Journal articles on the topic 'Kirchhoff plate theories'
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Markolefas, Stylianos, and Dimitrios Fafalis. "Strain Gradient Theory Based Dynamic Mindlin-Reissner and Kirchhoff Micro-Plates with Microstructural and Micro-Inertial Effects." Dynamics 1, no. 1 (July 31, 2021): 49–94. http://dx.doi.org/10.3390/dynamics1010005.
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In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).
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Lu, Pin, P. Q. Zhang, H. P. Lee, C. M. Wang, and J. N. Reddy. "Non-local elastic plate theories." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2088 (September 25, 2007): 3225–40. http://dx.doi.org/10.1098/rspa.2007.1903.
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A non-local plate model is proposed based on Eringen's theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.
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Zehnder, Alan T., and Mark J. Viz. "Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads." Applied Mechanics Reviews 58, no. 1 (January 1, 2005): 37–48. http://dx.doi.org/10.1115/1.1828049.
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The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.
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Zhao, Xue, Zhi Sun, Yichao Zhu, and Chunqiu Yang. "Revisiting Kirchhoff–Love plate theories for thin laminated configurations and the role of transverse loads." Journal of Composite Materials 56, no. 9 (March 2, 2022): 1363–77. http://dx.doi.org/10.1177/00219983211073853.
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The present article aims to re-derive a (de-)homogenization model for particularly investigating the behavior of thin laminated plates withstanding transverse loads. Instead of starting with Kirchhoff-type of assumptions, we directly apply perturbation analysis, in terms of the small parameter introduced by the thinness of composite plates, to the original three-dimensional governing elastostatic equations. The present article sees its intriguing points in the following three aspects. First, it is shown that transverse loads applied on a thin laminated plate induce an in-plane stress response, which essentially differs from the case of single-layered homogenous plates. A scaling law estimating the magnitude of the in-plane stresses due to transverse loads is then given, and a size effect in such induced in-plane stresses arises. Second, the stress state at any position of interest in the original three-dimensional configuration can be asymptotically estimated following a (de-)homogenization scheme, and the (de-homogenization) accuracy is shown, both theoretically and numerically, to be at a same order of magnitude as the thickness-to-size ratio. Third, the asymptotic analysis here identifies the right order of magnitude for the transverse normal strain, which is often set to vanish, leading to the so-called Poisson’s locking problem in classical thin plate theories.
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CHALLAMEL, NOËL, GJERMUND KOLVIK, and JOSTEIN HELLESLAND. "PLATE BUCKLING ANALYSIS USING A GENERAL HIGHER-ORDER SHEAR DEFORMATION THEORY." International Journal of Structural Stability and Dynamics 13, no. 05 (May 28, 2013): 1350028. http://dx.doi.org/10.1142/s0219455413500284.
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The buckling of higher-order shear plates is studied in this paper with a unified formalism. It is shown that usual higher-order shear plate models can be classified as gradient elasticity Mindlin plate models, by augmenting the constitutive law with the shear strain gradient. These equivalences are useful for a hierarchical classification of usual plate theories comprising Kirchhoff plate theory, Mindlin plate theory and third-order shear plate theories. The same conclusions were derived by Challamel [Mech. Res. Commun.38 (2011) 388] for higher-order shear beam models. A consistent variational presentation is derived for all generic plate theories, leading to meaningful buckling solutions. In particular, the variationally-based boundary conditions are obtained for general loading configurations. The buckling of the isotropic or orthotropic composite plates is then investigated analytically for simply supported plates under uniaxial or hydrostatic in-plane loading. An analytical buckling formula is derived that is common to all higher-order shear plate models. It is shown that cubic-based interpolation models for the displacement field are kinematically equivalent, and lead to the same buckling load results. This conclusion concerns for instance the plate models of Reddy [J. Appl. Mech.51 (1984) 745] or the one of Shi [Int. J. Solids Struct.44 (2007) 4299] even though these models are statically distinct (leading to different stress calculations along the cross-section). Finally, a numerical sensitivity study is made.
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Movchan, N. V., R. C. McPhedran, and A. B. Movchan. "Flexural waves in structured elastic plates: Mindlin versus bi-harmonic models." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2127 (September 22, 2010): 869–80. http://dx.doi.org/10.1098/rspa.2010.0375.
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The paper presents an analytical approach to modelling of Bloch–Floquet waves in structured Mindlin plates. The emphasis is given to a comparative analysis of two simplified plate models: the classical Kirchhoff theory and the Mindlin theory for dynamic response of periodic structures. It is shown that in the case of a doubly periodic array of cavities with clamped boundaries, the structure develops a low-frequency band gap in its dispersion diagram. In the framework of the Kirchhoff model, this band gap persists, even when the radius of the cavities tends to zero. A clear difference is found between the predictions of Kirchhoff and Mindlin theories. In Mindlin theory, the lowest band goes down to ω = 0 as the radius of the cavities tends to zero, which is linked with the contrasting behaviour of the corresponding Green functions.
