A boundary integral formulation of the linear elasticity problem for a multi-component composite is given. The fast BEM solver based on the adaptive cross approximation is then obtained by the data-sparse representation of the resulting Galerkin matrices. The solver is used to obtain effective elastic moduli of fibre and particle reinforced composites in three dimensions by means of the strain energy equivalence principle

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In this report we treat an optimization task, which should make the choice of nonwovens for making diapers faster. A mathematical model for the liquid transport in nonwoven is developed. Finite‐difference schemes are proposed for numerical solving of the differential problem. Parallel algorithms are considered and results of numerical experiments are given.

In surgical knee replacement, the damaged knee joint is replaced with artificial prostheses. An accurate clinical evaluation must be carried out before applying knee prosthe-ses to ensure optimal outcome from surgical operations and to reduce the probability of having long-term problems. Useful information can be inferred from estimates of the stress acting onto the bone-prosthesis system of the knee joint. This information can be exploited to tailor the prosthesis to the patient's anatomy. We present a compound system for pre-operative surgical planning based on structural simulation of the bone-prosthesis system, exploiting patient-specific data.

In this paper are discussed mathematical models for the liquid film generated by impinging jets. These models describe only the film shape under special assumptions about processes. Attention is stressed on the interaction of the liquid film with some obstacle. The idea is to generalize existing models and to investigate qualitative behavior of liquid film using numerical experiments. G.I. Taylor [Proc. R. Soc. London Ser. A 253, 313 (1959)] found that the liquid film generated by impinging jets is very sensitive to properties of the wire which was used as an obstacle. The aim of this presentation is to propose a modification of the Taylor's model, which allows to simulate the film shape in cases when the angle between jets is different from 180°. Numerical results obtained by discussed models give two different shapes of the liquid film similar as in Taylors experiments. These two shapes depend on the regime: either droplets are produced close to the obstacle or not. The difference between two regimes becomes larger if the angle between jets decreases. Existence of such two regimes can be very essential for some applications of impinging jets, if the generated liquid film can have a contact with obstacles.