Статті в журналах: "Mindlin"

1

Boley, Bruno A. "Raymond D. Mindlin." Journal of Applied Mechanics 55, no. 2 (June 1, 1988): 259. http://dx.doi.org/10.1115/1.3173669.

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2

Lazar, Markus. "Incompatible strain gradient elasticity of Mindlin type: screw and edge dislocations." Acta Mechanica 232, no. 9 (June 28, 2021): 3471–94. http://dx.doi.org/10.1007/s00707-021-02999-2.

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AbstractThe fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory of Mindlin type, unsolved for more than half a century, is solved in this work. Incompatible strain gradient elasticity of Mindlin type is the generalization of Mindlin’s compatible strain gradient elasticity including plastic fields providing in this way a proper eigenstrain framework for the study of defects like dislocations. Exact analytical solutions for the displacement fields, elastic distortions, Cauchy stresses, plastic distortions and dislocation densities of screw and edge dislocations are derived. For the numerical analysis of the dislocation fields, elastic constants and gradient elastic constants have been used taken from ab initio DFT calculations. The displacement, elastic distortion, plastic distortion and Cauchy stress fields of screw and edge dislocations are non-singular, finite, and smooth. The dislocation fields of a screw dislocation depend on one characteristic length, whereas the dislocation fields of an edge dislocation depend on up to three characteristic lengths. For a screw dislocation, the dislocation fields obtained in incompatible strain gradient elasticity of Mindlin type agree with the corresponding ones in simplified incompatible strain gradient elasticity. In the case of an edge dislocation, the dislocation fields obtained in incompatible strain gradient elasticity of Mindlin type are depicted more realistic than the corresponding ones in simplified incompatible strain gradient elasticity. Among others, the Cauchy stress of an edge dislocation obtained in incompatible isotropic strain gradient elasticity of Mindlin type looks more physical in the dislocation core region than the Cauchy stress obtained in simplified incompatible strain gradient elasticity and is in good agreement with the stress fields of an edge dislocation computed in atomistic simulations. Moreover, it is shown that the shape of the dislocation core of an edge dislocation has a more realistic asymmetric form due to its inherent asymmetry in incompatible isotropic strain gradient elasticity of Mindlin type than the dislocation core possessing a cylindrical symmetry in simplified incompatible strain gradient elasticity. It is revealed that the considered theory with the incorporation of three characteristic lengths offers a more realistic description of an edge dislocation than the simplified incompatible strain gradient elasticity with only one characteristic length.

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3

Xiang, Y., and G. W. Wei. "Exact Solutions for Vibration of Multi-Span Rectangular Mindlin Plates." Journal of Vibration and Acoustics 124, no. 4 (September 20, 2002): 545–51. http://dx.doi.org/10.1115/1.1501083.

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This paper presents the first-known exact solutions for the vibration of multi-span rectangular Mindlin plates with two opposite edges simply supported. The Levy type solution method and the state-space technique are employed to develop an analytical approach to deal with the vibration of rectangular Mindlin plates of multiple spans. Exact vibration frequencies are obtained for two-span square Mindlin plates with varying span ratios and two-, three- and four-equal-span rectangular Mindlin plates. The influence of the span ratios, the number of spans and plate boundary conditions on the vibration behavior of square and rectangular Mindlin plates is examined. The presented exact vibration results may serve as benchmark solutions for such plates.

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4

Ansari, R., M. Faghih Shojaei, V. Mohammadi, M. Bazdid-Vahdati, and H. Rouhi. "Triangular Mindlin microplate element." Computer Methods in Applied Mechanics and Engineering 295 (October 2015): 56–76. http://dx.doi.org/10.1016/j.cma.2015.06.004.

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5

Busse, Anke, Martin Schanz, and Heinz Antes. "A Poroelastic Mindlin-Plate." PAMM 3, no. 1 (December 2003): 260–61. http://dx.doi.org/10.1002/pamm.200310402.

