This paper presents a simple and efficient method for finding complex roots of dispersion equations occurring in many problems of elastodynamics. The method is characterized by high accuracy in root finding and absence of restrictions on function representation. The essence of the method is explained geometrically; initial guesses are found as the solutions to the appropriate problems of elastostatics. Numerical solutions to dispersion equations are obtained for two elastic isotropic waveguides: a plate of infinite cross-section and a rod of rectangular cross-section. For an infinite plate, the calculated results are in full conformity with those obtained by Newton-Raphson and bisection methods. For a waveguide of rectangular cross-section, the earlier unsolved problem of finding complex roots of dispersion equations is solved by the proposed method.

P.E. Srokosz and Chi Tran. A distributed implementation of parallel genetic algorithm for slope stability evaluation. (Received in the final form October 13, 2010) CAMES 2010 (17)

Parallel processing, the method of considering many small tasks to solve one large problem, has emerged as a key enabling technology in modern computing. Parallel computers can be simply classified into shared memory systems and distributed memory systems. The shared memory computers have a global memory attached to a number of processors enabling several processors to work concurrently on different parts of the same computation. A different approach towards building large parallel computers is to connect several processors via a network. Each processor has its own local memory. The cost of building these computers increases with the number of processors. The distributed memory multiprocessor systems are
scalable over a wider range than the shared memory computers. There are many intermediate computer architectures, each with its distinct programming model. Common between them is the notion of message passing. In all parallel processing, data must be exchanged between cooperating tasks. Several research groups have developed software packages such as Parallel Virtual Machine (PVM), the Message Passing Interface (MPI), and others. In this paper, hardware implementation of parallel information processing is introduced by application of a multicellular computer idea, in which working cells were composed of general purpose one-chip microcomputers. The influence of the cellular computer's structure size on quality and efficiency of calculations was analyzed. The optimal structure consisted of 4x4 cells which guaranteed achieving satisfactory recurrence of results for an assumed set of working parameters. This paper presents an idea and the results of trial computations regarding the problem of slope stability evaluation by variational calculus assisted by genetic algorithm.

*Keywords:* hardware implementation, slope stability, variational calculus, parallel genetic algorithm.

M.J. Sulewska. Neural modelling of compactibility characteristics of cohesionless soil. (Received in the final form July 30, 2010) CAMES 2010 (17)

Compaction is the method of in-situ soil modification to improve its engineering properties. Two key compactibility parameters are: the maximum dry density ρ_{d max} and the corresponding optimum water content *w*_{opt}. They are basic parameters for designing, constructing and controlling the compaction quality of earth structures (e.g. earth dams, highway embankments). Soil compactibility can be determined from the laboratory compactibility curve basing on Proctor's test. However, this test is destructive, time-consuming and expensive. To facilitate the determination of the cohesionless soil compactibility parameters, correlations between ρ_{d max} and *w*_{opt} and the basic parameters characterizing soil grain-size distribution (C_{U}, D_{10},
D_{20}, D_{30}, D_{40}, D_{50}, D_{60}, D_{70}, D_{80}, and D_{90}) were developed. Artificial neural networks are applied to determine models with good prediction quality. The neural models have higher accuracy than the classic statistical models.

*Keywords:* geotechnical engineering, cohesionless soil, compactibility characteristics, Artificial Neural Network.

A. Długosz. Multiobjective evolutionary optimization of MEMS structures. (Received in the final form November 12, 2010) CAMES 2010 (17)

The paper is devoted to the shape optimization of piezoelectric and electro-thermo-mechanical devices by the use of multiobjective evolutionary algorithm. In this paper, special implementation of multiobjective evolutionary algorithm is applied (MOOPTIM). Several test problems are solved in order to test efficiency of the algorithm. The results are compared with the Non-Dominated Sorting Genetic Algorithm (NSGA-II). The objective function values are calculated for each chromosome in every generation by solving a boundary value problem for the piezoelectricity and electro-thermal-mechanical analysis. In order to solve the boundary value problems, the finite element method is used. Different functionals based on the results derived from coupled field analyses are formulated. The aim of the multiobjective problem is to determine the specific dimensions of the optimized structures. Numerical examples for multiobjective shape optimization are enclosed.

*Keywords:* multiobjective optimization, evolutionary algorithm, piezoelectricity, electro-thermomechanical
analysis, coupled problems, finite element method, MEMS.

W. Beluch, P. Orantek. Evolutionary identification of laminates? granular parameters. (Received in the final form November 12, 2010) CAMES 2010 (17)

The paper deals with the identification of material constants in simple and hybrid laminates. It is assumed that identified constants are non-deterministic and can be described by means of different forms of the information granularity represented by interval numbers, fuzzy numbers or random variables. The Two- Stage Granular Strategy combining global (Evolutionary Algorithm) and local (gradient method supported by an Artificial Neural Network) optimization techniques is used to solve the identification problems. Finite Element Method in the granular form is used to solve the direct problem for laminates. Modal analysis methods are employed to collect measurement data

*Keywords:* laminate, information granularity, identification, evolutionary algorithm, artificial neural network, interval numbers, fuzzy numbers, random variables.

J. Mendakiewicz. Identification of solidification process parameters. (Received in the final form November 12, 2010) CAMES 2010 (17)

In the paper, the identification problems connected with estimation of cast iron and mould thermophysical parameters are discussed. The additional information necessary to solve the problem results from the knowledge of cooling (heating) curves at the set of points from casting (mould) domain. The course of cooling (heating) curves results from the temperature measurements done in the real conditions of technological process, but at the present stage of research the numerical solution of direct problem plays the
role of measured temperatures. In this place the problem of optimal sensors position in a system castingmould appears. Both the choice of measuring points and also the solution of inverse problem, using the gradient methods, require the application of sensitivity analysis methods. The theoretical considerations are illustrated by the examples of computations.

*Keywords:* solidification process, numerical techniques, sensitivity analysis, inverse problems, identification methods.

J.A. Kołodziej, M. Mierzwiczak Transient heat conduction by different versions of the Method of Fundamental Solutions - a comparison study. (Received in the final form September 14, 2010) CAMES 2010 (17)

The computational accuracy of three versions of the method of fundamental solutions (MFS) is compared. The first version of MFS is based on the Laplace transformation of the governing differential equations and of the boundary conditions. The second version of MFS is based on the fundamental solution of the governing differential equation and discretization in time. The third method approximates the temperature time derivative by finite difference scheme. As the test problems the 2D boundary-initial-value problems
(2D_BIVP) in square rectangular region Ω with known exact solutions are considered. Our numerical experiments show that all discussed methods achieve relatively accurate approximate solution but the third one offers less computational complexity and better efficiency.

*Keywords:* method of fundamental solutions, meshless method, transient heat conduction, initial-
boundary volume problem, boundary collocation method.