Composite laminated structures are prone to delamination. Rotorcraft flexbeams, apart from many other aerospace primary load carrying members are made up of composite laminated structures. A delaminated primary load carrying member can lead to catastrophic failure of the system of which it is a part. Delamination modeling and detection in composite laminated structures are challenging areas of ongoing research worldwide. Existing literature falls short of addressing effects of widthwise partial delamination on the modal characteristics of beams. To address this issue, a new partial delamination model for composite beams is proposed and implemented using the finite element method. Homogenized cross-sectional stiffness of the delaminated beam is obtained by the proposed analytical technique, including extension-bending, extension-twist and torsion-bending coupling terms, and hence can be used with an existing finite element method. A two-noded C1-type Timoshenko beam element with four degrees of freedom per node for dynamic analysis of beams is implemented. The results for different delamination scenarios and beams subjected to different boundary conditions are validated with available experimental results in the literature and/or with a 3-D finite element simulation using COMSOL. Results of the first torsional mode frequency for the partially delaminated beam are validated with the COMSOL results. The key point of the current work is that even partial delamination in long structures can be analyzed using a 1-D beam model, rather than using computationally more demanding 3-D or 2-D models. Rotor craft flexbeams are prone to delaminations, which in most realistic situations are partial along both the length and the width. However, the effect of partial delamination on the modal characteristics of the beam is not studied by researchers to the best of the author’s knowledge. Addressing this issue, a rotorcraft flexbeam is analysed here in the presence of delamination. A set of nonlinear governing equations for the rotating flexbeam are developed in hybrid basis. The flexbeam model developed has axial stretch, transverse displacement and flexural rotation in flapwise direction and twist as its degrees of freedom. The nonlinear governing differential equations are linearised and solved for eigenvalues and eigenvectors using a finite element method. The effects of angular speed and delamination size and location on the flexbeam modes are analysed. The results obtained using the proposed model are validated with the COMSOL 3-D finite element simulations. Next, the issue of delamination detection in beams is addressed. Mode shape curvature and Katz fractal dimension are used to detect the presence of partial delaminations in a beam. The effects of boundary conditions and location of delamination on the fractal dimension curve are studied. Usage of higher mode shape data for detection of delamination in beams is evaluated. Limitations of the Katz fractal dimension curve for delamination detection are enumerated. It is shown that fractal dimension measure and mode shape curvature can be used to detect the presence of partial delamination in beams. It is found that the torsional mode shape is best suited for partial delamination detection in beams. Apart from beams, Shell-and plate-like structures are also extensively used in aerospace structures. The modeling of multilayered plates is introduced herein with the intention to model delaminations in 2D. Carrera Unified Formulation(CUF)plate model, developed using variational formulations, is used to derive the stiffness matrices and to apply, the Principle of Virtual Displacement(PVD) and the Reissner Mixed Variational Theorem (RMVT). It is known that FEM implementation for plates leads to the phenomenon of numerical locking: the so-called membrane and shear locking effects. A well-known remedy for addressing locking is the use of the Mixed Interpolated Tensorial Components(MITC) technique. A strategy similar to MITC approach in the RMVT formulation is used to construct an advanced locking-free finite element to treat the multilayered plates. Composite laminated plates are prone to delamination. Implementation of delamination in the CUF frame work using nine-noded quadrilateral MITC9 elements is discussed. MITC9 elements are devoid of shear locking and membrane locking. Delaminated structures, as well as the corresponding healthy structures, are analysed for free vibration modes. The results from the present work are compared with those from available experimental or/and theoretical research articles or/and the 3-D finite element simulations. The effects of different kinds and different percentages of interfacial area of delaminations on the first three natural frequencies of the structure are discussed. The presence of the open-mode or breathing mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of the places between the second bending mode and the first torsional mode frequencies is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layer wise theory as compared to equivalent single layer theories for very large delaminations is stated. The effects of different kinds of delamination and its effect on the second bending and first torsional mode shapes are discussed.