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Li, Haonan, Wei Wang, and Linquan Yao. "Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories." Applied Sciences 12, no. 1 (December 27, 2021): 230. http://dx.doi.org/10.3390/app12010230.
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Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared.
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Lavrenko, Iaroslav, Olena Chaikovska, and Sofiia Yakovlieva. "Determination of eigen vibration modes for three-layer plates using the example of solar panels." International Science Journal of Engineering & Agriculture 2, no. 2 (April 1, 2023): 103–16. http://dx.doi.org/10.46299/j.isjea.20230202.10.
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Solar panels are considered as three-layer plates with a thick hard outer layer and a thin soft inner layer. To describe the mechanical behavior of the plates on the example of a solar panel, a model for anti-sandwich plates was used. The literature review includes scientific articles describing models for analytical and numerical calculations of three-layer plates. During the scientific study of the mechanical behavior of the solar plate under the influence of external factors, the method of finite element analysis using the element of the spatial shell was used. This type of elements is used for theories of single and multilayer plates. Shell elements were used for calculations and modeling of the natural forms of vibrations of three-layer plates. The paper presents scientific studies under static loading under different exposure conditions, as well as an analysis of self-oscillations of a three-layer plate using the Kirchhoff and Mindlin theories as an example. As part of the scientific work, a study of the mechanical model of a thin solar panel was carried out using finite element analysis in the ABAQUS program, taking into account different temperature conditions. The article provides analytical calculations of the application of various theories to determine the natural forms of plate vibrations.
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Gilbert, Robert P., Zhongyan Lin, and Klaus Hackl. "Acoustic Green's Function Approximations." Journal of Computational Acoustics 06, no. 04 (December 1998): 435–52. http://dx.doi.org/10.1142/s0218396x98000284.
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Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.
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Mohammadi, Meisam, Afshin Iranmanesh, Seyed Sadegh Naseralavi, and Hamed Farahmand. "Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory." Science and Engineering of Composite Materials 25, no. 3 (April 25, 2018): 439–51. http://dx.doi.org/10.1515/secm-2015-0415.
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Abstract In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.
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Kananipour, Hassan. "Static analysis of nanoplates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM." Latin American Journal of Solids and Structures 11, no. 10 (2014): 1709–20. http://dx.doi.org/10.1590/s1679-78252014001000001.
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Ebenfeld, Stefan. "A comparison of the plate theories in the sense of Kirchhoff-Love and Reissner-Mindlin." Mathematical Methods in the Applied Sciences 22, no. 17 (November 25, 1999): 1505–34. http://dx.doi.org/10.1002/(sici)1099-1476(19991125)22:17<1505::aid-mma90>3.0.co;2-k.
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Cen, Song, and Yan Shang. "Developments of Mindlin-Reissner Plate Elements." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/456740.
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Since 1960s, how to develop high-performance plate bending finite elements based on different plate theories has attracted a great deal of attention from finite element researchers, and numerous models have been successfully constructed. Among these elements, the most popular models are usually formulated by two theoretical bases: the Kirchhoff plate theory and the Mindlin-Reissener plate theory. Due to the advantages that onlyC0continuity is required and the effect of transverse shear strain can be included, the latter one seems more rational and has obtained more attention. Through abundant works, different types of Mindlin-Reissener plate models emerged in many literatures and have been applied to solve various engineering problems. However, it also brings FEM users a puzzle of how to choose a “right” one. The main purpose of this paper is to present an overview of the development history of the Mindlin-Reissner plate elements, exhibiting the state-of-art in this research field. At the end of the paper, a promising method for developing “shape-free” plate elements is recommended.
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S. Agrawal, Nikhil, P. B. Kulkarni, P. D. Pachpor, R. N. Khapre, and Dipak Nakhate. "A parametric study of residual stress in plate." International Journal of Engineering & Technology 7, no. 2.31 (May 29, 2018): 127. http://dx.doi.org/10.14419/ijet.v7i2.31.13424.
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Residual stress is a process-induced stress in a molded part that exists in the body in the absence of external loading or it exists in steel section of the unloaded state. Residual stress is also termed as ‘Locked Stress’. This paper presents to find out this lock stress analytically. The theoretical and analytical inputs are considered in terms of aspect ratio and these results are compared by percentage error. The previous study mentioned many experimental methods by which residual stresses were sorted out. A Plate is a flat surface having thickness small as compared to other two dimensions. Researchers are mainly focused on the treatment of the different plate theories related to Kirchhoff or Reissner/Mindlin. The developed ANSYS finite element model analyzed square and rectangular plate and compared the analytical results in terms of deflection and stress with theoretical results which are obtained from classical theory. Different boundary conditions for different plate size are considered and solved.
