An efficient numerical procedure is proposed to obtain mean-square stability regions for both single-degree-of-freedom and two-degree-of-freedom linear systems under parametric bounded noise excitation. This procedure reduces the stability problem to a matrix eigenvalue problem. Using this approach, ranges of applicability to the well-known stochastic averaging method are discussed. Numerical results show that the small parameter size in the stochastic averaging method can have a significant effect on the stability
regions. The influence of noise on the shape of simple and combination parametric resonances is studied.

*Keywords:* random vibration, stochastic averaging, mean square stability, bounded noise.

P. Gorzelańczyk. Method of fundamental solutions and random numbers for the torsion of bars with multiply connected cross sections. CAMES 2010 (17)

The torsion of bars with multiply connected cross section by means of the method of fundamental solutions (MFS) is considered. Random numbers were used to determine the minimal errors for MFS. Five cases of cross sections are examined. The numerical results for different cross sectional shapes are presented to demonstrate the efficiency and accuracy of the method. Non-dimensional torsional stiffness was calculated by means of numerical integration of stress function for one of the cases. This stiffness was compared with the exact stiffness for the first case and with the stiffness resulting from Bredt's formulae for thin-walled cross sections.

B.N. Rao and K.N. Rajesh. Mode I crack problems by coupled fractal finite element and meshfree method. CAMES 2010 (17)

This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with
element-free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two-dimensional linearelastic
cracked structures subjected to Mode I loading condition. FFEM is adopted for discretization of
domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region
interface elements are employed. The shape functions within interface elements which comprise both
the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus
ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best
features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions
are necessary and no post-processing (employing any path-independent integrals) is needed to determine
fracture parameters such as stress-intensity factors (SIFs) and T -stress. The numerical results show that
SIFs and T -stress obtained using the proposed method, are in excellent agreement with the reference
solutions for the structural and crack geometries considered in the present study. Also a parametric
study is carried out to examine the effects of the integration order, the similarity ratio, the number of
transformation terms, and the crack-length to width ratio, on the quality of the numerical solutions.

*Keywords:* crack, Element-free Galerkin method, Fractal Finite Element Method, Stress-Intensity Factor, T -stress, Linear-Elastic Fracture Mechanics, Mode I.

J. Kucwaj. The efficiency of the application of the heap lists to the algorithm of mesh generation. CAMES 2010 (17)

The paper presents an analysis of the efficiency of the application of heap lists data structures to the 2D
triangular mesh generation algorithms. Such efficiency is especially important for the frontal methods for
which the size of the generated mesh is controlled by a prescribed function in the considered domain. In
the presented approach two advancing front procedures are presented: first for points insertion and the
second for the Delaunay triangulation. If the heap lists are applied to the minimal size of frontal segment
selection, a better quality mesh is obtained.

*Keywords:* tree and lists data structure, frontal methods, Delaunay triangulation, grid generation, mesh adaptation.

J. Kucwaj. Numerical investigations of the convergence of a remeshing algorithm on an example of subsonic flow. CAMES 2010 (17)

The main goal of the paper is to analyze convergence of a remeshing scheme evaluated by the author [8] on the example of a potential flow around a profile. It is assumed that flow is stationary, irrotational, inviscid and compressible. The problem is led to solving nonlinear differential equation with additional nonlinear algebraic equation representing the so called Kutta-Joukovsky condition. For adaptation a remeshing scheme is applied. For every adaptation step mesh is generated using grid generator [7], which generates
meshes with mesh size function. The mesh size function is modified at every adaptation step by nodal values of the error indicator interpolation. The nonlinear algebraic system of equations obtained from discretizing of the problem, is solved by the application of the Newton-Raphson method.

*Keywords:* finite element method, fluid mechanics, grid generation, remeshing, Kutta-Joukovsky condition.

A.J. Nowak, J. Smołka, A. Fic, L. Kosyrczyk. CFD model of coupled thermal processes within coke oven battery as an example of complex industrial application. CAMES 2010 (17)

This paper describes results of the mathematical modelling of steady-state and transient physical phenomena
taking place in the heating channels of a coke oven battery. A formulated system of standard
Computational Fluid Dynamics (CFD) equations coupled with User Defined Functions is solved numerically
using commercial software Ansys Fluent. Finally, the developed 3-D model is used to examine the
influence of selected operating parameters on the resulting temperature, velocity and concentration fields
within considered object. The obtained results are briefly discussed considering their physical correctness
related to industrial measurements.

*Keywords:* computational fluid dynamics, coupled thermal problems, coke oven battery, combustion,
radiative heat transfer.