The primary purpose of this thesis is to find out the mechanism of cracking formation during filtration as well as improve the dewatering efficiency of Limestone and Vietnam coal. They are both fine materials, which negatively affect the filtration process. Experiments are executed by changing parameters like solid volume fraction of initial suspension, the height of filter cake and the applied pressure difference using the conventional pressure filtration. Permeability ratio is used as the relevance output parameter to quantify the degree of cracking. Otherwise, saturation and residual moisture content on filter cake are also calculated to evaluate the extent of dewatering. Almost the mechanism of cracking is assumpted and proved. Countermeasures are suggested to prevent the probability and degree of cracking on filter cake. Otherwise, steam pressure filtration is applied as a new method allow improve the dewatering efficiency and reduce the cracking.:Contents Abstract iii Acknowledgment v Contents vi List of Figure viii List of Tables xvi List of Symbols xvii Abbreviation xix 1. Background 1 1.1. The Filtration process 1 1.2. Conventional pressure filtration and steam pressure filtration 3 1.3. Filtration theory 6 1.4. Cake deliquoring - immiscible fluid displacement in porous media 16 1.5. Tensile stress between particles 20 1.6. Coal processing/ washing 24 2. Literature review 34 2.1. Cracking on filter cake and the dewatering process with and without cracking 34 2.2. Summary and focus of research 47 3. Material, methods and the result of capillary pressure curve and tensile stress versus saturation 51 3.1. Material used 51 3.1.1. Limestone 51 3.1.2. Vietnam Coal 52 3.2. Conventional filtration rig and steam pressure filtration rig 55 3.2.1. Conventional filtration rig 55 3.2.2. Steam pressure filtration rig 57 3.3. Filtration experimental 58 3.4. Relevant parameter 59 3.5. Analyze technique 65 3.6. Tensile stresses depend on saturation during deliquoring 66 4. The influence of operating parameters on cracks formation in case of limestone 69 4.1. Capillary pressure curve and tensile stress during the filtration in the case of limestone 69 4.2. Test were conducted using conventional pressure filtration 76 4.2.1. Particle size distribution effect 76 4.2.2. The solid volume fraction of suspension effect 82 4.2.3. Height of filter cake (filter cake deep/ filter cake thickness) effect 92 4.2.4. Pressure difference effect 101 4.3. The difference in the crack formation by using steam pressure filtration 111 4.4. General conclusion 116 5. The influence of operating parameters on cracks formation in the case of Vietnam coal 118 5.1. Capillary pressure curve and tensile stress during filtration in case of Vietnam coal 118 5.2. Test were conducted using conventional pressure filtration 122 5.2.1. The influence of the solid volume fraction on crack formation and saturation 122 5.2.2. The influence of the height of filter cake on crack formation and saturation 127 5.2.3. The influence of pressure difference on crack formation and saturation 134 5.3. Estimate the efficiency dewatering as well as the crack formation using steam pressure filtration 139 5.4. General conclusion 146 6. Overall conclusion and recommendation 148 6.1. Overall conclusion 148 6.2. Recommendation 150 References 152 Appendices 156 Appendix A: Data from CCWP. 156 Appendix B: Data from the crack formation with various operation parameters using conventional pressure filtration (CPF). 159 Appendix C: Data from steam pressure filtration. 167 Appendix D: Miscellaneous Information. 177

Multi-layered electronic packages increase in complexity with demands for functionality. Interfacial delamination remains a prominent failure mechanism due to mismatch of coefficient of thermal expansion (CTE). Numerous studies have investigated interfacial cracking in microelectronic packages using fracture mechanics, which requires knowledge of starter crack locations and crack propagation paths. Cohesive zone theory has been identified as an alternative method for modeling crack propagation and delamination without the need for a pre-existing crack. In a cohesive zone approach, traction forces between surfaces are related to the crack tip opening displacement and are governed by a traction-separation law. Unlike traditional fracture mechanics approaches, cohesive zone analyses can predict starter crack locations and directions or simulate complex geometries with more than one type of interface. In a cohesive zone model, cohesive zone elements are placed along material interfaces. Parameters that define cohesive zone behavior must be experimentally determined to be able to predict delamination propagation in a microelectronic package. The objective of this work is to study delamination propagation in a copper/mold compound interface through cohesive zone modeling. Mold compound and copper samples are fabricated, and such samples are used in experiments such as four-point bend test and double cantilever beam test to obtain the cohesive zone model parameters for a range of mode mixity. The developed cohesive zone elements are then placed in a small-outline integrated circuit package model at the interface between an epoxy mold compound and a copper lead frame. The package is simulated to go through thermal profiles associated with the fabrication of the package, and the potential locations for delamination are determined. Design guidelines are developed to reduce mold compound/copper lead frame interfacial delamination.