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Pandey, Akash, and A. Arockiarajan. "Performance studies on Macro fiber composite (MFC) under thermal condition using Kirchhoff and Mindlin plate theories." International Journal of Mechanical Sciences 130 (September 2017): 416–25. http://dx.doi.org/10.1016/j.ijmecsci.2017.06.034.
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Вильде, Мария Владимировна, Янина Александровна Парфенова, and Мария Юрьевна Сурова. "On the applicability limits of refined theories in describing of the flexural edge wave in plates." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 206–13. http://dx.doi.org/10.37972/chgpu.2020.28.36.023.
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Исследуются пределы применимости уточненных теорий изгиба пластины при описании дисперсии изгибной краевой волны и амплитуды её возбуждения парой сосредоточенных скручивающих моментов, приложенных на торце. Методом численного сравнения с решением трехмерной задачи показано, что теория типа Тимошенко пригодна для описания краевой волны на частотах, не превосходящих 30% от первой частоты запирания. Уточненная теория изгиба пластин с приведенной инерцией в сочетании с классическими граничными условиями позволяет уточнить скорость волны по сравнению с теорией Кирхгофа, но значительно искажает амплитуду. The applicability limits of refined plate bending theories in describing of the flexural edge wave dispersion and its excitation amplitude are investigated. The wave is excited by a pair of twisting couples applied to the edge of the plate. Numerical comparison with the solution of 3D problem shows that Uflyand-Mindlin theory is applicable at the frequencies up to 30% of the first cut-off. The higher order asymptotic theory of plate bending with modified inertia and classical boundary conditions allows to improve the describing of the velocity comparing to Kirchhoff theory, but leads to a considerable error in describing of the amplitude.
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Вильде, Мария Владимировна, Янина Александровна Парфенова, and Мария Юрьевна Сурова. "On the applicability limits of refined theories in describing of the flexural edge wave in plates." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 206–13. http://dx.doi.org/10.37972/chgpu.2020.28.36.023.
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Исследуются пределы применимости уточненных теорий изгиба пластины при описании дисперсии изгибной краевой волны и амплитуды её возбуждения парой сосредоточенных скручивающих моментов, приложенных на торце. Методом численного сравнения с решением трехмерной задачи показано, что теория типа Тимошенко пригодна для описания краевой волны на частотах, не превосходящих 30% от первой частоты запирания. Уточненная теория изгиба пластин с приведенной инерцией в сочетании с классическими граничными условиями позволяет уточнить скорость волны по сравнению с теорией Кирхгофа, но значительно искажает амплитуду. The applicability limits of refined plate bending theories in describing of the flexural edge wave dispersion and its excitation amplitude are investigated. The wave is excited by a pair of twisting couples applied to the edge of the plate. Numerical comparison with the solution of 3D problem shows that Uflyand-Mindlin theory is applicable at the frequencies up to 30% of the first cut-off. The higher order asymptotic theory of plate bending with modified inertia and classical boundary conditions allows to improve the describing of the velocity comparing to Kirchhoff theory, but leads to a considerable error in describing of the amplitude.
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Schmidt, R., and J. N. Reddy. "A Refined Small Strain and Moderate Rotation Theory of Elastic Anisotropic Shells." Journal of Applied Mechanics 55, no. 3 (September 1, 1988): 611–17. http://dx.doi.org/10.1115/1.3125837.
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A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Ka´rma´n type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.
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Kumar, Arun, Poornakanta Handral, Darshan Bhandari, and Ramsharan Rangarajan. "More views of a one-sided surface: mechanical models and stereo vision techniques for Möbius strips." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2250 (June 2021): 20210076. http://dx.doi.org/10.1098/rspa.2021.0076.
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Möbius strips are prototypical examples of ribbon-like structures. Inspecting their shapes and features provides useful insights into the rich mechanics of elastic ribbons. Despite their ubiquity and ease of construction, quantitative experimental measurements of the three-dimensional shapes of Möbius strips are surprisingly non-existent in the literature. We propose two novel stereo vision-based techniques to this end—a marker-based technique that determines a Lagrangian description for the construction of a Möbius strip, and a structured light illumination technique that furnishes an Eulerian description of its shape. Our measurements enable a critical evaluation of the predictive capabilities of mechanical theories proposed to model Möbius strips. We experimentally validate, seemingly for the first time, the developable strip and the Cosserat plate theories for predicting shapes of Möbius strips. Equally significantly, we confirm unambiguous deficiencies in modelling Möbius strips as Kirchhoff rods with slender cross-sections. The experimental techniques proposed and the Cosserat plate model promise to be useful tools for investigating a general class of problems in ribbon mechanics.
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Azrar, A., N. Fakri, A. A. Aljinaidi, and L. Azrar. "Flutter and parametric stability analysis of axially moving composite graphene sheets." MATEC Web of Conferences 286 (2019): 01008. http://dx.doi.org/10.1051/matecconf/201928601008.
