Elasticity Interpolation Type Reproducing Kernel Particle Method

The meshless method,which was born with the objective of eliminating partof the difficulties associated with reliance on a mesh to construct theapproximation, constructs the approximate functions by a set of scattered nodesonly. The meshfree method has the advantage of high precision and efficiency.These features make the meshless methods a hot point and the developmenttrend of numerical methods for science and engineering problems.A new approximation function based on the shape function, and the shapefunction is a coupling of a simple function with Kronecker δ property and aenhance function with format of the RKPM shape function, which hasinterpolation property on any point and no less than the kernel function highorder smoothness. The process of constructing this shape function and itsderivative is given. Through the curve and surface fitting, the validity of thepresent method has been proved. It provides basic conditions for establishing ahigh precision meshless methods.The interpolating reproducing kernel particle method for the plane problemof elasticity based on the interpolating reproducing kernel particle method andthe principle of minimum potential energy of elasticity is proposed. It can bedirectly applied boundary conditions and assure the high numerical precision.The interpolating reproducing kernel particle method for elastodynamicsbased on the interpolating reproducing kernel particle method and the integralweak form of elastodynamics is proposed, and the Newmark time integrationmethod is used for time history analyses.The interpolating reproducing kernel particle method for space axisymmetricbased on the interpolating reproducing kernel particle method and the space ofaxisymmetric problems integral control equations is proposed.The numerical results for some typical examples show that it has theadvantages of high accuracy, small calculating amount and directly imposed ofboundary conditions. It is a correctly and effectively engineering problemsnumerical simulation method.