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Academic literature on the topic 'Zig-zag theorie'

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Published: 14 March 2023

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Journal articles on the topic "Zig-zag theorie"

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Alvarado Cornejo, Marina d. A. "Zig-Zag y la irrupción editorial: La ciudad letrada “zigzagueante." Literatura y Lingüística, no. 23 (May 19, 2015): 81. http://dx.doi.org/10.29344/0717621x.23.111.

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ResumenEl objetivo de este trabajo es reconocer la importancia de la irrupción de la editorial Zig- Zag y su magazín homónimo en el proceso de legitimación y expansión de la producción literaria chilena durante las primeras dos décadas del siglo XX. Para esto, identificamos las estrategias desplegadas por la publicación semanal, las que analizamos a la luz de la noción “ciudad letrada” de Ángel Rama.Palabras clave: Editorial Zig-Zag, magazín Zig-Zag, legitimación de la producción literaria, “ciudad letrada”.Zig-Zag and the publishing emergence: The zigzagueante ciudad letradaAbstractThe aim of this paper is to recognize the importance of the emergence of Zig-Zag Publisher and its magazine with the same name, in the process of legitimation and expansion of the Chilean literary production during the first two decades of the twentieth century. For this purpose, we identify the strategies employedby the weekly publication, which are analyzed in light of the reappropriation of the notion of ciudad letrada by Angel Rama.Key words: Zig-Zag Publisher, magazíne Zig-Zag, legitimation of literary production,“ciudad letrada”.
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Icardi, U. "Applications of Zig-Zag Theories to Sandwich Beams." Mechanics of Advanced Materials and Structures 10, no. 1 (January 2003): 77–97. http://dx.doi.org/10.1080/15376490306737.

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Ferreira, A. J. M., C. M. C. Roque, E. Carrera, M. Cinefra, and O. Polit. "Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation." Journal of Composite Materials 45, no. 24 (May 10, 2011): 2523–36. http://dx.doi.org/10.1177/0021998311401103.

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In this article, we combine the Carrera's Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215–297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakami's Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples.
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Bierkens, Joris, and Andrew Duncan. "Limit theorems for the zig-zag process." Advances in Applied Probability 49, no. 3 (September 2017): 791–825. http://dx.doi.org/10.1017/apr.2017.22.

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AbstractMarkov chain Monte Carlo (MCMC) methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis–Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov processes (PDMPs). One such approach is based on the zig-zag process, introduced in Bierkens and Roberts (2016), which proved to provide a highly scalable sampling scheme for sampling in the big data regime; see Bierkenset al.(2016). In this paper we study the performance of the zig-zag sampler, focusing on the one-dimensional case. In particular, we identify conditions under which a central limit theorem holds and characterise the asymptotic variance. Moreover, we study the influence of the switching rate on the diffusivity of the zig-zag process by identifying a diffusion limit as the switching rate tends to ∞. Based on our results we compare the performance of the zig-zag sampler to existing Monte Carlo methods, both analytically and through simulations.
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Carrera, Erasmo. "Historical review of Zig-Zag theories for multilayered plates and shells." Applied Mechanics Reviews 56, no. 3 (May 1, 2003): 287–308. http://dx.doi.org/10.1115/1.1557614.

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This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1) Lekhnitskii (1935) was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2) Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian (1958), who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner (1984), who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3) On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, (LMT), Ambartsumian Multilayered Theory (AMT), and Reissner Multilayered Theory (RMT). As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4) LMT although very promising, has almost been ignored in the open literature. 5) Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6) RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references.
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SUN, HE, and HONG ZHU. "ON CONSTRUCTION OF ALMOST-RAMANUJAN GRAPHS." Discrete Mathematics, Algorithms and Applications 01, no. 02 (June 2009): 193–203. http://dx.doi.org/10.1142/s1793830909000154.

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O. Reingold et al. introduced the notion zig-zag product on two different graphs, and presented a fully explicit construction of d-regular expanders with the second largest eigenvalue O(d-1/3). In the same paper, they ask whether or not the similar technique can be used to construct expanders with the second largest eigenvalue O(d-1/2). Such graphs are called Ramanujan graphs. Recently, zig-zag product has been generalized by A. Ben-Aroya and A. Ta-Shma. Using this technique, they present a family of expanders with the second largest eigenvalue d-1/2 + o(1), what they call almost-Ramanujan graphs. However, their construction relies on local invertible functions and the dependence between the big graph and several small graphs, which makes the construction more complicated. In this paper, we shall give a generalized theorem of zig-zag product. Specifically, the zig-zag product of one "big" graph and several "small" graphs with the same size will be formalized. By choosing the big graph and several small graphs individually, we shall present a family of fully explicitly almost-Ramanujan graphs with locally invertible function waived.
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Хошгофтар, М. Дж., М. Карими, and С. Сейфури. "Нелинейный анализ изгиба пластин из слоистого композита с использованием уточненной зигзагообразной теории." Механика композитных материалов 58, no. 5 (November 2022): 905–26. http://dx.doi.org/10.22364/mkm.58.5.03.

