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Explicit Reproducing Kernel Particle Methods for large deformation problems

โœ Scribed by Sukky Jun; Wing Kam Liu; Ted Belytschko

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
707 KB
Volume
41
Category
Article
ISSN
0029-5981

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โœฆ Synopsis

The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference configuration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation.

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## Abstract The meshfree approximation functions for shell analysis to date are formulated using parametric coordinates, and this parametric description of shell kinematics limits the applications only to shell structures with simple geometries. On the other hand, construction of moving least squar