In this paper we are concerned with the elliptic PDEs with highly oscillating coefficients which model the behaviour of composite linear elastic materials. Analytical expressions for the effective coefficients are obtained for the case of layered materials using the theory of homogenisation....

In this paper the problem of blending parametric surfaces is discussed. We present a constructing method of blending surfaces by parametric discrete interpolation PDE splines. These functions are obtained from some boundary conditions and a given interpolation data point set, by minimizing a...

The inspection of damages detected in some blades of 300kW wind turbines revealed that the nature of these damages was probably due to a fatigue mechanism. The causes that had originated the failure (superficial cracks, geometric concentrator, abrupt change of thickness) have been studied,...

In this paper, an algorithm based on unstructured triangular meshes using standard refinement patterns for anisotropic adaptive meshes is presented. It consists of three main actions: anisotropic refinement, solution-weighted smoothing and patch unrefinement. Moreover, a hierarchical mesh...

A dyadic grid is a d-dimensional hierarchical mesh where a cell at level k is partitioned into two equal children at level k+1 by a hyperplane perpendicular to coordinate axis (kmodd). We consider here the finite element approach on adaptive grids, static and dynamic, for various functional...

This paper is devoted to the development of a model for the numerical simulation of hydraulic fracturing processes with 3d fracture propagation. It takes into account the efects of fluid flow inside the fracture, fluid leak-off through fracture walls and elastic response of the surrounding...

Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are...