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Search results for: SHELL
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On the exact equilibrium conditions of irregular shells reinforced by beams along the junctions
PublicationThe exact, resultant equilibrium conditions for irregular shells reinforced by beams along the junctions are formulated. The equilibrium conditions are derived by performing direct integration of the global equilibrium conditions of continuum mechanics. New, exact resultant static continuity conditions along the singular curve modelling reinforced junction are presented. The results do not depend on shell thickness, internal through-the-thickness...
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In-plane shear nonlinearity in failure behavior of angle-ply laminated shells
PublicationThe paper concerns the progressive failure analysis of laminates with the in-plane shear nonlinearity accounted for.The nonlinear shear response of the layer is described by the constitutive relation treating the stresses as a function of strains. Thus it can be easily incorporated into the displacement-based FEM codes. The brittle failure mechanisms of the fibers and the matrix of the layer are recognized with the use of the Hashin...
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Extended non-linear relations of elastic shells undergoing phase transitions
PublicationThe non-linear theory of elastic shells undergoing phase transitions was proposed by two first authors in J. Elast. 79, 67-86 (2004). In the present paper the theory is extended by taking into account also the elastic strain energy density of the curvilinear phase interface as well as the resultant forces and couples acting along the interface surface curve itself. All shell relations are found from the variational principle of...
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Thermo-elastic non-linear analysis of multilayered plates and shells
PublicationGeometrically nonlinear FEM analysis of multilayered composite plates and shells is performed in order to resolve the stability problem of the structures being under the influence of temperature field. The Riks-Wempner-Ramm algorithm with a specially modified multi-choice unloading condition has been implemented in authors’ numerical code. As the representation of multilayered medium the Equivalent Single Layer approach with the...
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On continuity conditions at the phase interface of two-phase elastic shells
PublicationW pracy rozwinięto ogólną nieliniową teorię powłok sprężystych podlegających przejściom fazowym typu martenzytowego. Przedstawione sformułowanie oparte jest na statycznie i kinematycznie ścisłym modelu powłokowym. Uwzględniono gęstośc energii odkształcenia, jak również siły i momenty zadane wzdłuż krzywoliniowego przejścia fazowego. W szczególności otrzymano statyczne warunki ciągłości wzdłuż koherentnego połączenia oraz połączenia...
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On shear correction factors in the non-linear theory of elastic shells
PublicationW pracy wyprowadzono analitycznie wartości korekcyjnych współczynników ścinania dla ścinania poprzecznego oraz dla momentów owinięcia w ramach nieliniowej sześcioparametrowej teorii powłok. Wartości wyprowadzono poprzez odpowiednie sformułowanie komplementarnej energii sprężystej. Na drodze analizy przy pomocy MES, badano wpływ wartości współczynników na położenie punktów bifurkacji, deformacje, całkowitą energię sprężystą układu...
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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Nonlinear FEM analysis of irregular shells composed of fiber metal laminates
PublicationThe paper deals with the analysis of failure initiation in shells made of Fiber Metal Laminates (FML). The elas-tic material law for orthotropic lamina is stated accounting for asymmetric in-plane stress and strain measures. The asymmetry results from the employed general nonlinear 6-field shell theory where the generalized dis-placements involve the translation and the proper rotation field. The novelty of the presented results...
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On modelling and non-linear elasto-plastic analysis of thin shells with deformable junctions
PublicationThe undeformed base surface of the irregular thin shell is modelled by the union of a finite number of regular smooth surface elements joined together along spatial curvilinear surface edges. The equilibrium conditions are formulated by postulating an appropriate form of the principle of virtual work, where also deformability of shell junctions is taken into account. The PVW is then discretised by C1 finite elements and the incremental-iterative...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers
PublicationThis work presents a generalized Kirchhoff–Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for heterogeneous and fibrous materials such as textiles, biomaterials, composites and pantographic structures. The presented theory is a direct extension of classical Kirchhoff–Love shell theory to incorporate...
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Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells
PublicationW pracy zaproponowano powłokowy element skończony pozwalający na uwzględnienie efektu piezoelektrycznego. Element został wykorzystany w podejściu Lagrange'a, które wymaga starannego dobrania definicji wielkości mechanicznych i elektrycznych. Zależności przemieszczenie-odkształcenie zbudowano na bazie teorii małych odkształceń i umiarkowanych obrotów. Założono liniowy rozkład pól odkształceń i pola elektrycznego po grubości powłoki....
