Academic literature on the topic 'Kirchhoff plate theories'
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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.
Full textAbstract:
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.
Full textAbstract:
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.
Full textAbstract:
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.
Full textAbstract:
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.
Full textAbstract:
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.
Full textAbstract:
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.
Dissertations / Theses on the topic "Kirchhoff plate theories"
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Chattopadhyay, Arka Prabha. "Free and Forced Vibration of Linearly Elastic and St. Venant-Kirchhoff Plates using the Third Order Shear and Normal Deformable Theory." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102661.
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Employing the Finite Element Method (FEM), we numerically study three problems involving free and forced vibrations of linearly and nonlinearly elastic plates with a third order shear and normal deformable theory (TSNDT) and the three dimensional (3D) elasticity theory. We used the commercial software ABAQUS for analyzing 3D deformations, and an in-house developed and verified software for solving the plate theory equations.
In the first problem, we consider trapezoidal load-time pulses with linearly increasing and affinely decreasing loads of total durations equal to integer multiples of the time period of the first bending mode of vibration of a plate. For arbitrary spatial distributions of loads applied to monolithic and laminated orthotropic plates, we show that plates' vibrations become miniscule after the load is removed. We call this phenomenon as vibration attenuation. It is independent of the dwell time during which the load is a constant. We hypothesize that plates exhibit this phenomenon because nearly all of plate's strain energy is due to deformations corresponding to the fundamental bending mode of vibration. Thus taking the 1st bending mode shape of the plate vibration as the basis function, we reduce the problem to that of solving a single second-order ordinary differential equation. We show that this reduced-order model gives excellent results for monolithic and composite plates subjected to different loads.
Rectangular plates studied in the 2nd problem have points on either one or two normals to their midsurface constrained from translating in all three directions. We find that deformations corresponding to several modes of vibration are annulled in a region of the plate divided by a plane through the constraining points; this phenomenon is termed mode localization. New results include: (i) the localization of both in-plane and out-of-plane modes of vibration, (ii) increase in the mode localization intensity with an increase in the length/width ratio of a rectangular plate, (iii) change in the mode localization characteristics with the fiber orientation angle in unidirectional fiber- reinforced laminae, (iv) mode localization due to points on two normals constrained, and (iv) the exchange of energy during forced harmonic vibrations between two regions separated by the line of nearly stationary points that results in a beating-like phenomenon in a sub-region of the plate. This technique can help design a structure with vibrations limited to its small sub-region, and harvesting energy of vibrations of the sub-region.
In the third problem, we study finite transient deformations of rectangular plates using the TSNDT. The mathematical model includes all geometric and material nonlinearities. We compare the results of linear and nonlinear TSNDT FEM with the corresponding 3D FEM results from ABAQUS and note that the TSNDT is capable of predicting reasonably accurate results of displacements and in-plane stresses. However, the errors in computing transverse stresses are larger and the use of a two point stress recovery scheme improves their accuracy. We delineate the effects of nonlinearities by comparing results from the linear and the nonlinear theories. We observe that the linear theory over-predicts the deformations of a plate as compared to those obtained with the inclusion of geometric and material nonlinearities. We hypothesize that this is an effect of stiffening of the material due to the nonlinearity, analogous to the strain hardening phenomenon in plasticity. Based on this observation, we propose that the consideration of nonlinearities is essential in modeling plates undergoing large deformations as linear model over-predicts the deformation resulting in conservative design criteria. We also notice that unlike linear elastic plate bending, the neutral surface of a nonlinearly elastic bending plate, defined as the plane unstretched after the deformation, does not coincide with the mid-surface of the plate. Due to this effect, use of nonlinear models may be of useful in design of sandwich structures where a soft core near the mid-surface will be subjected to large in-plane stresses.Doctor of Philosophy
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Ishaquddin, Mohammed. "Numerical solution of non-classical beam and plate theories using di erential quadrature method." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/4586.