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The dynamic analysis instability of axially moving rectangular composite graphene sheets with visco elastic foundation is modeled and numerically simulated for various boundary conditions based on the differential quadrature method (DQM). The partial differential equation of motion based on the nonlocal elasticity and the Kirchhoff plate theories is given. The Galerkin and harmonic balance methods are used for the linear and parametric vibration analysis. The influences of nonlocal parameter, the fibers orientation and the viscoelastic foundation effects on the dynamic behaviors of the rectangular graphene sheet as well as the instabilities induced by the time dependent axial speed and its excitation frequency are investigated.
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Lavrenko, Iaroslav, Olena Chaikovska, and Sofiia Yakovlieva. "Calculation of three-layer plates by methods of vibration theory." International Science Journal of Engineering & Agriculture 1, no. 4 (October 1, 2022): 27–42. http://dx.doi.org/10.46299/j.isjea.20220104.03.
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A three-layer plate with thick hard outer layers and a thin soft inner layer was studied. A model is considered on the example of an anti-sandwich panel to describe the mechanical behavior of a plate on the example of a solar panel. A review of the scientific literature was conducted, in which models of both analytical and numerical methods for calculating three-layer plates are displayed. The scientific work uses the method of finite element analysis using a spatial shell element, as well as the theory of single- and multi-layer plates. These elements combine the topology of volumetric elements and the kinematic and structural equations of a classical shell element. Shell elements based on continuum mechanics were used for numerical simulation. The study was carried out under static load under different conditions, and also the self-oscillations of the anti-sandwich were analyzed using the theories of Kirchhoff and Reisner-Mindlin. As part of the scientific work, a study of the mechanical model of a thin solar panel was carried out using finite element analysis taking into account different temperature conditions and comparing the results with existing studies
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Zabihi, A., R. Ansari, K. Hosseini, F. Samadani, and J. Torabi. "Nonlinear Pull-in Instability of Rectangular Nanoplates Based on the Positive and Negative Second-Order Strain Gradient Theories with Various Edge Supports." Zeitschrift für Naturforschung A 75, no. 4 (April 28, 2020): 317–31. http://dx.doi.org/10.1515/zna-2019-0356.
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AbstractBased on the positive and negative second-order strain gradient theories along with Kirchhoff thin plate theory and von Kármán hypothesis, the pull-in instability of rectangular nanoplate is analytically investigated in the present article. For this purpose, governing models are extracted under intermolecular, electrostatic, hydrostatic, and thermal forces. The Galerkin method is formally exerted for converting the governing equation into an ordinary differential equation. Then, the homotopy analysis method is implemented as a well-designed technique to acquire the analytical approximations for analyzing the effects of disparate parameters on the nonlinear pull-in behavior. As an outcome, the impacts of nonlinear forces on nondimensional fundamental frequency, the voltage of pull-in, and softening and hardening effects are examined comparatively.
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Firsanov, Val V., Q. H. Doan, and N. D. Tran. "STRESS-STRAIN STATE IN BOUNDARY LAYER OF THE CIRCULAR PLATES WITH VARIOUS THICKNESSES BASED ON THE REFINED THEORY." Problems of strenght and plasticity 82, no. 1 (2020): 32–42. http://dx.doi.org/10.32326/1814-9146-2020-82-1-32-42.
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A variant of the refined theory on calculation of the stress-strain state of circular plates with symmetrically various thicknesses according to an arbitrary law in the radial direction was presented. Equations of the plate state were established by using the three-dimensional elasticity theory. The required displacements were approximately calculated according to upright direction to the middle plane by polynomials with two degrees higher than in the classical Kirchhoff - Love theory. The differential equation at equilibrium in displacements with various coefficients was obtained by using means of the Lagrange variational principle. The direct integration of the equilibrium equations in the three-dimensional elasticity theory was used to determine the transverse normal and shear stresses. Of an isotropic circular plate with changing in thickness by using the analyzing Fourier chain, the obtained differential equilibrium equations in displacements with variable coefficients containing supplement components and taking into account of the effect of thickness on the stress-strain state of the plate. Examples of calculating the stress state of a circular plate with a thickness varying according to linear and parabolic laws under the action of a uniformly distributed load were considered. The limited difference method was employed to solve the boundary value problem. Comparison results of the refined and classical theories were investigated. It is demonstrated that the study on the stress state in the zones of its distortion (compounds, local loading zones, etc.) should use a refined theory, since the additional corresponding stresses of the “boundary layer” type are of the same order with the values of the main (internal) stress state. This is important to increase the reliability of strength calculations of such elements of aircraft-rocket structures as the power housings of aircraft, their various transition zones and connections, as well as objects in various engineering industries.
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Khudayarov, B. A. "Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories." Mechanical Engineering and Computer Science, no. 9 (December 2, 2018): 15–33. http://dx.doi.org/10.24108/0918.0001412.
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Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.