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6

Yu, S. D., and W. L. Cleghorn. "ACCURATE FREE VIBRATION ANALYSIS OF CLAMPED MINDLIN PLATES USING THE METHOD OF SUPERPOSITION." Transactions of the Canadian Society for Mechanical Engineering 17, no. 2 (June 1993): 243–55. http://dx.doi.org/10.1139/tcsme-1993-0015.

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The method of superposition is further developed to analyze free flexural vibration of clamped rectangular Mindlin plates. Comparison of results given by Mindlin’s theory of plates with those previously obtained by Reissner’s theory has shown that the rotatory inertia does not significantly affect plate flexural vibration. Accurate eigenvalues are presented for a number of values of plate aspect ratio along with two representative values of thickness ratio.

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7

Xue, Xiaofeng, Xuefeng Chen, Xingwu Zhang, Baijie Qiao, and Jia Geng. "Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification." Shock and Vibration 2016 (2016): 1–24. http://dx.doi.org/10.1155/2016/8618202.

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A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD) method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.

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8

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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9

Castro, Aloisio Arnaldo de. "arquivo pessoal de Guita Mindlin." PÓS: Revista do Programa de Pós-graduação em Artes da EBA/UFMG 11, no. 22 (July 19, 2021): 116–42. http://dx.doi.org/10.35699/2237-5864.2021.25864.

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Este artigo propõe o exame e a discussão das potencialidades de pesquisa do fundo documental Guita Mindlin como repositório de fontes primárias privilegiadas. Estas permitem elucidar aspectos relativos à sociogênese da Conservação-Restauração de livros e documentos no âmbito brasileiro. À luz dos aportes da História Cultural, este trabalho prioriza a análise do itinerário biográfico de Guita Mindlin no espaço social preservacionista brasileiro. Assim, suas práticas, narrativas e rede de sociabilidades são observadas como categorias analíticas elucidativas na construção historiográfica do campo da Conservação-Restauração de Documentos Gráficos no Brasil.

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10

Pozharskii, D. A. "On the generalized Mindlin problem." Doklady Physics 47, no. 7 (July 2002): 535–37. http://dx.doi.org/10.1134/1.1499195.

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11

Krause, Gerhard. "Maguerre‐Mindlin shallow shell elements." Engineering Computations 6, no. 1 (January 1989): 44–48. http://dx.doi.org/10.1108/eb023758.

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12

Galvão, Walnice Nogueira. "Antonio Candido e José Mindlin." Literatura e Sociedade, no. 12 (December 6, 2009): 38. http://dx.doi.org/10.11606/issn.2237-1184.v0i12p38-58.

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13

Oak-Key, Min, and Kim Yong-Woo. "Reduced minimization of Mindlin plate." International Journal for Numerical Methods in Engineering 37, no. 24 (December 30, 1994): 4263–84. http://dx.doi.org/10.1002/nme.1620372409.

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14

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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15

Wang, C. M. "Natural Frequencies Formula for Simply Supported Mindlin Plates." Journal of Vibration and Acoustics 116, no. 4 (October 1, 1994): 536–40. http://dx.doi.org/10.1115/1.2930460.

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This paper presents an explicit formula for the vibration frequencies of simply supported Mindlin plates in terms of the corresponding thin (Kirchhoff) plate frequencies. The formula has been obtained from an exact vibration analysis of simply supported rectangular Mindlin plates. When the formula was applied to other simply supported plate shapes such as skew plates, circular and annular sectorial plates, it was found to give almost exact solutions. It appears that the formula can be used to predict the frequencies accurately for any simply supported plate shape and thus should be valuable to designers as Mindlin vibration solutions are scarce.

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16

Hossain, Zakir, Tapan Mukerji, Jack Dvorkin, and Ida L. Fabricius. "Rock physics model of glauconitic greensand from the North Sea." GEOPHYSICS 76, no. 6 (November 2011): E199—E209. http://dx.doi.org/10.1190/geo2010-0366.1.

