Hermite Radial Basis Function Collocation Method For Bending Analysis Of Laminated Plates

Composite materials have been extensively used in the aerospace industry, foodpackaging, health care, etc. Therefore, it’s of great significance to study bending problemsof laminated plates. Now, there are analytical methods and numerical methods for solvingthese problems, and numerical methods are mainly the finite element method, the finitedifference method and meshless method. Because meshless method could avoid thegrid-dependent, partially or completely eliminate the difficulties caused by meshing,besides, the shape function of meshless method are of higher order continuity. So meshlessmethod has certain advantages to solve bending problems of small and big deflection of thelaminated plates.Based on the classical plate bending theory, Hermite radial basis function (HRBF)collocation method is used to solve the bending of the laminates. In-plane displacements u0and v0are constructed by general radial basis functions; while the deflection of w0isconstructed by Hermite radial basis functions in order to ensure the smoothness ofdeflection, besides, its shape function and its derivative has the property of Kronecker deltawhich makes the essential boundary conditions be easily implemented. Collocation methodis effective and easy to realize, meanwhile, in order to improve its stability, we adopt leastsquare collocation method as a discrete scheme to discrete the system equations andboundary conditions.Now based on the above theory, we construct the governing equations of laminatedplates with large deflection bending problem. Then, approximate these field variables withRBF and HRBF, discrete the control equations with least square collocation method. Finally, numerical calculation is used to discuss the selection of optimal parameters, andcompared the results with existing methods, shows that the proposed method here is ofeffectiveness, high accuracy and convergence.