Abstract

 
 
 A novel meshfree radial point interpolation approach which employs a new numerical integration scheme is introduced. The new integration scheme, namely Cartesian Transformation Method, transforms a domain integral into a double integral including a boundary integral and a one-dimensional integral, and thus allowing integration without discretizing domain into sub-domains usually called background mesh in traditional meshfree analysis. A new type of radial basis function that is little sensitive to user-defined parameters is also employed in the proposed approach. The present approach is applied to free vibration and buckling analysis of thin laminated composite plates using the classical Kirchhoff’s plate theory. Various numerical examples with different geometric shapes are considered to demonstrate the applicability and accuracy of the proposed method. 
 
 
Highlights
Finite element method (FEM) [1] is well-known in the engineering communities due to its advantages in solving partial differential equations
We thank our colleagues in Department of Engineering Mechanics for the valuable discussions
The main idea of the scheme is to transform a domain integral into a double one-dimensional integral, it is named as Cartesian Transformation Method (CTM)
Summary
Finite element method (FEM) [1] is well-known in the engineering communities due to its advantages in solving partial differential equations. The main idea of the scheme is to transform a domain integral into a double one-dimensional integral, it is named as Cartesian Transformation Method (CTM). Each horizontal ray is divided into a certain number of intervals, and Gauss points are selected within each interval, so that the line integral in Eq (11). In any numerical integration scheme, increasing the number of integration points will increase the accuracy of the evaluation, but computational time increases. In the case of standard Gauss quadrature for integrands in form of polynomials, an optimum number of integration points can be determined, see [1].
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