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The objective of this study was to establish a rock physics model of North Sea Paleogene greensand. The Hertz-Mindlin contact model is widely used to calculate elastic velocities of sandstone as well as to calculate the initial sand-pack modulus of the soft-sand, stiff-sand, and intermediate-stiff-sand models. When mixed minerals in rock are quite different, e.g., mixtures of quartz and glauconite in greensand, the Hertz-Mindlin contact model of single type of grain may not be enough to predict elastic velocity. Our approach is first to develop a Hertz-Mindlin contact model for a mixture of quartz and glauconite. Next, we use this Hertz-Mindlin contact model of two types of grains as the initial modulus for a soft-sand model and a stiff-sand model. By using these rock physics models, we examine the relationship between elastic modulus and porosity in laboratory and logging data and link rock-physics properties to greensand diagenesis. Calculated velocity for mixtures of quartz and glauconite from the Hertz-Mindlin contact model for two types of grains are higher than velocity calculated from the Hertz-Mindlin single mineral model using the effective mineral moduli predicted from the Hill’s average. Results of rock-physics modeling and thin-section observations indicate that variations in the elastic properties of greensand can be explained by two main diagenetic phases: silica cementation and berthierine cementation. These diagenetic phases dominate the elastic properties of greensand reservoir. Initially, greensand is a mixture of mainly quartz and glauconite; when weakly cemented, it has relatively low elastic modulus and can be modeled by a Hertz-Mindlin contact model of two types of grains. Silica-cemented greensand has a relatively high elastic modulus and can be modeled by an intermediate-stiff-sand or a stiff-sand model. Berthierine cement has different growth patterns in different parts of the greensand, resulting in a soft-sand model and an intermediate-stiff-sand model.

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17

Wu, Shen Rong. "Reissner-Mindlin plate theory for elastodynamics." Journal of Applied Mathematics 2004, no. 3 (2004): 179–89. http://dx.doi.org/10.1155/s1110757x04401090.

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Existence and uniqueness of solution are proved for elastodynamics of Reissner-Mindlin plate model. Higher regularity is proved under the assumptions of smoother data and certain compatibility conditions. A mass scaling is introduced. When the thickness approaches zero, the solution of the clamped Reissner-Mindlin plate is shown to approach the solution of a Kirchhoff-Love plate.

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18

Freund, Jouni Tapani. "Two-scale Reissner-Mindlin plate model." Rakenteiden Mekaniikka 50, no. 3 (August 21, 2017): 158–61. http://dx.doi.org/10.23998/rm.64920.

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A two-scale plate model, in which the displacement assumption consists of the Reissner-Mindlin and warping parts, is presented. To reduce the modelling error of the classical Reissner-Mindlin model, the warping part is chosen so that the overall displacement satisfies the full 3D elasticity equations as well as possible. Pressure loaded isotropic homogeneous plate is used as an application example.

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19

Loeb, Rodrigo Mindlin, and Eduardo de Almeida. "Biblioteca Brasiliana Guita e José Mindlin." Dearq, no. 13 (December 2013): 180–90. http://dx.doi.org/10.18389/dearq13.2013.16.

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20

Grenestedt, Joachim L. "Lamination parameters for Reissner-Mindlin plates." AIAA Journal 32, no. 11 (November 1994): 2328–31. http://dx.doi.org/10.2514/3.12296.

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21

McGee, O. G., J. W. Kim, and A. W. Leissa. "Sharp Corner Functions for Mindlin Plates." Journal of Applied Mechanics 72, no. 1 (January 1, 2005): 1–9. http://dx.doi.org/10.1115/1.1795221.

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Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

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22

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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23

Brezzi, F., and M. Fortin. "Numerical approximation of Mindlin-Reissner plates." Mathematics of Computation 47, no. 175 (September 1, 1986): 151. http://dx.doi.org/10.1090/s0025-5718-1986-0842127-7.

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24

Peyret, Nicolas, Marco Rosatello, Gaël Chevallier, and Jean-Luc Dion. "A Mindlin derived Dahl friction model." Mechanism and Machine Theory 117 (November 2017): 48–55. http://dx.doi.org/10.1016/j.mechmachtheory.2017.06.019.

