Vibration Analysis Of Composite Laminates Using Meshless Method

Because of its light weight, high strength, corrosion resistance, dielectric properties, laminated plate structures have been widely used in engineering, such as the wings of airplane, high speed rail carriages, car tire tread, satellite solar sail and ect. With working environment becoming worse, research on the vibration of the laminated structure draws more and more attention. Therefore, it has great engineering significance and application value to study.Frequencies, dynamic response and modal are the three basic vibration analysis of the laminated structure calculation. The finite element method is one of the most commonly used numerical method. Due to the limitations of its dependence on the grid, it will cause some problems such as difficulties in three dimensional element division, cells rupture, ect. This is the reason why the solutions of laminated plate have low accuracy and efficiency. Meshless method is a new kind of numerical method in recent two decades, which only requires a set of scattered nodes and boundary description without employing a mesh to discrete the problem domain.From the view of displacement method, there are degenerated plate theory(including classical plate theory, first-order shear deformation theory and higher-order shear deformation theory) and solid plate theory(including 3 dimensional plate theory and layerwise plate theory). However, in the process of computation, the degenerated plate theory was based on unreasonable theoretical assumptions(straight normal line hypothesis, no shear deformation, ect.) and the solid plate theory cost a lot of time.In this paper, the special characteristics of laminated plates has been taken into account. Considering the continuity of interlaminar displacement, strain, stress and the characteristics of meshless method and finite element method, the field functions couples of meshless and FEM discrete method based on the direction. By using the three-dimensional constitutive relation, transverse shear deformation and normal strain meet the requirements of continuity between layers. The field functions are approximated by using two-dimensional MLS approximation in the plane and one-dimensional linear interpolation approximation in the thickness direction, called MLS-L(Moving Least Square-Linear) approximation. Based on the Galerkin weak form, the discrete system equations have been established. The penalty function method is used to impose essential boundary conditions. Different boundary conditions, ratio of thickness to span, laying mode, shapes and loads have been take into consideration. Applying the generalized eigenvalue method, the New Mark method and modal rechecking method, the numerical results using the method(MLS-L) show high accuracy in dealing with orthogonal laminated plates.