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Ebrahimi, Farzad, and S. Hamed S. Hosseini. "Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation." Journal of Strain Analysis for Engineering Design 55, no. 1-2 (December 23, 2019): 53–68. http://dx.doi.org/10.1177/0309324719890868.
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Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.
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Tzou, H. S., and J. P. Zhong. "Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (September 1, 1993): 506–17. http://dx.doi.org/10.1115/1.2899129.
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Smart piezoelectric structures, conventional passive materials integrated with piezoelectric sensors, actuators, and control electronics, have great potentials in many engineering applications. This paper is devoted to a new theoretical development of generic piezoelectric shell distributed systems. System electromechanical equations and boundary conditions for a thick piezoelectric shell continuum with symmetrical hexagonal structure (Class C6v = 6 mm) are derived using Hamilton’s principle and linear piezoelectric theory. Further simplification leads to a set of new electromechanical system equations, three translated coordinates and two rotary coordinates, for piezoelectric shell continua including rotary inertias and transverse shears. For thin piezoelectric shells, the second set system equations are further simplified using Kirchhoff-Love’s assumptions. The converse effect induced electric forces/moments and boundary conditions can be used to control system dynamics via open or closed-loop control systems. Applications of the theories to a plate and shells of revolution (spherical, cylindrical, and conical shells) are demonstrated in case studies.
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Gholami, R., R. Ansari, and Y. Gholami. "Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions." Journal of Intelligent Material Systems and Structures 29, no. 5 (August 4, 2017): 944–68. http://dx.doi.org/10.1177/1045389x17721377.
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Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.
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R., Resmi, Suresh Babu V., and Baiju M. R. "Thermoelastic Damping Limited Quality Factor Enhancement and Energy Dissipation Analysis of Rectangular Plate Resonators Using Nonclassical Elasticity Theory." Advances in Materials Science and Engineering 2022 (April 4, 2022): 1–19. http://dx.doi.org/10.1155/2022/6759093.
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Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and needs to be alleviated in vibrating resonators to mitigate parameters by improving the thermoelastic damping limited quality factor, QTED. The maximum energy dissipation is also interrelated with the critical dimension h c of the plates, and by optimizing the dimensions, the peaking of energy dissipation can be diminished. As the size of the devices is scaled down, classical continuum theories become incompetent to explain the size-effect related mechanical nature at the micron and submicron levels, and, as a result, nonclassical continuum theories have been pioneered with the inception of internal length scale parameters. In this work, an analysis of isotropic rectangular microplates based on the Kirchhoff model and a higher order theory like Modified Couple Stress Theory is utilized to study size-dependent thermoelastic damping and its impact on the quality factor and critical dimensions. The Hamilton principle is adapted to derive the governing equations of motion, and the coupled heat conduction equation is employed to formulate the thermoelastic damping limited quality factor of the plates. Five different structural materials (PolySi, diamond, Si, GaAs, and SiC) are used for optimizing QTED and hc, which depends on two material performance index parameters: the thermoelastic damping index (TDI) and the material thermal diffusion length, l T . According to this work, the maximum QTED is attained for PolySi with the lowest TDI, and hcmax is obtained for Si with the maximum l T . The impacts of the dimensionless length-scale parameters (l/h), vibration modes, and boundary conditions (clamped-clamped and simply supported) on QTED and hc are also investigated. From the current analysis, QTED can be further enhanced by selecting higher vibration modes and clamped-clamped boundary conditions. QTED can be maximized by fixing the internal length scale parameter (l) and making the thickness of the beam equal to l. The analytical study is numerically simulated by using MATLAB 2015 software. Prior knowledge of QTED and hc will help designers to produce high-performance and low-loss resonators for the futuristic technological applications.
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Lyu, Yu-Ting, Tsung-Pin Hung, Herchang Ay, Hsiu-An Tsai, Yih-Cherng Chiang, and Ah-Der Lin. "Derivation and Verification of Laminated Composite T-Beam Theory." Applied Sciences 12, no. 21 (November 3, 2022): 11158. http://dx.doi.org/10.3390/app122111158.
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This study analyzes the composite laminated T-beams using the composite beam and laminated composite plate theories. The theoretical formula was derived assuming that the composite T-beam has one- and two-dimensional (1D and 2D) structures. The 1D analysis was performed according to the Kirchhoff-Love hypothesis, thereby considering only the axial strain to derive a relationship between the strain and displacement. The 2D analysis was performed considering the T-beam as a combination of two composite sheets. The effective stiffness of the beam was derived from the stress-strain and moment-curvature relationships. Furthermore, the deflection of the beam and the stress of each laminate were calculated. A simple support beam, made of AS4/3501-6 carbon/epoxy, was used as a composite laminated T-beam. MSC/NASTRAN finite element software was used for analysis. The accuracy of the theoretical formula and limitations of its use was verified using the finite element analysis. Higher accuracy of the theoretical formula was obtained at a composite beam aspect ratio greater than 15. The formula derived in this study is suitable for thin and long beams.