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Critical examination of benchmark problems for large rotation analysis of laminated shells
PublicationW pracy przedstawiono krytyczny przegląd przykładów testowych stosowanych w analizie dużych obrotów powłok warstwowych. Kilka przykładów wyselekcjonowanych z literatury zostało przeanalizowanych przy użyciu własnych programów autora bazujących na różnych poziomach nieliniowości geometrycznej. Wyniki analizy porównawczej pozwoliły na wysunięcie wniosków o przydatności badanych przykładów jako testów sprawdzających w analizie dużych...
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Modelling and FE-simulation of plastic ductile damage evolution in plates and shells
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Analysis of material properties of technical fabric for hanging roofs andpneumatic shells.
PublicationPrzedyskutowano zastosowanie w metodzie elementów skończonych specjalnego modelu elementu do analizy tkanin technicznych. Przedstawiono specjalne postępowanie z typowym elementem w płaskim w stanie naprężenia, tak aby uwzględnić można było zjawiska charakterystyczne dla tkanin technicznych. Zaproponowany model pozwala na zastosowanie niesprężystych związków konstytutywnych a w szczególności związków lepkoplastycznych. Opisano doświadczenia...
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Arc-length Algorithm Efficiency in the Analysis of Thermally Loaded Multilayered Shells
PublicationThis paper concerns the efficiency study of the arc-length algorithm in the geometrically non-linear analysis of thermally loaded multilayered shells. The thermal loading is considered as the one-way thermo-mechanical coupling effect. Two implementations of the arc-length method are examined: the path-following technique available in NX-Nastran and the RiksWempner-Ramm algorithm adopted in the authors’ computer code SHLTH. It is...
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Four-node semi-EAS element in six-field nonlineartheory of shells
PublicationW pracy sformułowano 4-węzłowy powłokowy element skończony dla konstrukcji powłokowych. Element opracowano w ramach nieliniowej 6-parametrowej teorii powłok z niesymetrycznymi miarami odkształceń membranowych. Kinematyka powłoki jest opisana przez dwa pola: translacji i obrotów, przy czym wszystkie trzy parametry obrotu traktowane są jako niezależne. W wyniku tego sformułowany element nadaje się do analizy struktur powłokowych...
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Fem analysis of cosserat plates and shells based on some constitutive relations
PublicationPrzeprowadzono studium doboru mikropolarnych współczynników konstytutywnych w pewnym modelu płyty Cosseratów. Wyznaczono ograniczenia na ich wartości i przeprowadzono parametryczną analizę wpływu tych współczynników na geometrycznie nieliniowe deformacje powłok z ortogonalnymi przecięciami płatów.
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Generation of random fields to reflect material and geometric imperfections of plates and shells
PublicationThe paper covers two patterns of random field generation: conditional acceptance – rejection method and Karhunen – Loève expansion. The generation of two-dimensional random fields is essential in plates and shells analysis, allowing for a relevant limit and critical state assessment of geometrically and ma-terially imperfect structures. The features of both generation methods dedicate them to selected problems.
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Modeling of Composite Shells in 6-Parameter Nonlinear Theory with Drilling Degree of Freedom
PublicationWithin the framework of a 6-parameter nonlinear shell theory, with strain measures of Cosserat type, constitutive relations are proposed for thin elastic composite shells. The material law is expressed in terms of five engineering constants of classical anisotropic continuum plus an additional parameter accounting for drilling stiffness. The theory allows for unlimited displacements and rotations. A number of examples are presented...
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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Analysis of magnetic field distribution inside ferromagnetic thin shells during degaussing process
PublicationAnalysis of the demagnetization of a large ferromagnetic object like a ship, was conducted. The approximate mathematical model in the form of a long cylindrical shell of constant magnetic permeability was applied. The discrete degaussing winding was assumed and the current density and magnetic flux density distribution in the ferromagnetic shell wall were determined. Based on the frequential and temporal analysis the recommended...
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Dynamic fracture of brittle shells in a space-time adaptive isogeometric phase field framework
PublicationPhase field models for fracture prediction gained popularity as the formulation does not require the specification of ad-hoc criteria and no discontinuities are inserted in the body. This work focuses on dynamic crack evolution of brittle shell structures considering large deformations. The energy contributions from in-plane and out-of-plane deformations are separately split into tensile and compressive components and the resulting...