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25

Martins, Ana Luiza. "Biblioteca Mindlin: a alegria da pesquisa." Revista BBM, no. 1 (September 11, 2018): 159–67. http://dx.doi.org/10.11606/issn.2595-5802.v1i1p159-167.

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A autora rememora as lembranças de sua experiência no convívio com Guita e José Mindlin na biblioteca pessoal do casal, hoje, Biblioteca Brasiliana Guita e José Minlin – BBM-USP. Relembra detalhes dos aspectos físicos do espaço e menciona algumas obras e textos que eram encontrados lá e a relação de Mindlin com eles. Recorda que a biblioteca era visitada por pesquisadores acadêmicos, mas também por jornalistas, escritores, bibliófilos e estudiosos do livro e que, dessas visitas, no início, eram realizadas pesquisas informais, que, posteriormente, foram sistematizadas e organizadas com regularidade, das quais resultaram obras fundamentais para a cultura nacional.

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26

SCHIAVONE, PETER, and R. J. TAIT. "THERMAL EFFECTS IN MINDLIN-TYPE PLATES." Quarterly Journal of Mechanics and Applied Mathematics 46, no. 1 (1993): 27–39. http://dx.doi.org/10.1093/qjmam/46.1.27.

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27

Kobayashi, Harutoshi, and Keiichiro Sonoda. "Rectangular mindlin plates on elastic foundations." International Journal of Mechanical Sciences 31, no. 9 (January 1989): 679–92. http://dx.doi.org/10.1016/s0020-7403(89)80003-7.

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28

Lipton, Robert, and Alejandro Daz. "Reinforced mindlin plates with extremal stiffness." International Journal of Solids and Structures 34, no. 28 (October 1997): 3691–704. http://dx.doi.org/10.1016/s0020-7683(96)00219-3.

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29

Canisius, T. D. G., and R. O. Foschi. "Mindlin finite strips with support displacements." Computers & Structures 49, no. 2 (October 1993): 329–39. http://dx.doi.org/10.1016/0045-7949(93)90112-q.

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30

Freund, J. "Shear-corrected Reissner-Mindlin plate model." Composite Structures 211 (March 2019): 144–53. http://dx.doi.org/10.1016/j.compstruct.2018.12.029.

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31

Huo-Yuan, Duan, and Liang Guo-Ping. "An improved Reissner–Mindlin triangular element." Computer Methods in Applied Mechanics and Engineering 191, no. 21-22 (March 2002): 2223–34. http://dx.doi.org/10.1016/s0045-7825(01)00376-0.

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32

Xiang, Y., S. Kitipornchai, K. M. Liew, and M. K. Lim. "Vibration of stiffened skew Mindlin plates." Acta Mechanica 112, no. 1-4 (March 1995): 11–28. http://dx.doi.org/10.1007/bf01177475.

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33

Irschik, H. "Membrane-type eigenmotions of Mindlin plates." Acta Mechanica 55, no. 1-2 (April 1985): 1–20. http://dx.doi.org/10.1007/bf01267975.

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34

El-Sabbagh, Adel, Wael Akl, and Amr Baz. "Topology optimization of periodic Mindlin plates." Finite Elements in Analysis and Design 44, no. 8 (May 2008): 439–49. http://dx.doi.org/10.1016/j.finel.2008.01.016.

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35

Licht, Christian, and Thibaut Weller. "An asymptotic Reissner–Mindlin plate model." Comptes Rendus Mécanique 346, no. 6 (June 2018): 432–38. http://dx.doi.org/10.1016/j.crme.2018.04.014.

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36

Shaochun, Chen, and Shi Dongyang. "Triangular elements for Reissner-Mindlin plate." Applied Mathematics and Mechanics 18, no. 3 (March 1997): 267–72. http://dx.doi.org/10.1007/bf02453370.

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37

Choi, Chang-Koon, and Yong-Myung Park. "Quadratic NMS Mindlin-plate-bending element." International Journal for Numerical Methods in Engineering 46, no. 8 (November 20, 1999): 1273–89. http://dx.doi.org/10.1002/(sici)1097-0207(19991120)46:8<1273::aid-nme754>3.0.co;2-n.

