Laminated Plate And Shell Structure Of Meshless Method And Its Application

Because of light weight, high strength, good dielectric properties, corrosion resis-tance of the laminated plate and shell structures constructed by the composite materialthin layer, laminated plate and shell structures are widely used in all kinds of engi-neering structures, such as the wings of the plate, ship deck, car body etc. With thedevelopment and application of smart structures, research of laminated smart (piezo-electric) structure is paid more and more attention. Among them, the deflection bend-ing deformation problem of laminated structures under the load or an electric field isone of the most basic questions.Thanks to the complexity of structures and bending problem, people try to usenumerical method to solving them. From the view of finite element method, thereare degenerated plate element (including plate element based on classical plate theoryor first-order shear deformation theory or higher-order shear deformation theory) andsolid plate element (including3dimensional plate theory and layerwise plate theory).However, in the process of computation, either unreasonable theoretical assumptions(straight normal line hypothesis, no shear deformation, etc.) or defects of Finite Ele-ment method (low order continuity, difculty three-dimensional element division, etc.),have led to the solutions of laminated plate and shell problems of low accuracy, evenfailed.In recent score years, the meshless method is a new kind of numerical method.It has become one of the most popular research topics in the field of computationalmechanics in engineering, because through only discrete nodes but not finite elementor boundary element, it can construct high order continuous approximation function.At first, this article creat a3-dimensional plate meshless method for bendingproblem of plate, which adopted to the layerwise theory of laminated structures, basedon Galerkin weak formulation. The unknown functions are approximated by using2-dimensional MLS approximation in the plane direction and1-dimensional linear in-terpolation approximation in the thickness direction. Because the MLS shape functionlacks of Kronecker delta property, we use the penalty function method to impose es-sential boundary conditions. Through a variety of shapes, diferent support and loadunder single plate, we explore the background size, supported domain size, stabilityof node distribution and self-locking, which demonstrate the validity and feasibility of the proposed method.Then, this article attempts to create a new kind of3-dimensional meshless methodwith high performance from the view of the requirement of laminated plate and shellstructures, by coupling the meshless method and finite element method. Accordingto the continuous requirements of interlaminar and whole displacements, strains andstresses, we present a directional coupled displacement theory. It can present a morereasonable deformation mode, reflect the efect of transverse shear strains and trans-verse normal strain, satisfy the continuous requirements of interlaminar strains andstresses by using fully3-dimensional constitutive relation. For simply, there is a scheme,called MLS-L, which indicates that use2-dimensional MLS approximation in the planedirection and1-dimensional linear interpolation approximation in the thickness direc-tion. During the realization of the element free Galerkin (EFG) method, we take MLS-L(Moving Least Square-Linear) approximation instead of MLS approximation to solvebending problem of multi-layer plate and give the construction of systematic discreteequations in detailed. We also analyze the schemes to resolve thickness self-locking inthe computation. Further, through the analysis of laminated structures, this methodcan pass patch tests and has higher precision of displacements and stresses.Finally, we attempted to promote the present method from the following threeparts: the first is from the construction of meshless shape function, using RPIM (RadialPoint Interpolation Method) instead of MLS. The second is from space dimension andcoupling, considering2-dimensional piezoelectric laminated beam. The third is fromthe discrete form of systematic equations, deriving the corresponding Euler-Lagrangeequations and enforcement by collocation method. Many examples have verified theapplicability and accuracy of the proposed method.