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Carrera, Erasmo. "Assessment of Theories for Free Vibration Analysis of Homogeneous and Multilayered Plates." Shock and Vibration 11, no. 3-4 (2004): 261–70. http://dx.doi.org/10.1155/2004/493584.
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This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness directionz. The effect of the Zig-Zag form of the displacement distribution inzas well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.
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García-Fogeda, Pablo, Fernando de la Iglesia, and Keyvan Salehi. "Acoustic and Dynamic Response of Unbaffled Plates of Arbitrary Shape." Applied Sciences 11, no. 17 (August 30, 2021): 8019. http://dx.doi.org/10.3390/app11178019.
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In this study, a method for determining the effects of fluids on the dynamic characteristics of an aerospace structure and the response of the structure when it is excited by the acoustical loads produced during a rocket launch, has been developed. Elevated acoustical loads are critical in the design of large lightweight structures, such as solar arrays and communication reflectors, because of the high acceleration levels. The acoustic field generated during rocket launch can be considered as a diffuse field composed of many uncorrelated incident plane waves traveling in different directions, which impinge on the structure. A boundary element method was used to calculate the pressure jump produced by an incoming plane wave on an unbaffled plate and the fluid–structure coupled loads generated through plate vibration. This method is based on Kirchhoff’s integral formulation of the Helmholtz equation for pressure fields. The generalized force matrix attributed to the fluid loads was then formulated, taking the modes of the plate in vacuum as base functions of the structural displacement. These modes are obtained using a finite-element model. An iteration procedure was developed to calculate the natural frequencies of the fully coupled fluid–plate system. Comparison of the results obtained using the proposed method with those of other theories and experimental data demonstrated its efficiency and accuracy. The proposed method is suitable for analyzing plates of arbitrary shape subjected to any boundary conditions in a diffuse field for low to medium values of the frequency excitation range.
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Li, Gang, and Yaochu Fang. "Failure Mode Analysis and Performance Optimization of the Hierarchical Corrugated Truss Structure." Advances in Mechanical Engineering 6 (January 1, 2014): 251591. http://dx.doi.org/10.1155/2014/251591.
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The theories of elastic plates and Kirchhoff's sandwich plates are used to analyze the failure modes of the second order hierarchical corrugated truss structure, and a plate model is presented. Besides the six competing failure modes obtained in the literature using the elementary elastic beam theory, another five competing failure modes have been identified herein, including the plate buckling, infinitely wide plate buckling, sandwich plate buckling, infinitely wide sandwich plate buckling, and surface wrinkling. Expressions for the compressive collapse strengths of these modes are derived and used to construct collapse mechanism maps for second order trusses, which is effective for selecting the geometries of second order trusses. By comparing with the result of the finite element method (FEM) it is shown that the plate model has higher accuracy than the beam model, and the infinite wide plate model has the highest accuracy when the length-width ratio of the large struts is greater than 1.0. Finally, three optimization models are proposed. The performance of a second order hierarchical corrugated truss structure has been optimized, and the geometric parameters under the optimal performance can be obtained, which can provide a more convenient way to achieve a desired scheme for designers.
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Reissner, Eric. "Reflections on the Theory of Elastic Plates." Applied Mechanics Reviews 38, no. 11 (November 1, 1985): 1453–64. http://dx.doi.org/10.1115/1.3143699.
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We depart from a three-dimensional statement of the problem of small bending of elastic plates, for a survey of approximate two-dimensional theories, beginning with Kirchhoff’s fourth-order formulation. After discussing various variational statements of the three-dimensional problem, we describe the development of two-dimensional sixth-order theories by Bolle´, Hencky, Mindlin, and Reissner which take account of the effect of transverse shear deformation. Additionally, we report on an early analysis by Le´vy, on a direct two-dimensional formulation of sixth-order theory, on constitutive coupling of bending and stretching of laminated plates, on higher than sixth-order theories, and on an asymptotic analysis of sixth-order theory which leads to a fourth-order interior solution contribution with first-order transverse shear deformation effects included, as well as to a sequentially determined second-order edge zone solution contribution.
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Mansuripur, Masud. "A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction." Nanophotonics 10, no. 1 (September 7, 2020): 315–42. http://dx.doi.org/10.1515/nanoph-2020-0348.
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AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.
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Zozulya, V. V. "A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories." Journal of Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/590480.
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A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.
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Khdeir, A. A. "Comparison between shear deformable and Kirchhoff theories for bending, buckling and vibration of antisymmetric angle-ply laminated plates." Composite Structures 13, no. 3 (January 1989): 159–72. http://dx.doi.org/10.1016/0263-8223(89)90001-9.
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Aidossov, Allayarbek, Galym Aidosov, and Saltanat Narbayeva. "Construction of mathematical models of the stressed-strained state of a material with a porous water-saturated base under dynamic load." Eastern-European Journal of Enterprise Technologies 5, no. 7 (113) (October 29, 2021): 25–35. http://dx.doi.org/10.15587/1729-4061.2021.238978.
