The main objective of the research in the area of intelligent materials - "thermal" shape memory alloys as well as magnetic shape memory materials - is the development of new methods and tools leading to new applications of these materials in active control of vibration and shape of structural elements. Also some research has been continued and carried out on the modelling of the martensitic transformation, i.e. the improvement of the existing 1D phenomenological models and the development of a new 3D model of the martensitic transformation. This is because most of the martensitic transformation models presented and available in the literature are well suited for the "pseudoelastic" behaviour only, but they are inaccurate in the case of the shape memory effect, or are usable only under certain conditions.

Intensive investigation has been carried out in the area of static and dynamic analysis of composite elements of structures (such as beams and plates) integrated with active elements made out of shape memory materials (Nitinol wires). This work has been focussed on the optimal selection of the position, location, orientation, and the relative volume fraction of the shape memory active elements within the structures. Also some interesting results have been obtained when the use of shape memory materials has been studied for active vibration and shape control of structural elements. Vibration of composite beams with shape memory alloy strips (Nitinol), as well as of a rotor with an active bearing support, have been all investigated numerically and experimentally - numerically by the use of the finite element method and experimentally on a special dedicated test rig. The numerical and experimental results point towards numerous applications for shape memory materials for active control of certain static and dynamic characteristics of structural elements, but on the other hand show also the limitations of their use and some significant disadvantages.

The past twenty years have brought a considerable increase in the use of composite materials. Modern composite materials are characterised by very high strength-to-weight ratios and very high durability in extreme conditions (under high stresses, temperatures, in moist atmospheres etc.). For these reasons composite materials are nowadays exploited in many fields of civil and mechanical engineering. They are widely used in the aircraft industry, motorization and also as structural elements in civil engineering. Because of their properties composite materials have found many applications in sport, space technology and even in medicine.

Elements of machines made of composite materials similarly to those made of isotropic materials can be exposed to many forms of fatigue damage that may grow during their exploitation. In case of unidirectional composite materials it is mostly fibre and matrix cracking, fibre and matrix debonding, and for laminated composite materials it is delamination of layers. The wide range of the applications for composite materials and the high requirements for their durability force us to carry on research programs in order to determine the influence of fatigue damage on their safe exploitation.

Various diagnostic methods for estimation of the location and size of damage in elements of structures are still being developed. The influence of these faults on the static and dynamic behaviour of structural elements has been investigated not only experimentally but also theoretically. It is found that fatigue damages results in changes in deflection and shape of structural elements, changes in natural frequencies and in modes of vibration. Changes in the amplitudes of forced vibration, resonant frequencies, and coupling of vibration modes are also observed in these cases. These reasons encourage many researchers to undertake extensive work on developing new models and new methods to study the influence of fatigue damage on changes in static and dynamic characteristics of structural elements. The results of this work obtained for elements of structures made of isotropic materials are widely presented in the literature. Because of the more complicated nature of composite materials there is a lack of suitable models as well as corresponding results of numerical investigations.

The main objective of the research in the area of the vibration and stability of structures is to develop new finite element models of composite constructional elements with damage in the forms of cracks or delamination. The influence of the damage (crack or delamination) location and size, as well as the influence of composite material anisotropy defined by the orientation and volume fraction of reinforcing fibres, have all been studied. Changes in natural frequencies and modes of vibration, changes in amplitudes of forced vibration, and resonant frequencies due to the damage, as well as changes in critical loads have been investigated.

The results obtained from numerical simulations have been also validated experimentally. For the purpose of the experimental measurements special composite specimens (beams and plates) have been prepared. The developed finite element models have been successfully verified for their compliance with the results of experimental measurements.

One of the diagnostic methodologies considered as a Structural Health Monitoring procedure is the one utilising Fibre Optic Sensors (FOS). FOS have high sensitivity, good resistance against water, chemicals and immunity towards electromagnetic interference. FOS technologies can be applied to metal, composite or sandwich structures. Depending upon the type of the technology used it has also a potential advantage to be embedded within the material of a structure itself especially in the case of composite materials. The drawback of fibre embedding is that if the surrounding material fails due to high stresses the fibre attached to the material can possibly debond leading to sensor failure.

The FOS technology allows measurements of either tensile or comprehensive strains that are applied along a sensor length. There is a linear relationship between the change in wavelength of the reflected light and strains in a fibre caused through externally applied loads or thermal expansion. To operate multiply sensors along a single optical fibre should have different Bragg wavelengths in order to differentiate between them. The number of signals recorded with special sensors can be integrated into an optical sensing fibre and depends upon the multiplexing method used, the strain range to be measured by an optical fibre, and the wavelength budget available for the incident light. The conventional method used to join sections of optical fibres is through fusion splicing. However the bondline at the physical discontinuity may have a short life because of concentration of high stresses and then the life of a sensor may be compromised by the fusion splice if a sensor is subject to long-term stress loadings.

