Vibration Analysis Of Laminated Composite Plates Based On First-order Shear Deformation Theory By Kriging Meshless Method

The laminated plate and shell structure is one of the most widely used in engineeringstructure. The static state and dynamic analysis of such structures is very important. It hasbeen one of the important research topic of computational solid mechanics. Differenttheories should be used for different plate. The thin plate commonly used classical platetheory, and the medium plate should be used first-order shear theory or higher-order sheartheory. As a result of the shear theory to make the governing equations become morecomplex, and this type problem must be solved by numerical methods. How to find asuitable method for the numerical analysis has the important practical significance andacademic value.The finite element method is a very mature and most widely used numerical method,which has been accepted by the engineering community, but it needs grid re-division andincrease costs while deal with large deflection, singularity or crack dynamic expansion,free boundary and so on. And the finite element method has a certain difficulty andcomplexity when constructC1continuity unit. However, meshless method is based ondiscrete points, without grid, is a new numerical methods which developed in the past20years. It can also be seen as a supplement or extension of the finite element method. Thisarticle will use the meshless method for numerical computation and analysis the vibrationof laminated plates.There are many types of meshless methods at present, for example, moving leastsquares (MLS) approximation, radial basis function (RBF) interpolation, both of them canbe used to approximate function. In this paper, the Kriging interpolation approximation is used to construct shape functions. It has the nature of the Kronecker Delta function, easy toimpose the essential boundary conditions, and it is also completeness. The governingequations and boundary conditions discretize by using collocation method which is astrong approach and has the advantages of a direct and simple.The classical laminated plate theory ignores the transverse shear strain, only suitablefor the thin plates. For the medium plate, transverse shear strain must be considered. Basedon first-order shear laminated plate theory, we use Kriging interpolation with collocationtype meshless method to analysis the vibration of composite structures. Firstly we studythe calculation results with influence domain size, and then the natural frequencies of thelaminated composite plates with different boundary conditions, side-to-thickness ratios,material and laying angel are computed by present methods. The optimal laying angeldesign of laminated plates is also studied, which has been entirely consistent with theexisting results. Finally, the forced vibration problems are studied by using the Newmarkmethod for time domain discrete. And the dynamic response under forced vibration isanalysed. Numerical results show that the analysis for vibration problem of laminatedplates by present method is effective and with high accuracy.