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We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using (Formula presented.)-elements for the discretisation of the plate as well as for the membrane deformations. Key to the formulation of the method is a convenient definition of jumps and averages of forms that are d-linear in terms of the element edge normals.

Many works can be found in the literature concerning the vibroacoustic modelling of submerged stiffened cylindrical shells, because of high interest in the industrial domain, in particular for aeronautical or naval applications. However, only a few of them take into account non-axisymmetric internal frames, as for instance engine foundations or floor partitions, that can play a role on the vibroacoustic behavior of the system. That is why a substructuring approach called the Condensed Transfer Function (CTF) approach is proposed in the first part of this thesis. The aim is to take advantage of both analytical models and element-based models, in order to be able to deal with the geometrical complexity, and to calculate at higher frequencies than with element-based methods only. The substructuring method is developed in the general case of thin mechanical structures coupled along curves. A set of orthonormal functions called condensation functions, which depend on the curvilinear abscissa along the coupling line, is considered. This set is then used as a basis for approximating and decomposing the displacements and the applied forces at the line junctions. Thanks to the definition and calculation of condensed transfer functions for each uncoupled subsystem and by using the superposition principle for passive linear systems, the behavior of the coupled subsystems can be obtained. The method is first developed and validated for plates and convergence criteria are defined in relation with the size of the basis of condensation functions. The CTF method is then applied to the case of a submerged stiffened cylindrical shell with non-axisymmetric internal frames. The system is partitioned in 3 types of subsystems: the submerged shell, the axisymmetric frames (stiffeners, bulkheads) and the non-axisymmetric frames. The submerged shell is described by a semi-analytical method based on the Flügge equations in the spectral domain. The axisymmetric frames are described by axisymmetric Finite Element models and the non-axisymmetric frames by Finite Element models. The CTF method is applied to different test cases in order to highlight the influence of non-axisymmetric internal frames on the vibroacoustic behavior of a submerged stiffened cylindrical shell, for different excitations particularly relevant in the naval domain: a point force, an acoustic plane wave, and a random pressure field (such as a diffuse sound field or a turbulent boundary layer for instance)., De nombreux travaux dans la littérature se sont concentrés sur la modélisation vibro-acoustique de coques cylindriques raidies immergées, du fait des nombreuses applications industrielles, en particulier dans le domaine aéronautique ou naval. Cependant, peu d'entre elles prennent en compte des structures internes non-axisymétriques telles que des supports moteurs, des planchers ou des carlingages, qui peuvent avoir une influence importante sur le comportement vibro-acoustique du système. C'est pourquoi une méthode de sous-structuration baptisée CTF est présentée dans cette thèse. Elle est développée dans le cas général de deux structures minces couplées le long d'une ligne. Un ensemble de fonctions orthonormées, baptisées fonctions de condensation, est défini afin d'approximer les forces et déplacements à la jonction entre les sous-systèmes. Des fonctions de transfert condensées sont définies pour chaque sous-système découplé. L'utilisation du principe de superposition, de l'équilibre des forces et de la continuité des déplacements permet de déduire le comportement des sous-systèmes couplés. La méthode est d'abord développée et validée dans le cas de plaques, puis ensuite appliquée au cas d'une coque cylindrique raidie immergée couplée à des structures internes non-axisymétriques. Le système est dans ce cas décomposé en 3 familles de sous-systèmes : la coque cylindrique immergée décrite par une méthode semi-analytique basée sur la résolution des équations de Flügge dans le domaine des nombres d’onde, les structures internes axisymétriques (raidisseurs, cloisons) décrites par éléments finis axisymétriques et les structures non-axisymétriques décrites pas des modèles éléments finis. La méthode CTF est appliquée à différents cas tests afin de montrer l'influence des structures internes non-axisymétriques sur le comportement vibro-acoustique d'une coque cylindrique pour différents types d'excitations pertinents dans le domaine naval : une force ponctuelle, une onde plane acoustique et un champ de pression aléatoire (tel qu'un champ acoustique diffus ou une couche limite turbulente).

U radu su analizirana naprezanja, deformacije, pomaci i raspored temperature u toplinski opterećenoj konstrukciji sastavljene od 3 paralelno postavljene ploče. Ploče su ukliještene s donje strane, a s gornje su međusobno povezane preko idealno krute ploče. Idealno kruta ploča se ne deformira već prenosi sve pomake donjih ploča. Konstrukcija je opterećena dovođenjem topline na srednju ploču. Numerička analiza se provodi pomoću programskog paketa ABAQUS. Kao konačni elementi koristit će se ljuskasti konačni elementi (Shell). Opisana je metoda konačnih elemenata, gdje i kako se primjenjuje, navedeni su elementi koji se koriste za analizu u radu. Bit će prikazano kako konvergencija elemenata, tj. stupnjeva slobode utječe na točnost rezultata. Verifikacija i konvergencija konačnih elemenata na jednostavnijem je provedena za 3 različita opterećenja. Jednostavniji element prestavlja gredu opterećenu toplinski i ukliještenu s jedne strane za koju postoji analitičko rješenje, dok za neke vrste opterećenja analitičko rješenje neće postojati. Rezultati dobiveni pomoću programskog paketa ABAQUS su uspoređeni s onima dobivenim analitički. Kao i za verifikaciju, provedena je analiza modela za 3 različita toplinska opterećenja. Nakon toga je provedena analiza konstrukcije pomoću odabranih ljuskastih konačnih elemenata. Prikazana je raspodjela pomaka, naprezanja, temperatura i deformacija duž elemenata. Mreža je u početku modelirana s manjim brojem elemenata, dok kasnije se broj elemenata povećava kao i točnost rezultata. In this paper has been analyzed the stresses, strains, displacements and temperature distribution in heat loaded construction composed of 3 parallel plates. The plates are pinched on the lower side, and coupled on upper side with an ideal rigid plate. Ideal rigid plate are not deformable but transfers all movements of the lower plate. The construction is loaded by heat on the middle plate. Numerical analysis of this work is carried out using the software package ABAQUS. As the final elements will be used shell finite elements. The paper describes the finite element method, where and how to apply, listed are elements used in this paper. It will be shown how the convergence of elements, ie. degrees of freedom affects on the accuracy of the results. Verification and convergence of finite elements of simply model have been conducted for 3 different loads. Simpler element represents beam loaded with heat and pinched on one side of which there is an analytical solution, while for some types of loads analytical solution will not exist. Results obtained by using the software package ABAQUS were compared with those obtained analytically. Then, has been analyzed selected structures using shell finite elements. The distribution of displacements, stresses, temperature and strain along the elements has been shown. The mesh was initially modeled with a smaller number of elements, and later the number of elements increases like the accuracy of the results.