Axisymmetric analysis of cylindrical contacts is considered in the context of axisymmetric assemblies such as shrink-fits. Fretting fatigue induces sub-critical cracks along the contact interface of press fits especially when they are subjected to vibration. The surface and near surface stresses play a major role in the fretting fatigue crack initiation process. Assuming near surface contact stresses to be largely independent of the actual geometry of components in contact, half-plane analyses and experimental results obtained from a strip configuration are often cited in the literature to predict and understand crack initiation in the actual components (ASTM STP 1425). This thesis starts with half plane and strip models for cylindrical contact such as in a shrink fitted shaft. Different traction profiles underpinning a typical fretting contact constitute a study of different geometrical parameters and friction coefficients. The cylindrical shrink fitted contact is considered using mixed boundary formulation. The different cases of contact such as full slip, partial stick-slip and full stick are considered. A formulation for cyclically varying tractions is attempted using dynamic elasticity. Finally, the problem of cylindrical cracks is highlighted to understand interface delamination in a fiber reinforced composite. Stress functions in conjunction with Fourier transforms are used for analysis. Dynamic potentials based on Helmholtz decomposition are used for dynamic loading.For static loading Love’s stress function is used for axisymmetric problems while Airy’s stress function is used for 2D problems. Solution procedures for solving traction boundary and mixed boundary conditions are described. Preliminary experiments are described to appreciate the contact stresses and crack initiation in cylindrical contact. Photoelastic fringes in a cylinder under a band of pressure illustrate fretting contact stresses concentrated close to the surface with the core of the cylinder relatively unstressed. Further, some material testing experiments using a specially designed cylindrical fretting rig demonstrated typical features of fretting fatigue crack initiation for providing the theoretical motivation. Fretting fatigue induces the initiation of a number of sub critical cracks along the contact interface of components in mechanical assemblies especially under vibration. The dominant crack among the initiated cracks may grow in size to the critical length in the presence of bulk cyclic loading finally resulting in fracture of the entire component. Fretting fatigue leads to unexpected failure of the component well below the expected life. It is therefore, critical to analyse, detect and control fretting. The blade root-disk joint in gas turbines as a critical example of fretting fatigue has spurred extensive research effort. There is relatively little literature available on cylindrical fretting in shrink fitted joint focused in this thesis. Analytical solutions for static fretting tractions are presented using both axisymmetric and plane elastic stress functions for later comparison. While Fourier transforms in conjunction with Airys stress functions are exploited for attacking plane problems, Loves axisymmetric stress functions are explored for cylindrical fretting. Near surface stresses are of great interest in fretting fatigue research. Although two dimensional models provide general understanding of stresses caused during fretting, these models become inadequate to explain the interaction of local stresses with the bulk stresses inevitably present in cylindrical components. Global stress analysis tools are desirable for estimating the fatigue life of components experiencing fretting. While numerical techniques immensely aid fatigue life estimation they have their limitation when it comes to coated components. Stress analysis of coated cylinders unveils the intricate influence of the elastic mismatch as well as the width of the loading for varying friction coefficients. Comparison of results obtained from axisymmetric elasticity with plane elasticity is discussed in detail. The validity and scope of relying on plane fretting results to cylindrical fretting contacts is examined by comparing the results obtained for three different traction profiles. Fretting is generally modeled as a stress boundary value problem wherein the normal and frictional shear stresses are prescribed on the cylindrical surface. In reality fretting generally turns out to be a mixed boundary value problem with unknown regions of stick and slip requiring prescribing traction and displacement simultaneously. This belongs to a formidable class of unsolved contact mechanics problems in cylindrical axisymmetric elasticity. The famous spherical axisymmetric Hertz problem has no cylindrical counterpart except in the limiting case of a cylinder of large radius. These aspects are investigated for studying the hub-shaft interfacial geometry. A conformal contact profile is considered to model a shrink fit; the contact pressure is zero at the ends of contact. The case of full slip condition is analysed assuming a frictionless contact. With friction, partial stick-slip condition is analysed. The unknown contact traction is resolved in terms of Chebyshev expansions whose unknown coefficients are solved using Schmidt method. The unknown contact length and stick zone length are determined through an iterative procedure. A rigid uneven undulating axisymmetric hub in total contact over an elastic shaft under full stick condition is analysed for obtaining the near surface stresses for a given value of hub penetration. Even though the stresses oscillate in fretting, almost all the analyses reported in the literature use static formulation. Understanding this need, a dynamic analysis for modeling fretting of a cylinder subjected to harmonic pressure and shear is attempted. The Pochhammer dispersion relation becomes a prerequisite for a dynamic analysis. The results show that the