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Для исследования изгибного поведения композитных пластин и сандвич-конструкций использована модифицированная зигзагообразная теория, основанная на теории сдвигового деформирования первого порядка для некоторых кусочно-линейных функций перемещений в плоскости. Эта теория не зависит от коэффициента коррекции на сдвиг и может быть применена к разным инженерным задачам, связанным с динамикой конструкций. Для получения точных результатов при больших деформациях в уравнении совместности фон Кармана учтены члены нелинейной деформации. Определяющие уравнения и связанные с ними граничные условия получены с помощью принципа виртуальной работы. Численные результаты сопоставлены с результатами других теорий и установлено их превосходное согласование. Результаты, представленные графически и таблично, иллюстрируют превосходство рассмотренной модели при предсказании полей напряжений и перемещений. Предложенная модель применима к нелинейным задачам с большими прогибами.
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Brischetto, S., E. Carrera, and L. Demasi. "Free Vibration of Sandwich Plates and Shells by Using Zig-Zag Function." Shock and Vibration 16, no. 5 (2009): 495–503. http://dx.doi.org/10.1155/2009/573674.

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This paper analyses the free vibration response of sandwich curved and flat panels by introducing the zig-zag function (—1)kζk(ZZF) in the displacement models of classical and higher order two-dimensional shell theories. The main advantage of ZZF is the introduction of a discontinuity in the first derivative, zig-zag effect, of the displacements distribution with correspondence to the core/faces interfaces. Results including and discarding ZZF are compared. Several values of face-to-core stiffness ratio (FCSR) and geometrical plate/shell parameters have been analyzed. Both fundamental vibration modes and those corresponding to high wave numbers are considered in the analysis. It is concluded that: (1) ZZF is highly recommended in the free vibration analysis of sandwich plates and shells; (2) the use of ZZF makes the error almost independent by FCSR parameter; (3) ZZF is easy to implement and its use should be preferred with respect to other `more cumbersome' refined theories.
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Carrera, E., M. Filippi, and E. Zappino. "Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories." European Journal of Mechanics - A/Solids 41 (September 2013): 58–69. http://dx.doi.org/10.1016/j.euromechsol.2013.02.006.

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Icardi, Ugo, and Federico Sola. "Assessment of recent zig-zag theories for laminated and sandwich structures." Composites Part B: Engineering 97 (July 2016): 26–52. http://dx.doi.org/10.1016/j.compositesb.2016.04.058.

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Dissertations / Theses on the topic "Zig-zag theorie"

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Nygren, Clara. "On Meyniel's conjecture and the Zig-Zag Theorem : Cops and robbers on random graphs." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-175951.

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This essay will present the vertex pursuit game of cops and robbers and the problem that made it famous: Meinyel's conjecture. The conjecture stood unproved from 1987 until 2010 when Łuczak and Prałat proved the conjecture with their "Zig-Zag Theorem", which is also covered in the essay.
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URRACI, ANDREA. "Development of accurate and efficient structural models for analysis of multilayered and sandwich structures of industrial interest." Doctoral thesis, Politecnico di Torino, 2020. http://hdl.handle.net/11583/2829677.

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VERSINO, DANIELE. "Refined theories and Discontinuous Galerkin methods for the analysis of multilayered composite structures." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2497085.

