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Damage detection using the discrete wavelet transformation (DWT) of temperature field recorded on the surface of a plate structure is discussed. Defects in the form of voids and inclusions of various magnitude are considered. Computer-simulated experiments including the ones accounting for white noise and real thermal experiments are applied. Transient heat transfer problems are analysed. The efficiency of DWT in damage detection is studied by way of a number of examples. Haar, Daubechies 4, 6 and 8 wavelets in 1D and 2D DWT are used. The usefulness of the Lipschitz exponent evaluated with the use of DWT is discussed. The issue of denoising the thermal response signals using the soft threshold shrinkage procedure is also taken up.

Abstract. The paper addresses the problems of the sensitivity analysis and optimal design of multi-span sandwich panels with a soft core and flat thin steel facings. The response functional is formulated in a general form allowing wide practical applications. Sensitivity gradients of this functional with respect to dimensional, material and support parameters are derived using adjoint variable method. These operators account for the jump of the slope of a Timoshenko beam or a Reissner plate at the position of concentrated active load or reaction, thus extending the sensitivity operators known in literature. The jump of slope is the effect of shear deformation of the core. Special attention is focussed on sensitivity and optimisation allowing for variable support position and stiffness, because local phenomena observed in supporting area of sandwich plates often initiate failure mechanisms. Introducing optimally located elastic supports allows to reduce the unfavourable influence of temperature on the state of stress. Several examples illustrate the application of derived sensitivity operators and demonstrate their exactness.

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A b s t r a c tProblems of forced vibrations, eigenvibrations and stability of linear elastic frames and beams are considered in the paper. Using the adjoint variable method sensitivity derivatives with respect to small variations of the position and stiffness of elastic hinges are derived. The stractural response is measured by an integral functional on displacements or by the eigenvalues. Illustrative examples are presented. I n t r o d u c t i o nIn the majority of papers on structural optimization and sensitivity analysis attention has been focused on dimensional or form optimization. MrSz (1975) first formulated the problems of optimal design of supports and joints. This idea was further developed in a series of papers by Szel~g and Mr6z (1978) and Garstecki and Mr6z (1987). It has been shown that the generalized formulation of optimization problems taking into account not only dimensional or configuration variables, but also variable supporting conditions, can lead to better results since the structural response to external loads and to distortions is sensitive to support variations. Extensions of the formulation to problems of minimum stiffness of optimally located supports for dynamic and stability response has been presented by/~kesson and Olhoff (1988) and Olhoff and .~kesson (1991).Considering a support as a joint between a structure and a foundation, the above problems can be generalized for joints between substructures. Surprisingly, the latter problem has not been discussed in literature from the point of view of structural sylithesis. The effect of joint flexibility in frames subjected to static loads has been demonstrated by Chen and Lui (1987). Structural sensitivity for variable location and stiffness of elastic hinges in structures subjected to loads and initial distortions was studied by Garstecki (1988). The problem of the optimal location of hinges was discussed in the literature in the context of the optimal stiffness of beams (Masur 1970) and columns (Olhoff 1986). However, hinges appeared there as singular points of vanishing cross-section and resulted from simplifying assumptions, namely from the negligence of shear force or stress constraints. In engineering applications these hinges were avoided by the introduction of geometrical constraints to the formulation of the optimization problem.The present paper supplements the previous research by considering dynamic and stability problems. The sensitivity analysis is carried out with respect to variations of the position and stiffness of elastic hinges. For a better understanding only simple types of hinges are considered, where the discontinuity of the slope of deflection line occurs, however, the results can easily be generalized for hinges in which discontinuities of other kinematic fields occur, e.g. the discontinuity of the torsion angle. For the sake of completeness we will allow for the distributed variation of the beam's crosssection and a step-wise change of cross-section at the points where hinges occur. The formulation is limi...