The detection of defects as well as their location, orientation and size is performed using measurements of surface temperature either at some selected points or on selected surface areas or lines. The response temperature of a structure is caused by statically, quasi-statically or dynamically applied thermal load on some structural boundary parts or within its domain. On the basis of results of measurements, an inverse heat transfer problem is formulated for a model structure and next solved. The inverse solution is constructed by minimizing the properly defined distance norm of measured and model temperatures. The model temperature distribution is calculated using the finite element model of a structure, while in minimizing the distance norm functional the gradient-oriented methods are used. The proper sensitivities of introduced identification functional are also derived. Some simple examples illustrate the applicability of the proposed approach.
*Keywords:* identification, sensitivity, thermographic methods, path-independent integrals.

A. Knitter-Piątkowska, Z. Pozorski and A. Garstecki. Application of discrete wavelet transformation in damage detection. Part I: Static and dynamic experiments. CAMES 2006 (13)

The paper demonstrates the potential of Discrete Wavelet Transform (DWT) in damage detection. Efficiency of the method is demonstrated by the way of examples. In this study the numerically simulated static and dynamic experiments were used. One dimensional DWT was used to signal processing. Measurement errors were accounted for by introduction of white noise.
*Keywords:* damage detection, wavelet transformation.

K. Ziopaja, Z. Pozorski and A. Garstecki. Application of discrete wavelet transformation in damage detection. Part II: Heat transfer experiments. CAMES 2006 (13)

A non-destructive method of damage detection based on heat transfer experiments and 2-D Discrete Wavelet Transform (DWT) is discussed. In this paper real experiments with the use of thermography measurement techniques are substituted by numerically simulated experiments. The plates were modeled as 2-D and 3-D structures. Two kinds of structures are considered: homogeneous in undamaged state and non-homogenous. Measurement errors are accounted for by introduction of a white noise. The efficiency of the method is demonstrated by the way of numerous examples.
*Keywords:* damage detection, wavelet transformation, infrared thermography.

S. Czarnecki and T. Lewiński. Shaping the stiffest three-dimensional structures from two given isotropic materials. CAMES 2006 (13)

The paper concerns layout optimization of elastic three dimensional bodies composed of two isotropic materials of given amount. Optimal distribution of the materials corresponds to minimization of the total compliance or the work of the given design-independent loading. The problem is discussed in its relaxed form admitting composite domains, according to the known theoretical results on making the minimum compliance problems well posed. The approach is based upon explicit formulae for the components of Hooke's tensor of the third rank stiff two material composites. An appropriate derivation of these formulae is provided. The numerical algorithm is based on COC concept, the equilibrium problems being solved by the ABAQUS system. Some of the optimal layouts presented compare favourably with the known benchmark solutions. The paper shows how to use commercial FEM codes to find optimal composite designs within linear elasticity theory.

E. Majchrzak and B. Mochnacki. Sensitivity analysis and inverse problems in bio-heat transfer modelling. CAMES 2006 (13)

In the paper the problems connected with numerical modelling of bio-heat transfer processes are discussed. The mathematical model of phenomena discussed bases on the Pennes equation, at the same time the steady and transient tasks are considered. The basic equation is supplemented by the adequate geometrical, physical, boundary and (in the case of transient heat transfer) initial conditions. In the first part of the paper the examples of direct solutions are discussed. Next the possibilities of sensitivity analysis applications in the domain of bio-heat transfer are presented. In the final part the selected solutions of inverse problems are shown. On the stage of numerical simulations both in the case of direct and inverse problems, as a rule, the different variants of the boundary element method have been used.

W. Ostachowicz, M. Krawczuk, A. Żak and P. Kudela. Damage detection in elements of structures by the elastic wave propagation method. CAMES 2006 (13)

This paper presents certain results of the analysis of elastic wave propagation in one-dimensional (1-D) and two-dimensional (2-D) elements of structures with damage. The problem of the elastic wave propagation has been solved by the use of the Spectral Element Method (SEM). In this approach elements of structures are modelled by a number of spectral finite elements with nodes defined at appropriate Gauss-Lobatto-Legendre points. As approximation polynomials high order orthogonal Lagrange polynomials are used. In order to calculate the elements characteristic stiffness and mass matrices the Gauss-Lobatto quadrature has been applied. In the current analysis damage in the form of crack has been considered. It has been assumed that the damage can be of an arbitrary length, depth, and location and can be simulated as a line spring of varying stiffness. Numerical calculations illustrating the phenomena of the elastic wave propagation in isotropic media have been carried out for the case of an aluminium rod and beam as well as a flat aluminium panel and plate.

Z. Waszczyszyn and L. Ziemiański. Neurocomputing in the analysis of selected inverse problems of mechanics of structures and materials. CAMES 2006 (13)

The main goal of the paper is to show great potential of Artificial Neural Networks (ANNs) as a new tool in the identification analysis of various problems in mechanics of structures and materials. The basics of ANNs are briefly written focusing on the Back Propagation Neural Networks (BPNNs) and their features and possibilities in the analysis of inverse problems. Two groups of problems are analyzed: I) BPNNs are used in five problems as independent tools for the parametric identification and implicit modelling of physical relations, II) BPNNs are parts or procedures in three hybrid FEM/ANN systems or programs. Using measured eigenfrequencies the following problems are discussed: 1) identification of damage parameters of a steel beam, 2) attachment of an additional mass to increase the accuracy of prediction of damage parameters in a beam, 3) identification of location an additional mass attached to a steel plate. Implicit simulation of physical relations is discussed on two problems: 1) concrete fatigue durability of concrete as a function of concrete strength and characteristics of fatigue cycles (besides BPNN also the Fuzzy Weight NN was applied), 2) soil-structure interaction of displacement response spectra of a real building subjected to paraseismic excitations (besides BPNN the application of Kalman filtering is discussed for the NN learning). The following problems of Group II are investigated: 1) using BPNN in the hybrid Monte Carlo method for the reliability analysis of a steel girder, 2) application of BPNN to the calibration of control parameters in the updating of a FE program for dynamic analysis of a plane frame, 3) on-line methods for the NN constitutive model formulation basing on measurements of structural displacements.

T. Burczyński, W. Beluch, A. Długosz, P. Orantek and A. Skrobol. Intelligent computing in inverse problems. CAMES 2006 (13)

This paper presents a review of intelligent computing techniques in solving inverse mechanics problems. These techniques are based on Evolutionary Algorithms (EAs) and the coupling of Evolutionary Algorithms (EAs) and Artificial Neural Networks (ANNs) in the form of Computational Intelligence Systems (CISs). The main attention was focused on the identification of the defects such as voids or cracks in structures on the basis of the knowledge about displacements, temperature and eigenfrequencies. The identification of the unknown number, position, size and kind of defects in the elastic structures is shown. The paper contains a lot of tests and numerical examples.
*Keywords:* intelligent computing (IC), evolutionary algorithms (EAs), artificial neural networks (ANNs), fuzzy inference system (FIS), computational intelligent system (CIS), finite element method (FEM), boundary element method (BEM).