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Laminated multilayered composite and sandwich plates and shells are widely used for military and civilian aircraft, aerospace vehicles, and naval and civil structures because of their high specific stiffness and strength and tailoring capabilities. Moreover, composite materials are increasingly adopted for primary load-bearing structures in the form of thick laminates with a large number of layers. Those structures are subjected to complicated load paths and may exhibit critical deformation effects due to transverse shearing and transverse-normal stretching, with the consequential susceptibility to environmental and inter-laminar damage effects. One of the key aspects of the analysis of composite structures is the accurate prediction of the stress field; it can be obtained employing several numerical methods that can provide very detailed results at an high computational cost. This approach is well suited for small parts but cannot be applied to complex structures or for damage-tolerance analysis. Thus, accurate and computationally efficient models are required for the design and analysis of multilayered composites. Moreover, multilayered composites are affected by intelaminar damage that is one of the major reasons of failure. Since the delamination's presence has to be taken into account, damage tolerance analysis have to be carried out in order to understand the structure's capabilities to continue bearing loads without incurring in critical failure. The crack-growth simulation is a challenging task for the finite element method because it involves domain's separation and stress singularities at the crack tip. It is therefore necessary to introduce methods that account for crack-tip singularities and that allow to model both the initiation and the crack-growth process. The present work is divided into two main parts: in the fist one, going from chapter 2 to chapter 5, Refined Zigzag Theory, RZT, is introduced and employed formulate and develop plate and shell finite elements, in the second one, from chapter 6 to 7, the Discontinuous Galerkin method applied to structural problems is presented, a beam and a shell DG elements are formulated and the DG method is used besides a cohesive zone model to the study of the delamination's propagation process in laminate composite materials. In the following chapter Refined Zigzag theory is introduced starting from the Mindlin displacement model and passing from the Di Sciuva displacement field; then, the piece-wise linear zigzag functions that characterize RZT are obtained according to appropriate kinematic assumptions. In chapter 3 the equilibrium equations and the virtual work statement are derived for flat and curved shell elements for linear static analysis. The RZT displacement model for the plate element is obtained from the Reissner-Mindlin displacement field, while the displacement model employed for the curved RZT shell is built up on the Naghdi's displacement field. The tangent matrix computation is then modified to take into account for geometric non-linearities and the Element Independent Corotational Framework, that is used for geometric non-linear analysis in presence of small strains, is presented. The virtual work statement is then used in chapter 4 where three finite elements are developed in the RZT framework. The first one is a triangular plate finite element, the second one is a three-node flat shell finite element with drilling degree of freedom and the last one is a bilinear four-node curved shallow shell element.The two three-node elements employ the so called anisoparametric or interdependent interpolation to remove the shear locking effect and particular attention has been payed to the interaction of this strategy with the RZT displacement field. Moreover, the three-node flat shell element formulation has been extended to the geometric non-linear analysis. The four-node shallow shell element is used instead to understand the issues arising from the extension of RZT to curved manifolds. The two shell elements are built up paying particular attention to the ABAQUS user element specifications. The RZT-based accuracy has been assessed by way of numerical experiments and the results are presented in chapter 5. When available, analytical solutions have been employed as reference results, for complex problems the reference solution has been, instead, obtained from ABAQUS shell or solid elements. In the following two chapters the Discontinuous Galerkin method applied to elliptic problems is introduced and is employed to formulate two finite elements. In chapter 6 the DG formulation of the variational principle is presented starting from an intuitive point of view and then the rigorous mathematical of the method is derived from the equilibrium equations. The DG method is then specialized for two types of numerical flux and its formulation is extended, using the Cohesive Zone Model(CZM), to non-linear problems that involve interface separation and crack propagation. In chapter 7 two DG finite elements, a Timoshenko beam and a six-node curved shell, are developed and their accuracy is assessed by means of numerical experiments. Moreover, the shell element is based on an hybrid DG-CZM formulation and its performances have been validated employing two single mode tests: the double cantilever beam test(DCB) and the end notched flexure test(ENF).
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Kennington, Raymond William. "Random allocations: new and extended models and techniques with applications and numerics." 2007. http://hdl.handle.net/2440/41885.

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This thesis provides a general methodology for classifying and describing many combinatoric problems, systematising and finding theoretical expressions for quantities of interest, and investigating their feasible numerical evaluation. Unifying notation and definitions are provided. Our knowledge of random allocations is also extended. This is achieved by investigating new processes, generalising known processes, and by providing a formal structure and innovative techniques for analysing them. The random allocation models described in this thesis can be classified as occupancy urn models, in which we have a sequence of urns and throw balls into them, and investigate static, waiting-time and dynamic processes. Various structures are placed on the relationship(s) between cells, balls, and the selection of items being distributed, including varieties, batch arrivals, taboo sets and blocking sets. Static, waiting-time and dynamic processes are investigated. Both without-replacement and with-replacement sampling types are considered. Emphasis is placed on the distributions of waiting-times for one or more events to occur measured from the time a particular event occurs; this begins as an abstraction and generalisation of a model of departures of cars parked in lanes. One of several additional determinations is the platoon size distribution. Models are analysed using combinatorial analysis and Markov Chains. Global attributes are measured, including maximum waits, maximum room required, moments and the clustering of completions. Various conversion formulae have been devised to reduce calculation times by several orders of magnitude. New and extended applications include Queueing in Lanes, Cake Displays, Coupon Collector's Problem, Sock-Sorting, Matching Dependent Sets (including Genetic Code Attribute Matching and the game SET), the Zig-Zag Problem, Testing for Randomness (including the Cake Display Test, which is a without-replacement test similar to the standard Empty Cell test), Waiting for Luggage at an Airport, Breakdowns in a Network, Learning Theory and Estimating the Number of Skeletons at an Archaeological Dig. Fundamental, reduction and covering theorems provide ways to reduce the number of calculations required. New combinatorial identities are discovered and a well-known one is proved in a combinatorial way for the first time. Some known results are derived from simple cases of the general models.
http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1309598
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2007
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Kennington, Raymond William. "Random allocations: new and extended models and techniques with applications and numerics." Thesis, 2007. http://hdl.handle.net/2440/41885.

