REPRODUCING KERNEL PARTICLE METHODS FOR STRUCTURAL DYNAMICS

This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from cl assical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian f unction or a cubic spline function, flexible window functions are impl emented to provide refinement in the solution process; It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved throu gh an increase in the critical time step when the frequency range is l ow and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide in sight into RKPMs. The predictions of the theories are confirmed throug h numerical experiments by performing reconstructions of given functio ns and solving elastic and elastic-plastic one-dimensional (1-D) bar p roblems for both small and large deformation as well as three 2-D larg e deformation non-linear elastic problems. Numerical and theoretical r esults show the proposed reproducing kernel interpolation functions sa tisfy the consistency conditions and the critical time step prediction ; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH)methods. In contrast with what has been reported i n SPH literature, we do not find any tensile instability with RKPMs.