The research performed by our team related to the FOS is connected with building a Finite Element Model of analysed structural elements and establishing structural parameters. For the most often used optical sensors the very important filed is the displacement field. The family of special finite elements with different forms of damage developed in this group are successfully applied for modelling changes in the displacement field caused by the appearance of such damage and the correctness of the numerical tools developed has been proven in many previous publications. From numerical simulations strains in structures with or without failures can be observed and compared. This information is undoubtedly very important for Structural Health Monitoring purposes.

Localising alarming symptoms of failures in structural elements is the main goal of the research carried out. The damage identification procedures can be implemented in the case of real and working structural elements and at the same time can improve the safety of large structures, like offshore engineering structures, air-plane fuselages or wings. The application of this damage monitoring technology can potentially result in great benefits to operators through improved safety and reduced operational costs. Frequently, structural damage within erosive environments may be very difficult to locate using conventional Non Destructive Inspection (NDI) techniques. Lengthy structural down-time is often required to allow these inspections to take place and this can result in significant maintenance costs. The ability for rapidly evaluation of the integrity of structures, ideally during service, through integrated SHM systems would have a substantial, positive impact on the costs.

The main objective of our research in this area is the development of special finite elements in order to analyse the propagation of elastic waves in structural elements with damage. These special finite elements (spectral finite elements) can be formulated as so-called "frequency domain" spectral finite elements or "time domain" spectral finite elements.

In the case of the frequency domain spectral finite elements they are formulated on the basis of shape functions, which are the exact solutions of the system of differential equations in the frequency domain, governing a particular problem. The exact solutions are used next as interpolating functions in the spectral formulation of the problem. Such an approach guarantees that a built-up model describes appropriately the mass and stiffness distributions within finite elements. As a consequence the "exact" dynamic stiffness matrix is found and as thus the total number of equations of a studied system can be significantly reduced in comparison with the "traditional" finite element approach.

The time domain spectral elements are an efficient and accurate tool which can be successfully applied for simulation of wave propagation phenomena, wave scattering by discontinuities, in 1D, 2D, and 3D structures. The time domain SEM is very versatile and can be used for analysis of elastic wave propagation in isotropic and anisotropic structures of complex geometry. The formulation process of the stiffness and mass matrices in the SEM is analogous to the classical FEM formulation. A key idea of the SEM is adoption of specific shape functions. In an element, a set of local shape functions is defined consisting of Lagrange polynomials and basedon orthogonal Legendre polynomials. Local element nodes are obtained as roots of an equation based on the first derivative of the Legendre polynomial and are defined as Gauss-Lobatto-Legendre (GLL) points. The Lagrange interpolating polynomials pass through the GLL points. In this manner the highest interpolation accuracy is achieved. Thanks to the orthogonality of the approximation functions the mass matrix is diagonal. In this way the cost of numerical calculation is much less expensive than in the case of the classic FEM approach. Transformation to the global coordinate system and the assembly process are virtually the same as in the FEM. Finally, a wave propagation problem is reduced to a well-known ordinary differential equation. The second order differential equation can be solved very efficiently. It is effect of a very fast direct or indirect time integration algorithms adjusted to take full advantage of the diagonal mass matrix property.

As a result of the research carried out new methods have been proposed and developed for modelling and analysis of the propagation of elastic waves in elements of structures. Also new methods have been developed for damage detection and identification, as well as methods for identification of certain mechanical parameters of analysed elements of structures.

New models of spectral finite elements have been developed and published in numerous international journal papers. These models can be applied in studies of the problems of transverse wave propagation in beams and plates with damage in the forms of fatigue cracks. It has been shown that fatigue cracks within these structures are the source of additional reflected waves, and also they reduce the amplitudes of propagating waves. These effects can be utilised as diagnostic symptoms. Also the influence of damping, initial forces and stresses on the amplitudes of propagating waves has been extensively investigated. It has been found that the influence of the initial stresses on the propagation of elastic waves in beams can be neglected in practice - however, the damping has a strong influence in these cases especially in the interface zone of materials having different damping properties.

Besides the main stream of work a problem of the propagation of elastic waves in composite beams, plate or shell structures with or without stiffeners, with cracks or delamination has been studied and some interesting results have been obtained also in this case. These results indicate a strong influence of composite material properties (i.e. lamination angle, relative volume fraction of reinforcing fibres, etc.) on the interaction between the propagating elastic waves and the damage.

Additionally research has been carried out in the area of damage detection methods based on changes in the propagation of elastic waves. It has been found here that the elastic waves can be highly distorted by even small imperfections, which fact has a great significance for successful damage detection. Numerical results obtained in this case have been experimentally verified. The experimental measurements have been conducted in order to investigate the propagation of elastic waves in structural elements made out of composite materials. The measurements have been done in two series. In the first series composite beams have been tested, while in the second series the propagation of elastic waves in composite plates has been investigated.