Full textAbstract:
For effcient design of the nano/micro scale structural systems, detailed analysis and through
understanding of size-dependent mechanical behaviour at nano/micro scale is very critical. Various
approaches have been used to investigate the mechanical behaviour of small scale structures,
for instance, experimental approach, atomistic and molecular dynamics simulations, multi-scale
modelling, etc. However, the application of these methods for practical problems have their
own limitations, some are very cumbersome and expensive, others need high computational resources
and remaining are mathematically involved. The non-classical continuum theories with
micro-structural behaviour have proven to be very efficient alternative, which assures reasonable
accuracy with less complexity and computational efforts as compared to other approaches.
The non-classical theories are governed by higher order differential equations and introduce
additional degrees of freedom (related to curvature and triple derivative of displacements) and
material parameters to account for scale effects. A considerable amount of analytical work on
beams and plates is conducted based on these theories, however, numerical treatment is limited
to only few speci fic applications.
The primary objective of this research is to develop a comprehensive set of novel and effcient
differential quadrature-based elements for non-classical Euler-Bernoulli beam and Kirchhoff
plate theories. Both strong and weak form differential quadrature elements are developed,
which are fundamentally different in their formulation. The strong form elements are formulated
using the governing equation and stress resultant equations, and the weak form elements are
based on the variational principles. Lagrange interpolations are used to formulate the strong
form beam elements, while the weak form beam elements are constructed for both Lagrange
and Hermite interpolations. The plate elements (strong and weak) are developed using two
different combinations of interpolation functions in the orthogonal directions, in the first choice,
Lagrange interpolations are assumed in both orthogonal directions and in the second case
Lagrange interpolation are assumed in one direction and Hermite in the another. The capability
of these elements is demonstrated through non-classical Mindlin's simpli ed fi rst and second
strain Euler-Bernoulli beam / Kirchhoff plate theories, which are governed by sixth
and eighth order differential equations, respectively. The accuracy and applicability of the
beam elements is veri fied for bending, free-vibration, stability, dynamic/transient and wave
propagation analysis, and the plate elements for bending, free-vibration and stability analysis.
The strong form differential quadrature element developed for first strain gradient Euler-
Bernoulli theory demonstrated excellent agreement with the exact solutions with less number of
nodes for static, free vibration and buckling analysis of prismatic and non-prismatic beams for
different combinations of boundary conditions, loading and length scale parameters. Similar
performance was demonstrated by the weak form quadrature element which was formulated
using Hermite interpolation functions. The Lagrange interpolation based weak form quadrature
element exhibited inferior performance as compared to the above two elements, and needed more
number of nodes to obtain the accurate results. Good performance was shown by both strong
and weak form differential quadrature elements for dynamic and wave propagation analysis.
With fewer number of elements and nodes the velocity response and the group speeds were
predicted accurately using these elements. Based on the finding it was concluded that the
beam elements produced accurate results with reasonable number of nodes and can be effciently
applied for different analysis of non-classical Euler-Bernoulli prismatic and non-prismatic beams
for any choice of loading, boundary conditions and length scale parameters. The performance of
strong and weak form beam elements developed for second strain gradient Euler-Bernoulli beam
theory was also validated for static, free vibration, stability, dynamic and wave propagation
analysis. Similar performance was demonstrated by the weak and strong form beam elements
developed for second strain gradient Euler-Bernoulli beam theory.
The strong form elements developed for fi rst strain gradient Kirchhoff plate theory demonstrated
excellent performance for static bending, free vibration and stability analysis. Deflections,
frequencies and buckling loads obtained using the single element with fewer number of
nodes compare well with the exact solutions for different loading, boundary conditions and
length scale values. The results obtained using the weak form quadrature elements also compared
well with available literature results, however, for the plates which include one or more
clamped edges need more number of nodes to obtain converged solutions as compared to the
strong form elements. This aspect of weak form quadrature elements needs further investigation. Similar set of strong and weak form DQ elements developed for second strain gradient
Kirchhoff plate theory also exhibited similar performance for static bending, free vibration and
stability analysis.