stresses do not decay away from the contact, in contrast to the static results. This shows the propagation of stresses along the axial direction. Further extension of the dynamic analysis to a layered cylinder is also described. The results obtained on contact stresses and contact tractions under the cylindrical contact represent a significant advance to the literature for modeling fretting fatigue crack initiation and propagation. Formulating cylindrical crack problems is somewhat similar to cylindrical contacts. Such cylindrical cracks arise from the debonding along the fiber-matrix interface of a composite. A unified formulation for the problem of a pressurised cylindrical crack as also a pair of 2D parallel cracks in infinite media is attempted using Love’s stress function in conjunction with Fourier transforms. The results obtained for stress intensity factors, strain energy release rate, mode mixity, crack opening and sliding displacements are compared with that of a 2D pair of parallel cracks obtained using the unified formulation. The asymptotic situation of a large crack length to spacing ratio is examined in detail. In the case of a pair of parallel cracks, this implies a single crack in mode-I as far as the total energy release rate is concerned while at the same time retaining an asymptotic value for the mode mixity. This unique feature of near field mixed mode blending smoothly to mode-I in the far field is also seen for the stress field around a symmetrically branched crack. Thus, this thesis presents a collection of cylindrical elastostatic and elastodynamic axisymmetric solutions to provide better understanding of fretting and delamination problems encountered in press fit assemblies.

No description available.

Laminated carbon fibre-reinforced polymer (CFRP) composites are already well established in structural applications where high specific strength and stiffness are required. Damage in these laminates is usually localised and may involve numerous mechanisms, such as matrix cracking, laminate delamination, fibre debonding or fibre breakage. Microstructures in CFRPs are non-uniform and irregular, resulting in an element of randomness in the localised damage. This may in turn affect the global properties and failure parameters of components made of CFRPs. This raises the question of whether the inherent stochasticity of localised damage is of significance for application of such materials. This PhD project is aimed at developing numerical models to analyze the effect of material randomness on delamination damage in CFRP materials by the implementation of the cohesive-zone model (CZM) within the framework of the finite-element (FE) method. Both the unidirectional and cross-ply laminates subjected to quasi-static loading conditions were studied. The initiation and propagation in delamination of unidirectional CFRP laminates were analyzed. The CZM was used to simulate the progress of that failure mechanism in a pre-cracked double-cantilever beam (DCB) specimen loaded under mode-I employing initially, a two-dimensional FE model. Model validation was then carried out comparing the numerical results with experimental data. The inherent microstructural stochasticity of CFRP laminates was accounted for in the simulations, and various statistical realizations for a half-scatter of 50% of fracture energy were performed, based on the approximation of that parameter with the Weibull s two-parameter probability density function. More detailed analyses were undertaken employing three-dimensional DCB models, and a number of statistical realizations based on variation of fracture energy were presented. In contrast to the results of two-dimensional analyses, simulations with 3D models demonstrated a lower load-bearing capacity for most of the random models as compared to the deterministic model with uniform material properties. The damaged area and the crack lengths in laminates were analyzed, and the results showed higher values of those parameters for random realizations compared to the uniform case for the same levels of applied displacement. The effect of material randomness on delamination in CFRP cross-ply laminates was also investigated. Initially, two-dimensional finite-element analyses were carried out to study the effect of microstructural randomness in a cross-ply laminate under bending with the direct introduction of matrix cracks with varying spacings and delamination zones. A considerable variation in the stiffness for cases with different crack spacings suggested that the assumption of averaged distributions of defects can lead to unreliable predictions of structural response. Three-dimensional uniform, deterministic cross-ply laminate models subjected to a tensile load were analyzed to study the delamination initiation and propagation from the tips of a pre-existing matrix crack. The material s stochasticity was then introduced, and a number of random statistical realizations were analyzed. It was observed that by neglecting the inherent material randomness of CFRP laminates, the initiation conditions for delamination as well as the character of its propagation cannot be properly detected and studied. For instance, the delamination crack length value for all the simulated random statistical realizations predicted its higher magnitudes compared to the uniform (deterministic) case for the same value of applied strain. Furthermore, the location of delamination initiation was shown to be different for different random statistical realizations. Another aspect, emphasizing the importance of microstructural randomness, was the scatter in the magnitudes of global strain at the instance of initiation and subsequent propagation of delamination. In summary, the material randomness in CFRPs can induce randomness in localised damage and it can affect the global properties of laminates and critical failure parameters. These effects can be investigated computationally through the use of stochastic cohesive-zone elements.