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This thesis provides a general methodology for classifying and describing many combinatoric problems, systematising and finding theoretical expressions for quantities of interest, and investigating their feasible numerical evaluation. Unifying notation and definitions are provided. Our knowledge of random allocations is also extended. This is achieved by investigating new processes, generalising known processes, and by providing a formal structure and innovative techniques for analysing them. The random allocation models described in this thesis can be classified as occupancy urn models, in which we have a sequence of urns and throw balls into them, and investigate static, waiting-time and dynamic processes. Various structures are placed on the relationship(s) between cells, balls, and the selection of items being distributed, including varieties, batch arrivals, taboo sets and blocking sets. Static, waiting-time and dynamic processes are investigated. Both without-replacement and with-replacement sampling types are considered. Emphasis is placed on the distributions of waiting-times for one or more events to occur measured from the time a particular event occurs; this begins as an abstraction and generalisation of a model of departures of cars parked in lanes. One of several additional determinations is the platoon size distribution. Models are analysed using combinatorial analysis and Markov Chains. Global attributes are measured, including maximum waits, maximum room required, moments and the clustering of completions. Various conversion formulae have been devised to reduce calculation times by several orders of magnitude. New and extended applications include Queueing in Lanes, Cake Displays, Coupon Collector's Problem, Sock-Sorting, Matching Dependent Sets (including Genetic Code Attribute Matching and the game SET), the Zig-Zag Problem, Testing for Randomness (including the Cake Display Test, which is a without-replacement test similar to the standard Empty Cell test), Waiting for Luggage at an Airport, Breakdowns in a Network, Learning Theory and Estimating the Number of Skeletons at an Archaeological Dig. Fundamental, reduction and covering theorems provide ways to reduce the number of calculations required. New combinatorial identities are discovered and a well-known one is proved in a combinatorial way for the first time. Some known results are derived from simple cases of the general models.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2007
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Book chapters on the topic "Zig-zag theorie"

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Geraci, Carlo. "Phase theory, linearization and zig-zag movement." In Explorations of Phase Theory: Interpretation at the Interfaces, 133–60. Berlin, New York: Mouton de Gruyter, 2009. http://dx.doi.org/10.1515/9783110213959.133.

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Gomes, Ivan Lima. "Reshaping Comic Books in a Socialist Regime." In The Comics World, 72–88. University Press of Mississippi, 2021. http://dx.doi.org/10.14325/mississippi/9781496834645.003.0005.

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The nearly one thousand days of Salvador Allende’s socialist government in Chile (1970–1973) are remembered as one of the twentieth century’s most significant experiences of left-wing national rule in Latin America. During that period, one of the region’s largest publishers, Zig-Zag, was acquired by the Unidad Popular (UP) government. Renamed Quimantú, it mounted an impressive publishing program, one which included comic books. In this chapter, Ivan Lima Gomes examines Quimantú’s theory of comics and its impact on Chile’s comics world, especially the influence of associated intellectuals like Armand Mattelart, Ariel Dorfman, and Manuel Jofré. An analysis of how Quimantú and its editorial line were created, and how it adapted the superhero genre to its mandate, reveals the historical peculiarities of UP’s cultural policy. These in turn helped establish and consolidate the "Chilean road to socialism" among youth, and its efforts to reshape the Chilean comics world.
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Conference papers on the topic "Zig-zag theorie"

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Goodrich, Michael T. "Zig-zag sort." In STOC '14: Symposium on Theory of Computing. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2591796.2591830.

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Filippi, Matteo, and Erasmo Carrera. "Advanced Zig-Zag Beam Theories for Sandwich Structures Analyses." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86783.