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Dynamics based on six-field theory of shells in the context of energy-conserving scheme
PublicationPraca dotyczy zaproponowanego algorytmu zachowującego energię w całkowaniu równań ruchu powłok sprężystych sformułowanych w ramach teorii sześcioparametrowej. Zawiera podstawowe założenia konieczne do formułowania schematów i podstawowe testy numeryczne. Aproksymacja przestrzenna zagadnienia oparta jest o Metodę Elementów Skończonych zaś aproksymacja w czasie wykorzystuje regułę punktu środkowego. Przykłady analizy dynamicznej...
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The large rotations theory of elasto-viscoplastic shells subjected to thedynamic and thermal loads.
PublicationPrzedstawiono problemy sprężysto- lepkoplastycznej analizy geometrycznie nieliniowych płyt i powłok poddanych obciążeniom dynamicznym w różnych temperaturach. W obliczeniach zastosowano teorię ścinania pierwszego rzędu i konstytutywne prawo Chaboche´a w wariantach z uwzględnieniem wpływu temperatury na stałe materiałowe. Do całkowania równań ruchu użyto metody różnic centralnych, a do całkowania równań konstytutywnych regułę...
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Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
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Large thermo-elastic displacement and stability FEM analysis of multilayered plates and shells
PublicationThe paper concerns the load capacity analysis of thermally loaded multilayered plates and shells. The multilayered body is treated as an equivalent single layer whose kinematics is consistent with first order shear deformation theory. The authors focus on the thermo-elastic stability problem of the thin-walled structures. The equilibrium paths are traced with the use of Riks-Wempner-Ramm algorithm. By making use of the Tsai-Wu...
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Large rotations in first-order shear deformation FE analysis of laminated shells
PublicationAbstrakt: Teoria powłok o skończonych obrotach w ramach modelu ścinania pierwszego rzędu stanowi podstawę zaprezentowanego w pracy algorytmu MES statycznej, geometrycznie nieliniowej analizy konstrukcji warstwowych. Szczególną uwagę zwrócono na właściwy opis skończonych obrotów przy zastosowaniu kątów Eulera oraz procedurę uaktualniania parametrów obrotowych. Przedstawiono sformułowanie przyrostowe w stacjonarnym opisie Lagrange´a....
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Examination of selected failure criteria with asymmetric shear stresses in the collapse analysis of laminated shells
PublicationThe paper is concerned with failure analysis of composite shells performed with the usage of the nonlinear 6‐parameter shell theory with drilling rotation degree of freedom. This special theory embodies naturally unlim-ited translations and rotations and is suitable for analysis of irregular shells for instance with various, partic-ularly orthogonal, intersections. The presence of the drilling rotation is inherently accompanied...
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Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells
PublicationMixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based onthe three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotationfields, both strain and stress resultant fields are treated as independent. The elements are derived in the frame-work of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells.The...
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Drilling couples and refined constitutive equations in the resultant geometrically non-linear theory of elastic shells
PublicationIt is well known that distribution of displacements through the shell thickness is non-linear, in general. We introduce a modified polar decomposition of shell deformation gradient and a vector of deviation from the linear displacement distribution. When strains are assumed to be small, this allows one to propose an explicit definition of the drilling couples which is proportional to tangential components of the deviation vector....
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2-D constitutive equations for orthotropic Cosserat type laminated shells in finite element analysis
PublicationWe propose 2-D Cosserat type orthotropic constitutive equations for laminated shells for the purpose of initial failure estimation in a laminate layer. We use nonlinear 6-parameter shell theory with asymmetric membrane strain measures and Cosserat kinematics as the framework. This theory is specially dedicated to the analysis of irregular shells, inter alia, with orthogonal intersections, since it takes into account the drilling...
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Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model
PublicationIn this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical...
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A simple and efficient hybrid discretization approach to alleviate membrane locking in isogeometric thin shells
PublicationThis work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff–Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based...
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A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers
PublicationThis article presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting, and bending - both in-plane and out-of-plane. These capabilities allow for the simulation of large sheets of heterogeneous and fibrous materials either with or without matrix, such as textiles, composites, and pantographic structures. The work...
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A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation
PublicationA new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four existing prominent bending models. Through an essential set of elementary nonlinear bending test cases, the membrane and bending stresses of each model are examined analytically. Only the proposed bending model passes all the test cases, while the other bending models either fail or only pass the test cases for...
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Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids
PublicationFor two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat...