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Materials of beams, plates, slabs, strips have been commonly applied in various fields of industry and agriculture as flat elements in the structures for machinery and construction. They are associated with the design of numerous engineering structures and facilities, such as the foundations of various buildings, airfield and road surfaces, floodgates, including underground structures. This paper reports a study into the interaction of the material (of beams, plates, slabs, strips) with the deformable base as a three-dimensional body and in the exact statement of a three-dimensional problem of mathematical physics under dynamic loads. The tasks of studying the interaction of a material (beams, plates, slabs, strips) with a deformable base have been set. A material lying on a porous water-saturated viscoelastic base is considered as a viscoelastic layer of the same geometry. It is assumed that the lower surface of the layer is flat while the upper surface, in a general case, is not flat and is given by some equation. Classical approximate theories of the interaction of a layer with a deformable base, based on the Kirchhoff hypothesis, have been considered. Using the well-known hypothesis by Timoshenko and others, the general three-dimensional problem is reduced to a two-dimensional one relative to the displacement of points of the median plane of the layer, which imposes restrictions on external efforts. In the examined problem, there is no median plane. Therefore, as the desired values, displacements and deformations of the points in the plane have been considered, which, under certain conditions, pass into the median plane of the layer. It is not possible to find a closed analytical solution for most problems while experimental studies often turn out to be time-consuming and dangerous processes
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Bokov, Igor, Natalia Bondarenko, and Elena Strelnikova. "INVESTIGATION OF STRESS-STRAIN STATE OF TRANSVERSELY ISOTROPIC PLATES UNDER BENDING USING EQUATION OF STATICS {1,2} –APPROXIMATION." EUREKA: Physics and Engineering 5 (September 30, 2016): 58–66. http://dx.doi.org/10.21303/2461-4262.2016.00159.
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The study examined the construction of the fundamental solution for the equations of statics {1,2} – approximation for transversely isotropic plates under bending with the action of concentrated force. Equations {1,2} -approximation were obtained by the decomposition method in the thickness coordinate using the Legendre polynomials. These equations take into account all the components of the stress tensor, including the transverse shear and normal stresses. Since the classical theory of Kirchhoff-Love doesn’t take account of these stresses, the study on the basis of refined theories of stress-strain state of transversely isotropic plates under the action of concentrated force effects is an important scientific and technical problem. The fundamental solution of obtained equations results using a two-dimensional Fourier integral transform and inverse treatment techniques, built with the help of a special G-function. This method allows reducing the system of resolving differential equations for statics of flat plates and shells to a system of algebraic equations. After that, the inverse Fourier transform restores the fundamental solution. The work was carried out numerical studies that demonstrate patterns of behavior of components of the stress-strain state, depending on the elastic constants of transversely isotropic material. The results play a decisive role in the study of boundary value problems in the mechanics of thin-walled elements of constructions, including under the influence of concentrated and local diverse forces.
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de Benito Delgado, Miguel, and Bernd Schmidt. "A hierarchy of multilayered plate models." ESAIM: Control, Optimisation and Calculus of Variations, October 7, 2020. http://dx.doi.org/10.1051/cocv/2020067.
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We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of Γ-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary significantly in the small film direction and which also may have a (small) pre-stress. By computing the Γ-limits in the energy regimes in which the scaling of the pre-stress is non-trivial, we arrive at linearised Kirchhoff, von Kármán, and fully linear plate theories, respectively, which contain an additional spontaneous curvature tensor. The effective (homogenised) elastic constants of the plates will turn out to be given in terms of the moments of the pointwise elastic constants of the materials.
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ÇALIK KARAKÖSE, Ülkü Hülya. "Convergence studies for static analysis of thin plates on Pasternak Foundations." DÜMF Mühendislik Dergisi, March 9, 2023. http://dx.doi.org/10.24012/dumf.1228192.
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Convergence studies for the static analysis of thin plates resting on Pasternak foundations is performed. The plates are discretized using two different finite elements, the formulations of which are based on the Kirchhoff and Reissner-Mindlin plate theories. The shear locking problem which arises when full integration is used in the finite element implementation of Reissner-Mindlin plate theory is eliminated with selective integration. The Pasternak foundation is accounted for by adding the parameter matrices of an existing soil finite element to the stiffness matrix terms of the plate finite elements corresponding to deflections. Convergence rates for different boundary conditions, plate thicknesses and soil parameters are obtained and given comparatively through numerical examples.
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Urgessa, Girum, Wondwosen Ali, and Javad Esfandiari. "MACROMECHANICAL ANALYSIS OF SPHERICALLY VOIDED BIAXIAL CONCRETE SLABS." Proceedings of International Structural Engineering and Construction 6, no. 1 (May 2019). http://dx.doi.org/10.14455/isec.res.2019.106.