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This work aims at evaluating the capabilities of several higher-order beam formulations for stress and dynamic analyses of layered sandwich structures. The structural models are conceived within the framework of the Carrera Unified Formulation (CUF) that allows one to generate (and compare) an infinite number of displacement fields. The number and the type of functions that are selected to generate the kinematic expansions are input parameters of the problem. Besides the well-known Taylor- and Lagrange-type expansions, great attention is paid to a new class of advanced higher-order zig-zag theories, which are written as combinations of continuous piecewise polynomial functions. Numerical simulations are performed on laminated and sandwich beams with very low length-to-depth ratio values. Also, structures with soft layers made of viscoelastic materials are considered to investigate the different dissipation mechanisms.
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Cho, Y. B., E. J. Plaskacz, R. C. Averill, and R. F. Kulak. "Explicit Dynamic Finite Element Analysis of Laminated Composite Automotive Structures Using a New Composite Plate Element." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-1189.

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Abstract Composite materials are being considered for use in the front end structures of vehicles to help reduce overall vehicle mass and, thus, improve fuel efficiency. Acceptance of composite material in structural members will depend on their ability to do crash energy management. Numerical simulations can greatly aid in the design of these critical structures and reduce the number of crash tests. A new finite element, which is based on laminated plate theory with cubic zig-zag approximations, was developed to model the relevant mechanics that occur in composite materials during crash events. The element was cast in the internal force format for use with explicit integration solvers. In the plate theory, the in-plane displacement fields in a laminate are assumed to be piecewise cubic functions and vary in a zig-zag fashion through the thickness of the laminate. The zig-zag functions are obtained by satisfying the continuity of transverse shear stresses at layer interfaces. This in-plane displacement field assumption accounts for discrete layer effects without increasing the number of degrees of freedom as the number of layers is increased. The transverse normal strain predictions are improved by assuming a constant variation of transverse normal stress through the thickness in a laminate. The finite element is developed with the topology of an eight-noded brick. Each node has five engineering degrees of freedom, three translations and two rotations. Thus, this element can be conveniently implemented into general purpose finite element codes. Consistent and lumped mass matrices are derived. The developed element is implemented into Argonne National Laboratory’s in-house code, NEPTUNE, which utilizes explicit direct integration method. In NEPTUNE the internal force vector is calculated from the developed element at each time step. Numerical performance of the current element is investigated in this research.
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Cho, Maenghyo, and Jinho Oh. "Higher order zig-zag plate theory for coupled thermo-electric-mechanical smart structures." In 19th AIAA Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2001. http://dx.doi.org/10.2514/6.2001-1403.

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Baranski, Andrzej, and Sherrill Biggers, Jr. "Postbuckling analysis of delaminated composite plates using zig-zag theory with contact conditions." In 41st Structures, Structural Dynamics, and Materials Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2000. http://dx.doi.org/10.2514/6.2000-1750.

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Carrera, Erasmo, Stefano Valvano, and Matteo Filippi. "Higher-Order Shell Element for the Static and Free-Vibration Analysis of Sandwich Structures." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86784.

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An advanced shell finite element with a variable kinematic field based on a new zig-zag power function is proposed for the analysis of sandwich shell structures. The kinematic field is written by using an arbitrary number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain is a combination of zig-zag power functions depending on the shell thickness coordinate. As in the classical layer-wise approach, the shell thickness can be divided into a variable number of mathematical subdomains. The expansion order of each subdomain is an input parameter of the analysis. This feature enables the solution to be locally refined over generic regions of the shell thickness by enriching the kinematic field. The advanced finite shell elements with variable kinematics are formulated in the framework of the Carrera Unified Formulation. The finite element arrays are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modelling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on linear static stress analysis and the free-vibration analysis of sandwich shell structures.
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Averill, R., and Y. Yip. "An efficient thick beam theory and finite element model with zig-zag sublaminate approximations." In 36th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-1211.

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Oh, Jinho, and Maenghyo Cho. "Higher Order Zig-Zag Theory for Fully Coupled Thermo-Electric-Mechanical Smart Composite Shell." In 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-2263.

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Cho, Maenghyo, Jinho Oh, and Jun-Sik Kim. "Dynamic Analysis for Delaminated Composites Using DKQ Concept Based on Higher-Order Zig-Zag Theory." In 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-1684.

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Carrera, Erasmo, Matteo Filippi, Alfonso Pagani, and Enrico Zappino. "Node-dependent kinematics, refined zig-zag and multi-line beam theories for the analysis of composite structures." In 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-0425.

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