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38

Aalto, J. "From Kirchhoff to Mindlin plate elements." Communications in Applied Numerical Methods 4, no. 2 (March 1988): 231–41. http://dx.doi.org/10.1002/cnm.1630040215.

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39

Kulikov, G. M., and S. V. Plotnikova. "Efficient mixed Timoshenko-Mindlin shell elements." International Journal for Numerical Methods in Engineering 55, no. 10 (2002): 1167–83. http://dx.doi.org/10.1002/nme.540.

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40

Zhang, Qi, Shaofan Li, A‐Man Zhang, Yuxiang Peng, and Jiale Yan. "A peridynamic Reissner‐Mindlin shell theory." International Journal for Numerical Methods in Engineering 122, no. 1 (September 16, 2020): 122–47. http://dx.doi.org/10.1002/nme.6527.

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41

Constanda, Ch, and P. Schiavone. "Flexural Waves in Mindlin-Type Plates." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 74, no. 10 (1994): 492–93. http://dx.doi.org/10.1002/zamm.19940741015.

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42

Wang, C. M., and C. H. Ang. "Moment Value at the Center of Circular Plates Under Central Point Load." Journal of Applied Mechanics 66, no. 3 (September 1, 1999): 815–18. http://dx.doi.org/10.1115/1.2791763.

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It is a well-known fact that the bending moment at the center of a circular plate under a central point load becomes infinite. So, “what is a sensible finite moment value, that one may adopt, at the center of a circular plate under a central point load?” This study addresses this interesting and fundamental question. In order to obtain a finite value to the bending moment, we draw upon the exact deflection expressions from the classical and higher-order plate theories of Mindlin and of Reddy, and make some reasonable assumptions such as the maximum deflection of Mindlin plate being equal to the maximum deflection of the corresponding Reddy plate and the constancy of the Mindlin shear correction factor.

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43

Trung, Nguyen Thoi, Phung Van Phuc, Tran Viet Anh, and Nguyen Tran Chan. "Dynamic analysis of Mindlin plates on viscoelastic foundations under a moving vehicle by CS-MIN3 based on C0-type higher-order shear deformation theory." Vietnam Journal of Mechanics 36, no. 1 (February 28, 2014): 61–75. http://dx.doi.org/10.15625/0866-7136/36/1/2974.

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A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed to improve the performance of the existing three-node Mindlin plate element (MIN3) for static and dynamic analyses of Mindlin plates. In this paper, the CS-MIN3 is extended to the C0-type higher-order shear deformation plate theory (C0-HSDT) and incorporated with damping-spring systems for dynamic analyses of Mindlin plates on the viscoelastic foundation subjected to a moving vehicle. The plate-foundation system is modeled as a discretization of triangular plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. A two-step process for transforming the weight of a four-wheel vehicle into loads at nodes of elements is presented. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of others available numerical results. A parametric examination is also conducted to determine the effects of various parameters on the dynamic response of the plates on the viscoelastic foundation subjected to the moving vehicle.

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44

Dimaki, Andrey V., Roman Pohrt, and Valentin L. Popov. "SIMULATION OF FRICTIONAL DISSIPATION UNDER BIAXIAL TANGENTIAL LOADING WITH THE METHOD OF DIMENSIONALITY REDUCTION." Facta Universitatis, Series: Mechanical Engineering 15, no. 2 (August 2, 2017): 295. http://dx.doi.org/10.22190/fume170503007d.

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The paper is concerned with the contact between the elastic bodies subjected to a constant normal load and a varying tangential loading in two directions of the contact plane. For uni-axial in-plane loading, the Cattaneo-Mindlin superposition principle can be applied even if the normal load is not constant but varies as well. However, this is generally not the case if the contact is periodically loaded in two perpendicular in-plane directions. The applicability of the Cattaneo-Mindlin superposition principle guarantees the applicability of the method of dimensionality reduction (MDR) which in the case of a uni-axial in-plane loading has the same accuracy as the Cattaneo-Mindlin theory. In the present paper we investigate whether it is possible to generalize the procedure used in the MDR for bi-axial in-plane loading. By comparison of the MDR-results with a complete three-dimensional numeric solution, we arrive at the conclusion that the exact mapping is not possible. However, the inaccuracy of the MDR solution is on the same order of magnitude as the inaccuracy of the Cattaneo-Mindlin theory itself. This means that the MDR can be also used as a good approximation for bi-axial in-plane loading.