This thesis focuses on the incorporation of carbon nanoparticles within continuous fibre reinforcements by liquid composite moulding processes, in order to provide enhanced electrical and delamination properties to the multiscale composites. The mechanisms controlling the flow and filtration of these nanoparticles during liquid composite moulding are studied, in order to develop a predictive 1-D model which allows design of the processing of these composite materials. Five different carbon nanoparticles at 0.25 wt% loading, three unmodified and one surface modified carbon nanotube systems and one carbon nanofibre system, were utilised to modify a commercial two-component epoxy resin utilised to impregnate carbon and glass reinforcements at high fibre volume fraction by resin transfer moulding. The dispersion of the nanofillers in the prepolymer was carried out by ultrasonication, high shear mixing or triple roll milling or a combination of the three. Electrical conductivity measurements of the carbon nanoparticle liquid suspensions during dispersion, alongside optical microscopy imaging and rheological analysis of these allowed the selection of the concentration of nanofiller and the appropriate dispersion technique for each nanoparticle system. The resin transfer moulding process required adaptation to incorporate the dispersion and modify degassing steps, especially when utilising unmodified carbon nanoparticles suspensions, due to their higher viscosity and tendency to be filtered. Nanoparticle filtration was identified by electrical conductivity measurements and microscopy of specimens cut at increasing distances from the inlet. Cake filtration was observed for some of the unmodified systems, whereas deep bed filtration occurred for the surface modified CNT material. Property graded composites were obtained due to filtration, where the average electrical conductivity of the carbon and glass composites produced increased by a factor of two or one order of magnitude respectively. The effect of filler on the delamination properties of the carbon fibre composites was tested under mode I. The results do not show a statistically significant improvement of delamination resistance with the presence of nanoparticles, although localised toughening mechanisms such as nanoparticle pull-out and crack bridging as well as inelastic deformation have been observed on fracture surfaces. Particle filtration and gradients in concentration resulted in non-linear flow behaviour. An 1-D analytical and a finite difference model, based on Darcy’s law accompanied by particle mass conservation and filtration kinetics were developed to describe the flow and filtration of carbon nanoparticle filled thermosets. The numerical model describes the non-linear problem by incorporating material property update laws, i.e. permeability, porosity and viscosity variations on concentration of retained and suspended particles with location and time. The finite difference model is consistent and converges to the analytical solution. The range of applicability of the analytical model is limited to lower filtration coefficients and shorter filling lengths, providing an approximate solution for through thickness infusion; whereas the numerical model presents a solution outside this range, i.e. in-plane filling processes. These models allow process design, with specified carbon nanoparticle concentration distributions achieved via modifying the nanofiller loading at the inlet as a function of time.

Ce travail s’intéresse au renforcement mécanique de films lubrifiants auto-assemblés en milieu aqueux par réticulation. Deux stratégies ont été suivies. La première consiste à réticuler physiquement un film de tensioactifs cationiques par coadsorption d’un copolymère associatif anionique. La deuxième est de réticuler chimiquement un film de copolymères triblocs par la création de liaisons covalentes entre les différentes macromolécules. Nous étudions l’auto-assemblage des films par microbalance à cristal de quartz et microscopie à force atomique (AFM). Nous discutons ensuite les effets de la réticulation sur la morphologie des films (caractérisée par AFM), et sur leurs propriétés mécaniques mesurées avec l’appareil à mesure de force SFA-nanotribomètre. Cette étude a montré que dans les deux cas, la réticulation modifie les propriétés des films lubrifiants et permet une augmentation de la cohésion des films adsorbés. / In this work, we study the effect of cross-linking on boundary lubricant films in aqueous media. Two strategies have been followed. First, we investigate a physical network on a cationic surfactant bilayer by coadsorption of an anionic copolymer. Secondly a tribloc copolymer film was chemically cross-linked by creating some chemical bounds between macromolecules. We study film self-assembling by Quartz Crystal Microbalance and Atomic Force Microscopy. We discuss then on the effect of cross-linking on the morphology of the film and its mechanical properties by combining AFM and Surface Force Apparatus SFA-nanotribometer. We have shown that in both cases, lubricant films properties are modified and the cohesion of the adsorbed films is increased by cross-linking.

