Anita Uściłowska

First of subjects of research was dynamical response of offshore structures; numerical experiment of a dynamics of an articulated tower under wave loading; the researches have been focused on the numerical experiment. The numerical methods for solving initial value problem have been developed. Such offshore structures may manifest chaotic motion. Due to this feature the study concerning deterministic chaos were performed. Some parameters of chaotical systems have been calculated (Poincare map, Lapunow Coefficient).

The numerical method used for solving initial value problem has been improved. The Runge-Kutta methods have been implemented in affine arithmetics. This arithmetics is extended version of an interval arithmetics.

The other branch of researches is numerical solving of boundary value problems using meshless methods. First paper related to Laplace boundary value problem solved by Trefftz methods was presented in 1996 on First Conference on Trefftz Methods.

The linear Boundary Value Problems (BVP) of mechanics and fluid mechanics have been concerned and solved by Trefftz methods. Moreover, the research was focused in on of the Trefftz method, i. e. Method of Fundamental Solutions (MFS). The range of problem of mechanics and fluid mechanics was extended on nonlinear problems. So, the other supporting methods i.e. Picard iterations, Homotopy Analysis Method (HAM) were introduced and implemented for solving problems of nonlinear mechanics (as deflection of a plate with variable, nonlinear material characteristics) or fluid mechanics (flow of non-Newtonian fluids in porous medium).

The development of applying of meshless methods reached solving problems described by a system of partial differential equations and proper boundary conditions (i.e. dynamics of large displacement of von Karman plate). The dynamics of some mechanical system was calculated by proposed and introduced combination of numerical methods: one meshless method combined with method for treating time dependency of the system, and nonlinearities of the system.

The other range of problems solved by MFS are biomechanical ones, as torsion of long bones (which is the most common reason of bone fracture). This phenomenon is modeled as a torsion of a bar made of orthotropic functionally graded material.

The problem of auxetic material (behaviour under soliton wave loading) is the subject of investigation, as well. The nonlinear initial-boundary value problem was solved by implementation of MFS and HAM.

In last two years the implementation of MFS for problems of metal forming was the subject of the research. The effective stresses and effective strains are calculated for such problems as elastic-plastic torsion of a bar, upsetting of a cylinder, stamping.