One dimensional elastic infinite composit media discretized by boundary point method explored from convergence point of view

Jan Novak


Nowadays a number of computational methods to estimate the mechanical fields inside the composite materials are available. Usually the main role plays the Finite Element Method and the periodic field assumption. On the other hand, there exists a number of applications in engineering practice where a strongly non-periodic character of composite medium can be also encountered (e.g. biological materials, foams, concrete, etc.). Then it becomes to be convenient to use the infinite medium with separated inclusions theory. Similarly to previous works of Maz'ya, Kanaoun, Romero etc. the theory of integral equations and their discretization using Gauss approximating functions is presented. The influence of the nodal discretization refinement or the initial setup of an H-dimensionless parameter on the quality of final approximation is also discussed.

The method itself produces due to a regular discretization grid the Toeplitz structured matrices. Such systems can be advantageously solved using iterative solvers based on Fast Fourier Transform technique. On the other hand, although less efficient, direct solvers exhibit other advantages and can be used with great benefit in the case of ill-posed systems.

The effort of this work is to point out the main benefits and difficulties of the Boundary Point Method application on the simplest one-dimensional example.


Boundary Point Method; Boundary Element Method; perturbation; infinite media; inclusion; integral equation; composite media; heterogeneous materials

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ISSN 1801-1217 (Print)
ISSN 1805-9422 (Online)
Published by the Czech Technical University in Prague, Faculty of Mechanical Engineering