The main objective of the research in the area of adaptive finite elements is the improvement of existing, and development of new algorithms and programs for the static adaptive analysis of structures. Recently new research has been started on the adaptive modal analysis of complex structures. The main tasks in this particular topic are related to the development of new suitable algorithms and computer programs based on adaptive methods for the finite element method.

Apart from the main implementation problem of hierarchical modelling of complex structures resulting from different degrees of freedom of different theories used for description of various parts of complex structures there are also other implementation problems. They deal with application to complex structures of the most common displacement formulation of the finite element methods, and with employment of the Residual Equilibration Methods (REM) for error estimation. The displacement FEM is sensitive (in the sense that special approach is necessary) to such phenomena as: the improper solution limit of the 3D elasticity model when transverse order of approximation q equals one, shear or shear-membrane locking, and boundary layers typical for thin or thick-walled members of the complex structures. Also REM may suffer from the latter two numerical phenomena. It is also sensitive to edge and corner singularities.

Even though the proposed 3D approach enables usage of the same 3D degrees of freedom within all the complex structure, regardless of the locally applied models, this approach does not remove incompatibility of the first order Reissner-Mindlin model with the hierarchic shell models and with the 3D elasticity. The source of this incompatibility are: the plain stress assumption and kinematic assumption of the theory (no elongation of the normals to the mid-shell surface during deformation). The incompatibility due to the second of the mentioned assumptions can be removed through application of the transition approximations of the displacement field between the first order shell model and hierarchic shell models or three-dimensional elasticity model, while the first one is an inherent feature of the first order shell models and cannot be easily resolved. In our proposition we are not afraid of the latter incompatibility. The method proposed for such situations is controlling the modelling error within the transition zone. This can be done with the same methodology which is used for the first order model itself. Such a control leads to movement of the transition area into the region where this error is acceptable. If such an action is not effective enough then the first order model has to be replaced with the first of the higher order shell models compatible with the description of the remaining part of the complex structure.

Three phenomena - improper solution limit of the 3D elasticity model (with transverse order of approximation q equal to one), locking, and boundary layers need special treatment within displacement FEM formulation (this is also true for some of these phenomena within other FEM formulations). The approach proposed offers local (element level) a posteriori numerical tools for detection and assessment of the mentioned phenomena. This idea is totally original New numerical tools are proposed for detection of the improper solution limit phenomenon, locking phenomena (either shear or shear-membrane), as well as for dectection of boundary layers. The additional advantage is that the proposed tools are compatible with the error estimation procedures that facilitates their implementation. In our proposition two local problems have to be solved for the chosen element of the potentially affected region and the obtained solutions have to compared.

In contrast to a typical case of simple structures a posteriori error estimation within complex structures has to include not only the approximation error but also the modelling error which results from application of mechanical models simplified with respect to 3D elasticity. For the purpose of approximation and modelling error estimation application of the Residual Equilibration Method for all mechanical models included, i.e. 3D-based first order and hierarchic shell models and 3D elasticity model have been proposed. The method is applied twice. First we apply it to approximation error estimation for the elements conforming three mentioned models. For the second time the method is applied for total error estimation within the elements conforming two shell models. The upper bound property of the global total error estimate can be proved for the hierarchic shell models only. Local modelling error indicators are obtained as a difference of the total and approximation indicators.

Some improvement of the estimation in the case of locking, boundary effect and boundary singularities can be gained by constraining local problems or introduction of higher order splitting functions for equilibration instead of linear ones.

The main objective of the research carried out in the area of the development and optimisation of sensor networks for damage detection is a search for optimal sensor placements for structural health monitoring purposes. When the positions of the sensors are chosen optimally in a structure then measured data carry most information useful for damage detection. In order to solve the problem of the optimal sensor placements a good optimisation procedure is required. Very effective tools, which can be applied here, are the methods of genetics algorithms (GA) or neural networks (NN).

In the case of GA the optimisation search procedures simulate natural evolution. Possible candidate solutions are coded as chromosomes. Random operations based on natural selection principles are used to evolve the initial population. In order to obtain "better" offspring the genetic operations such like: selection, reproduction, crosover, and mutation are employed. For proper realisation of these operations a right objective function must be determined. For solution of the problem of optimal piezo transducers (PZT) placements in a real structure chromosomes, which are binary coded, are used. Each substring in every chromosome represents one coded variable, which may be: position x and y of a sensor, position x and y of damage. The objective function may be based on the relation between energy transmitted and/or received for every relevant sensor. Then for every sensor an index can be introduced and based on such an index "the best" sensor (position) can be identified. Also as the objective function a function expressing the difference between a well-known position of a defect in a mathematical model, and calculated position of the defect, can be used. In this case "the best" sensor is such a sensor for which the objective function is equal zero or is near to zero.