Analysis Of Composite Laminates Using Element-free Galerkin Method And Higher-order Shear And Normal Deformable Plate Theory Based On Legendre Polynomial

Because of light weight, high strength, corrosion resistance of thelaminated plate structures constructed by the composite material layer,laminated plate structures are widely used in all kinds of engineeringstructures, such as the aerospace industry, food packing, health etc. Therefore,it’s of great engineering significance to study bending and dynamics problemof laminated plates. The mechanics analysis of laminated plates is animportant research direction of computational mechanics. It’s mainly containsthat using what kind of shear theory and numerical method will make theanalysis more effective. Now, there are some methods to solve thesedeformation problems, such as finite element method, finite differencemethod and meshless method. Meshless method is a new kind of numericalmethod in recent score years. It can avoid the grid-dependent, and the shapefunction is of higher order continuity. So, meshless method has advantages insolving bending problems of the laminated plates.People are usually use the classical plate theory, first-order sheardeformation theory or high-order shear deformation theory to analysis theproblem of laminated plate. These shear theories are based on the differentapproximate assumptions, such as the straight normal line hypothesis ofclassical plate theory and the linear hypothesis of first-order shear theory, etc.These assumptions are ignored the normal extrusion deformation, that directlyinfluence the approximate degree of physical model, thus affect thecalculation accuracy.In this paper we use the higher-order shear and normal deformable plate theory (HONSDPT) accounts for the influence of the transverse normal andthe transverse shear deformations for laminated plates and using the meshlessmethod for numerical analysis. The three-dimensional plate displacement isresolved into multiplication of thickness and the in-plane displacement, anduse Legendre polynomials as basis function in the thickness direction of theplate, it’s no need to do any hypothesis transverse shear deformation, avoidsthe complexity of traditional higher order shear theory. At the same time, theorthogonality of the Legendre polynomial improves the computationalefficiency. By using2-dimensional Moving Least Square (MLS)approximation in the plane direction, and use the penalty function method toimpose essential boundary conditions, create a3-dimensional laminated platediscrete equation based on Galerkin weak formulation. The problem ofbending and vibration with different boundary conditions, side-to-thicknessratios, and lamination schemes are calculated by the element-free Galerkinmethod based on higher-order shear and normal deformation plate theory. Thenumerical examples show that the proposed method is simple and has a higheraccuracy and convergence, and can correctly calculate interlaminar stress,achieve the effect of higher-order shear deformation theory.