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Kulkarni, Shripad Dattatraya. "Discrete kirchhoff finite elements for piezoelectric hybrid plates based on smearld and zigzag third order theories." Thesis, 2007. http://localhost:8080/xmlui/handle/12345678/3000.
Full textBook chapters on the topic "Kirchhoff plate theories"
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Brank, Boštjan, Adnan Ibrahimbegović, and Uroš Bohinc. "On Discrete-Kirchhoff Plate Finite Elements: Implementation and Discretization Error." In Shell and Membrane Theories in Mechanics and Biology, 109–31. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02535-3_6.
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Mikhailovskii, E. I., and A. V. Yermolenko. "On Nonlinear Theory of Rigid-Flexible Shells Without the Kirchhoff Hypotheses." In Theories of Plates and Shells, 157–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-39905-6_19.
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"Intermediate Theory Between Kirchhoff–Love and Uflyand–Mindlin Plate Theories: Truncated Uflyand–Mindlin Equations." In Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories, 239–321. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813236523_0005.
Full textConference papers on the topic "Kirchhoff plate theories"
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Han, Shilei, and Olivier A. Bauchau. "Three-Dimensional Plate Theory for Flexible Multibody Dynamics." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47249.
Full textAbstract:
In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.
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Wang, Cynthia D., and C. M. Wang. "A Comparative Study on the Linear Wave Response of a Very Large Floating Body Modelled by a Plate based on Kirchhoff and Mindlin Plate Theories." In SNAME 7th International Conference and Exhibition on Performance of Ships and Structures in Ice. SNAME, 2006. http://dx.doi.org/10.5957/icetech-2006-157.
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It has been a general practice to model a very large, mat-like, floating body (such as ice floes and mega-floats) by an elastic thin plate with free edges. However, the classical thin plate (Kirchhoff) theory has a limitation when the wavelengths are less than ten times the body thickness. This is because it neglects the effects of transverse shear deformation and the rotary inertia of the plate. To overcome this drawback, we propose the use of the first-order shear deformable plate (Mindlin) theory to represent floating bodies. In this paper we present the comparison of both plate theories when used to calculate the effect of waves on a large floating body.
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Bauchau, Olivier A., and Shilei Han. "Advanced Plate Theory for Multibody Dynamics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12415.
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In flexible multibody systems, many components are often approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theory, form the basis of the analytical development for plate dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, several high-order and refined plate theory were proposed. While these approaches work well for some cases, they typically lead to inefficient formulation because they introduce numerous additional variables. This paper presents a different approach to the problem, which is based on a finite element discretization of the normal material line, and relies of the Hamiltonian formalism of obtain solutions of the governing equations. Polynomial solutions, also known as central solutions, are obtained that propagate over the entire span of the plate.
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Guo, Yujie, and Hornsen Tzou. "UV-Activated Frequency Control of Beams and Plates Based on Isogeometric Analysis." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67667.
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A new LaSMP smart material exhibits shape memory behaviors and stiffness variation via UV light exposures. This dynamic stiffness provides a new noncontact actuation mechanism for engineering structures. Isogeometric analysis utilizes high order and high continuity NURBS as basis functions which naturally fulfills C1-continuity requirement of Euler-Bernoulli beam and Kirchhoff plate theories. The UV light-activated frequency control of LaSMP laminated beam and plate structures based on the isogeometric analysis is presented in this study. 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, the length of LaSMP patches on beams is varied, which further broadens its frequency variation ranges. Studies suggest that 1) the newly developed IGA is an effective numerical tool and 2) the maximum frequency change ratio of beam and plate structures respectively reach 24.30% and 6.37%, which demonstrates the feasibility of LaSMPs induced vibration control of structures.