V diplomski nalogi je predstavljena problematika masivnih betonov, tj. betonov, pri katerih je potrebna kontrola zaradi povišanja temperature v betonskem prerezu, ki je posledica sproščanja hidratacijske toplote ob vezanju cementa, in s tem povezanim nastankom razpok. Opisana je sestava cementa in vpliv sestave cementa na sproščanje hidratacijske toplote. Hidratacija je opisana po fazah, ki si sledijo med vezanjem cementa. Natančneje sta predstavljeni dve vrsti cementa, in sicer CEM I 42,5 R ter CEM III/B 32,5 N SR-LH, ki se med seboj bistveno razlikujeta glede na količino sproščene hidratacijske toplote. Podan je tudi izraz za opisovanje hitrosti sproščanja toplote med procesom hidratacije. V nadaljevanju naloge je prikazana diskretizacija problema in izpeljava enačb končnega elementa za povezan problem temperature in vlage. Izpeljane enačbe so nato uporabljene za sestavo sistema linearnih algebrajskih enačb, s pomočjo katerega izračunamo vrednosti temperature in koncentracije vlage v izbranih točkah. S pomočjo izpeljanih enačb je bil izdelan računalniški program v programskem okolju MATLAB, ki nam v nadaljevanju služi za numerično temperaturno vlažnostno analizo masivnega betona. V zadnjem delu diplomske naloge so predstavljeni rezultati treh analiz. Najprej analiziramo stopnjo povezanosti problema, pri čemer dobimo pri nepovezanem in delno povezanem problemu pričakovane rezultate. Nasprotno so pri povezanem problemu rezultati nezanesljivi, zato v nadaljevanju slednjega ne obravnavamo.. Z drugo analizo pokažemo, da za oceno temperature in koncentracije vlage v betonu upoštevanje delne povezanosti problema med fazo hidratacije ni potrebno, saj je razlika med povezanim in delno povezanim problemom zanemarljiva. S tretjo analizo pa pokažemo nujnost uporabe cementov z nizko stopnjo hidratacijske toplote pri izdelavi masivnih betonov. The present thesis deals with problems regarding mass concrete, in which the temperature rises due to the heat of cement hydration during the curing phase. A rise of temperature in concrete may result in cracking of young concrete. In the first part of the thesis cement composition and its influence on the released hydration heat is described. The hydration process is explained by its individual phases which occur during hardening of concrete. Two types of cement are presented, the CEM I 42,5 R and CEM III/B 32,5 N SR-LH. The hydration heat released by those two types of cement differs significantly. Also an analytical expression is given for evaluation of heat release of cement. Next, the discretization of the problem and the derivation of the coupled equations is made for a single finite element. The derived equations are used to form a system of linear algebraic equations, which is needed for calculation of the temperature and moisture distribution. Also the derived equations are used to write a computer program in MATLAB environment. The program is used as a tool for numerical hygrothermal analysis of mass concrete. The last part of the thesis presents the results of three different. The purpose of the first analysis is to investigate the influence of the coupling degree between heat and moisture transfer. While the results of non-coupled and semi-coupled models seem reliable, the results of a fully-coupled model are not realistic and therefore are not used in further analyses. The second analysis confirmed there is not much influence of semi-coupling on temperature fields, so the equations can be solved separately and still give useful results. The third analysis shows the necessity of low heat cement use in mass concrete structures.

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The clear benefit of the approach is that no mesh needs to be generated prior to running the analysis. This is achieved by utilising the isogeometric concept whereby computer-aided design data are used to construct not only the geometry discretisation but also the displacement and traction approximations. In this manner, significant savings can be made in the engineering design and analysis process. This paper also demonstrates that, compared with a standard boundary-element method implementation using quadratic Lagrangian shape functions, superior accuracy is achieved using the present approach for the same number of degrees of freedom. It further illustrates practical applications of the method, comparing against results obtained with a standard boundary-element method and finite-element method for verification. In addition, a propeller is analysed as a sample to show the ability of the present method to handle complex three-dimensional geometries.

We consider an optimal control problem defined by semilinear parabolic partial differential equations, with control and state constraints, where the state constraints and cost functional involve also the state gradient. The problem is discretized by using a finite element method in space and an implicit -scheme in time for state approximation, while the controls are approximated by blockwise constant ones. We propose a discrete penalized gradient projection method, which is applied to the continuous problem and progressively refines the discretization during the iterations, thus reducing computing time and memory. We prove that strong accumulation points in of sequences generated by this method are admissible and weakly extremal for the continuous problem. Finally, numerical examples are given.