneously. In addition, the degenerated assembled element can be used to study of buckling analysis scale effect of Kirchhoff laminated plates.To verify the applicability and accuracy of the present element, example with simply supported boundary condition is examined, the numerical results of the present element can coincide with analytical results. And the numerical results show the present elements can capture scale effect of microstructure and rapid convergence. Moreover, to study the finite element method based on new modified couple stress theory of buckling analysis scale effect,example with various boundary conditions and geometric shapes on composite laminated Mindlin plates is examined.