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Tzou, H. S., and J. P. Zhong. "Theory on Hexagonal Symmetrical Piezoelectric Thick Shells Applied to Smart Structures." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0179.
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Abstract 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 dynamic equations, three translational coordinates and two rotatory coordinates, and boundary conditions, electric and mechanical, for a thick piezoelectric shell continuum with symmetrical hexagonal structure (Class C6v = 6mm) are derived using Hamilton’s principle and linear piezoelectric theory. The thick shell system equations are simplified to thin piezoelectric shells using Kirchhoff-Love’s assumptions. Converse effect induced electric forces/moments and boundary conditions can be used to alter system dynamics via open or closed loop control systems. Applications of the theories to a thick plate and a spherical shell are demonstrated in case studies.
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Pydah, Anup. "An Accurate Discrete Model for the Dynamics of Web-Core Sandwich Plates." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50938.
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An accurate discrete model is presented here for the dynamics of simply supported web-core sandwich plates using the elasticity approach. By modelling the face-plates as 3D solids and the core webs using a plane stress idealization for transverse bending and classical one-dimensional models for lateral bending and torsion, the non-classical effects of transverse shear deformation, thickness-stretch and rotary inertia are completely accounted for in both, the face-plates and webs. Vibrational frequency results obtained using this model are used to highlight the errors of the commonly used model based on the classical Kirchhoff hypothesis for the face-plates, indicating the importance of using refined theories for modelling the face-plates.
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Kulpe, Jason A., Michael J. Leamy, and Karim G. Sabra. "Determination of Acoustic Scattering From a Two-Dimensional Finite Phononic Crystal Using Bloch Wave Expansion." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34404.
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In this study the acoustic scattering is determined from a finite phononic crystal through an implementation of the Helmholtz-Kirchhoff integral theorem. The approach employs the Bloch theorem applied to a semi-infinite phononic crystal (PC) half-space. The internal pressure field of the half-space, subject to an incident acoustic monochromatic plane wave, is formulated as an expansion of the Bloch wave modes. Modal coefficients of reflected (diffracted) plane waves are arrived at via boundary condition considerations on the PC interface. Next, the PC inter-facial pressure, as determined by the Bloch wave expansion (BWE), is employed along with the Helmholtz-Kirchhoff integral equation to compute the scattered pressure from a large finite PC. Under a short wavelength limit approximation (wavelength much smaller than finite PC dimensions), the integral approach is employed to calculate the scattered pressure field for a large PC subject to an incident wave with two distinct incident angles. In two dimensions we demonstrate good agreement of scattered pressure results of large finite PC when compared against detailed finite element calculations. The work here demonstrates an efficient and accurate uniform computational framework for modeling the scattered and internal pressure fields of a large finite phononic crystal.
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Kang, Namcheol, and Arvind Raman. "Aeroelastic Flutter of a Flexible Disk Rotating in an Enclosed Compressible Fluid." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48421.
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The aeroelastic stability of a thin, flexible disk rotating in an enclosed compressible fluid is investigated analytically through a discretization of the field equations of a rotating Kirchhoff plate coupled to the acoustic oscillations of the surrounding fluid. The discretization procedure exploits Green’s theorem and exposes two different gyroscopic effects underpinning the coupled system dynamics: one describes the gyroscopic coupling between the disk and acoustic oscillations, and another arises from the disk rotation. The discretized dynamical system is cast in the compact form of a classical gyroscopic system and acoustic and disk mode coupling rules are derived. Effects of eigenvalue veering of structure and acoustic dominated modes are investigated in detail. For the undamped system, coupled structure-acoustic traveling waves can destabilize through mode coalescence leading to flutter instability. Regions in parameter space are identified where structure-acoustic traveling waves of specific wave numbers destabilize. The results are expected to be relevant for the design of high speed, low vibration, low noise hard disk drives and optical data storage systems.