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Numerical implementation of meshless methods for beam problems

Rosca V. E., Leitao V. M. A.

Archives of Civil Engineering

2012

Vol. 58, nr 2

175-184

For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. A flexible computational procedure for solving 1D linear elastic beam problems is presented that currently uses two forms of approximation function (moving least squares and kernel approximation functions) and two types of formulations, namely the weak form and collocation technique, respectively, to reproduce Element Free Galerkin (EFG) and Smooth Particle Hydrodynamics (SPH) meshless methods. The numerical implementation for beam problems of these two formulations is discussed and numerical tests are presented to illustrate the difference between the formulations.

Numerical Aspects of Penetration Simulation

Morka A., Zduniak B., Niezgoda T.

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

2011

Vol. 2, Nr 3 (5)

21-30

Several numerical methods were studied as means of solution to a penetration problem. The Element Free Galerkin (EFG), Smooth Particle Hydrodynamics (SPH), Finite Element Analysis (FEA) methods were considered. The above mentioned algorithms implemented in the LS-DYNA code were applied. Additionally, the mesh density was taken into consideration. The reference case assumed an average node to node distance of 1 mm. The finer and coarser mesh densities were analysed. The full 3D models of the projectile and target were developed with a strain rate and temperature dependent material constitutive relations. An impact of 12.7x108 mm B32 armour piercing projectile on a 80 mm thick block of 7017 aluminium alloy was modelled. The results obtained by a computer simulation were validated and then verified by experimental data. The study of the erosion criteria involves defining the most efficient and reliable way of removing the failed and extremely deformed parts of the projectile and targets. Generally, EFG method applied to solve the perforation/penetration problems can be characterized as a very stable, reliable and effective method.