Les matériaux composites sont largement utilisés dans les structures aéronautiques. Les travaux présentés ici visent à mettre en place une méthode de calcul permettant de prédire les délaminages dans ces structures stratifiées soumises à des chargements dynamiques tout en assurant des coûts de calculs compatibles dans un contexte industriel. Une méthode de décomposition de domaine en dynamique est d’abord utilisée, afin de coupler des modélisations et des pas de temps de calcul différents. Une modélisation fine est utilisée uniquement dans les zones en cours de dégradation. Une représentation macroscopique du stratifié par des éléments de coque 3D est développée et employée dans le reste de la structure. Les coûts de calcul sont ainsi réduits tout en assurant une bonne précision des résultats. Pour éviter un remaillage avec l’avancée du délaminage, une approche multi-échelle en temps et en espace est ensuite proposée. Un maillage global de coque 3D de l'ensemble de la structure est défini. Des maillages utilisant une représentation fine du matériau sont utilisés localement. Des pas de temps adaptés sont utilisés dans les deux types de maillage. / The part of composite materials in aeronautic structures is increasing due to their specific properties and the mass reduction they enable. Accurate numerical simulations are thus needed in order to design these structures, particularly to verify if they could resist dynamic charges such as soft bodies impact. Nevertheless, using a refined model to represent phenomenon such as delamination leads to computing time and dofs number incompatible with an industrial context. The aim of the present work is to propose a multi-scale method in space and time to solve dynamic impact problems on laminate structures. A domain decomposition method for dynamic problems is first used to couple different kinds of models and time discretisations. A refined model for the laminate is used in the degradating areas only - elsewhere, a coarser representation using 3D-shell elements is used. This approach reduced the cost of the simulation giving accurate results. To avoid a remeshing due to delamination propagation within the structure, a multi-scale method is then proposed. A global 3D shell elements mesh for the whole structure is defined. Local meshes based on a refined representation of the laminates are used only if required. Coupling between global and local representation is done using velocity field.

Chování laminátových desek namáhaných na tlak či na smyk může být výrazně ovlivněno přítomností delaminací, tedy oblastí, kde je porušena vazba mezi sousedními vrstvami. Cílem této práce je rozšířit znalosti o chování delaminovaných desek, a to především o chování desek s větším počtem delaminací a desek s delaminacemi libovolného tvaru, neboť taková podoba porušení laminátu více odpovídá poškození vznikajícího v důsledku nízkorychlostního dopadu cizího tělesa na laminátovou desku. Disertační práce se skládá ze tří hlavních částí. V první části jsou stručně nastíněny postupy využívané při analýze boulení delaminovaných desek a jsou diskutována omezení těchto analýz. Dále jsou v této části shrnuty hlavní poznatky o boulení delaminovaných desek. V druhé části práce je popsán výpočtový model použitý v rámci disertační práce pro analýzu boulení delaminovaných desek. Schopnost modelu předpovědět chování delaminovaných desek je pak dokumentována na několika ověřovacích úlohách. Třetí část disertační práce se skládá ze tří samostatných studií chování desek s několika delaminacemi eliptického či kruhového tvaru a jedné studie zabývající se možností náhrady obecného tvaru delaminace kruhem či elipsou. Je probírán vliv řady parametrů na chování delaminovaných desek, konkrétně vliv orientace vrstev laminátu a dále vliv počtu, tvaru, orientace a umístění delaminací. Na základě těchto studií jsou pak zformulována doporučení ohledně postupu při posuzování únosnosti delaminovaných konstrukcí.