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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.

Finite-elemenet method for laminated beam-plates composite using layerwise displacement theory

Rosca V. E., Poterasu V. F., Taranu N., Rosca B. G.

Engineering Transactions

2002

Vol.50, iss.3

165-176

The paper uses the layerwise theory, i.e. the zigzag behaviour of the in-plane displacements through the thickness, and the Lagrange interpolation functions for finite element to compute the stresses and displacements in beams made by composite materials. The layerwise method can determine the interlaminar stresses and other localized effects with the same accuracy as 2D finite element method but less computer effort. We present as illustration two examples.