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Chemical composition of shells from red (Strongylocentrotus franciscanum) and green (Strongylocentrotus droeba-chiensis) sea urchin
PublicationThe shells from red and green sea urchins accounted for 47.9 and 40.7% of their body weights, respectively. The red and green sea urchin shells contained 91.08 and 90.77% minerals and 4.06 and 4.99% proteins, respectively. The shells did not contain any chitin. Sea urchin shells had a relatively large amount of naphthoquinone pigments, 121 mg per 100 g in red and 163 mg per 100 g in green species. The small quantities of glucosamine...
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Nitrogen/Oxygen Enriched Hierarchical Porous Carbons Derived from Waste Peanut Shells Boosting Performance of Supercapacitors
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Analysis of EN 1993-1-6 guidelines about determining amplitudes of equivalent imperfections of steel cylindrical shells subjected to uniform external pressure
PublicationCivil engineering structures should be designed with reference to relevant standards. One of them is a Eurocode 3 standard EN 1993-1-6:2007: Design of steel structures Part 1-6: Strength and Stability of Shell Structures. According to this standard, the value of buckling load can be determined using different approaches: classical hand calculations (stress design) and geometrical and material non-linear analysis of an imperfect...
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Porous, High Capacity Coatings for Solid Phase Microextraction by Sputtering
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Pharmacokinetics and bioequivalence of a liquid formulation of hydroxyurea in children with sickle cell anemia
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Experiences of people with dementia and informal caregivers with post‐diagnostic support: Data from the international COGNISANCE study
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Nieliniowa statyka 6-parametrowych powłok sprężysto plastycznych. Efektywne obliczenia MES
PublicationGłównym zagadnieniem omawianym w monografii jest sformułowanie sprężysto-plastycznego prawa konstytutywnego w nieliniowej 6-parametrowej teorii powłok. Wyróżnikiem tej teorii jest występujący w niej w naturalny sposób tzw. stopień 6 swobody, czyli owinięcie (drilling rotation). Podstawowe założenie pracy to przyjęcie płaskiego stanu naprężenia uogólnionego na ośrodek typu Cosseratów. Takie podejście stanowi oryginalny aspekt opracowania....
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Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym
PublicationW pracy zaprezentowano analizę powłok z materiałów gradientowych dla zakresu dużych przemieszczeń. Macierz konstytutywna została wyprowadzona dla elementu powłokowego o 6 stopniach swobody w węźle w teorii ośrodka mikropolarnego. Zaprezentowano wyniki numeryczne dla swobodnie podpartej kwadratowej płyty FGM i porównano je z wynikami z literatury oraz uzyskanymi w programie Abaqus.
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Analiza numeryczna i analityczna przekrycia w kształcie powłoki synklastycznej o podstawie kwadratowej
PublicationW pracy poruszono problem obliczania przekrycia żelbetowego w kształcie powłoki synklastycznej ściętej o podstawie kwadratowej. Przedstawiono obliczenia analityczne i numeryczne sił w powłoce. Powłoka jest poddana działaniu głównie sił ściskających, co jest korzystne dla tego typu konstrukcji. W strefie brzegowej i podporowej konieczne jest wymiarowanie na mimośrodowe ściskanie i rozciąganie z uwagi na znaczący wzrost momentów...
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Numerical Model of Femur Part
PublicationThe aim of the study is to create a new more accurate method of femur part modelling by using the finite element method. According to this new method, a femur part is treated as a complex structure composed of trabecular bone (internal part) and cortical bone (external part). The internal part is modelled as a scaffold, thus the external part is modelled as a coat (i.e. covering). Applying the programme ABAQUS, there were created...
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Deformations of the steel schell of a vertical cylindrical tank caused by underpressure
PublicationUnderpressure in a tank with a fixed roof may arise in the final stage of its construction as well as during its usage. This article presents stages of deformations of the tank shell and their development from the occurrence of the first deformation to either removal of the causes of underpressure or cracking of the steel shell.
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Calculation of an ultimate load value of a silo with geometric imperfections in the shape of eigenforms
PublicationThe ultimate load value of a silo with initial geometric imperfections was measured. The structure was loaded with wind. Imperfections were assumed as translations of the shell nodes from perfect geometry taken from eigenforms and their combinations. Two variants of the maximum deflection placement with respect to the direction of wind pressure were proposed. The first consists in applying the maximum wind pressure to the element...