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The use of spherically voided biaxial concrete slab (SVBS) system, which uses hollow plastic balls as infill material, has increased widely because of its reduced weight-to-strength and weight-to-stiffness ratios when compared to solid concrete slabs. However, SVBS is a heterogeneous composite structure in which building a representative continuum model poses a significant challenge. To mitigate this challenge, the feasibility of determining the macromechanical structural behavior of spherically voided biaxial concrete slabs is studied using plate theories, aided by mechanical properties that were determined from a homogenization process of the representative volume element (RVE). This paper presents numerical analysis results of SVBS using both Mindlin-Reissner (thick) and Kirchhoff-Love (thin) plate theories. The results from both theories predicted the slab behavior reasonably well and they were within 10% of each other with the exception of the prediction of the twisting moment. Possible explanation of this deviation is provided in the paper.
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Ji, Ming, and Kazuaki Inaba. "Theoretical Analysis of Free Vibration and Transient Response of Rectangular Plate-Cavity System Under Impact Loading." Journal of Pressure Vessel Technology, March 11, 2023, 1–32. http://dx.doi.org/10.1115/1.4062121.
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Abstract This paper presents a theoretical method to solve the free vibration and transient responses of a rectangular plate-cavity system. The spectral collocation method was used to solve the resonant frequencies and corresponding mode shapes of rectangular plates based on Kirchhoff thin-plate and Mindlin-Reissner thick plate theories. A linear velocity potential function was employed to model the fluid pressure applied to the plate surface. Unlike in previous studies, it was not assumed that the wet-mode shapes were the same as the dry-mode ones. Rather, the wet modes were assumed to be the superposition of the dry modes; then, the resonant frequencies and corresponding mode shapes of the wet modes could be obtained by solving the equations of the coupled system by exploiting the orthogonality of dry modes. Using dry modes' orthogonality and superposition of the wet modes, the transient responses of the rectangular plate-cavity system under impact loading can be solved. A method for estimating the resonant frequencies of the coupled system is proposed based on parametric studies to determine the influence of the fluid properties and plate materials on resonant frequencies. As a result, the resonant frequencies and transient responses obtained from the proposed theoretical methods are in excellent agreement with those obtained finite element analysis.
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NOORI, Ahmad Reshad. "Bending Analysis of Functionally Graded Sandwich Circular Plates via the Complementary Functions Method." Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, September 30, 2022, 673–84. http://dx.doi.org/10.21605/cukurovaumfd.1190287.
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In this study, the flexural response of sandwich circular plates with Functionally Graded (FG) material is investigated theoretically. The core of the sandwich circular plates, whose material properties change throughout their thickness, is considered to be isotropic homogeneous and the face sheets are assumed to be FG. The governing equations of the static behavior of the considered plates are obtained in canonical form with the aid of the minimum total energy principle based on the Kirchhoff–Love and Mindlin–Reissner plate theories. For the numerical solutions of these equations, the Complementary Functions Method (CFM) is implemented. In this research, the effects of material gradient index, radius-thickness ratios, shear deformation effects and different boundary conditions on the bending behavior of FG sandwich circular plates are parametrically investigated. The efficient applicability of the CFM to this type of problem and the accuracy of the suggested method are demonstrated by comparing the results obtained with the existing literature.
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Guo, Yujie, and Hornsen Tzou. "Ultraviolet-Activated Frequency Control of Beams and Plates Based on Isogeometric Analysis." Journal of Vibration and Acoustics 140, no. 3 (February 9, 2018). http://dx.doi.org/10.1115/1.4038948.
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A new light-activated shape memory polymer (LaSMP) smart material exhibits shape memory behaviors and stiffness variation via ultraviolet (UV) light exposures. This dynamic stiffness provides a new noncontact actuation mechanism for engineering structures. Isogeometric analysis (IGA) utilizes high order and high continuity nonuniform rational B-spline (NURBS) as basis functions which naturally fulfills C1-continuity requirement of Euler–Bernoulli beam and Kirchhoff plate theories. Compared with the traditional finite elements of beams and plates, IGA does not need extra rotational degrees-of-freedom while providing accurate results. The UV light-activated frequency control of LaSMP fully and partially laminated beam and plate structures based on the IGA is presented in this study. For the analysis of LaSMP partially laminated plates, the finite cell approach in the framework of IGA is proposed to handle NURBS geometries containing trimming features. The accuracy and efficiency of the proposed isogeometric approach are demonstrated via several numerical examples in frequency control. The results show that, with LaSMPs, broadband frequency control of beam and plate structures can be realized. Furthermore, changing LaSMP patch sizes on beams and plates further broadens its frequency control ranges. Studies suggest that: (1) the newly developed IGA combining finite cell approach is an effective numerical tool and (2) the maximum frequency manipulation ratios of beam and plate structures, respectively, reach 24.30% and 16.75%, which demonstrates the feasibility of LaSMPs-induced vibration control of structures.