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45

Wang, Xian-Zhong. "Vibration Analysis and Energy Transmission of Finite Coupled Mindlin Plates." International Journal of Structural Stability and Dynamics 17, no. 07 (September 2017): 1771007. http://dx.doi.org/10.1142/s0219455417710079.

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Power flow analysis of finite coupled Mindlin plates and energy transmission through the structure are investigated by employing the method of reverberation-ray matrix (MRRM). The rectangular Mindlin plates are connected at an arbitrary angle. Both in-plane and out-of-plane waves propagation solutions are considered by establishing the dual local coordinates in each plate. The boundary conditions at the plate edges, continuous conditions at the driving force locations, and coupling conditions at the line junction between several rectangular plates are established and solved simultaneously. Then the flexural and in-plane vibrations of the finite coupled Mindlin plate are obtained by using the MRRM, which are verified by comparing the results obtained with those by the finite element method (FEM). The vibration behaviors of coupled plates such as L-shaped structure, T-shaped structure and box-shaped structure are calculated and verified.

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46

Vazic, Bozo, Erkan Oterkus, and Selda Oterkus. "Peridynamic Model for a Mindlin Plate Resting on a Winkler Elastic Foundation." Journal of Peridynamics and Nonlocal Modeling 2, no. 3 (January 10, 2020): 229–42. http://dx.doi.org/10.1007/s42102-019-00019-5.

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AbstractIn this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation. In order to achieve static and quasi-static loading conditions, direct solution of the peridynamic equations is utilised by directly assigning inertia terms to zero rather than using widely adapted adaptive dynamic relaxation approach. The formulation is verified by comparing against a finite element solution for transverse loading condition without considering damage and comparing against a previous study for pure bending of a Mindlin plate with a central crack made of polymethyl methacrylate material having negligibly small elastic foundation stiffness. Finally, the fracture behaviour of a pre-cracked Mindlin plate rested on a Winkler foundation subjected to transverse loading representing a floating ice floe interacting with sloping structures. Similar fracture patterns observed in field observations were successfully captured by peridynamics.

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47

Zhang, Hai-Yan, Jie-Cong Yao, and Shi-Wei Ma. "Scattering of S0 Lamb Mode from a Blind Hole in a Plate Using Mindlin/Mindlin Plate Theory." Chinese Physics Letters 31, no. 3 (March 2014): 034301. http://dx.doi.org/10.1088/0256-307x/31/3/034301.

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48

Carnicer, Roberto S., and Stefano Alliney. "A Mindlin–Reissner Variational Principle to Analyze the Behavior of Moderately Thick Plates." Applied Mechanics Reviews 42, no. 11S (November 1, 1989): S32—S38. http://dx.doi.org/10.1115/1.3152404.

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In the present work a method to solve the plate behavior under the assumption of the Mindlin plate theory is analyzed by means of finite element techniques, avoiding the tendency of the thin element to lock when the thickness of the plates becomes very small. A different formulation is developed from the Mindlin–Reissner principle for general boundary conditions. Numerical examples to evaluate the noninfluence of locking on clamped and simple support plates are calculated.

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49

Nicodemo, Thiago Lima. "A invenção das brasilianas no século XX: alguns capítulos da história da Coleção Guita e José Mindlin." Revista BBM, no. 1 (September 11, 2018): 169–78. http://dx.doi.org/10.11606/issn.2595-5802.v1i1p169-178.

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O texto aqui apresentado é um desdobramento de pesquisa realizada no Fundo Rubens Borba de Moraes da Biblioteca Brasiliana Guita e José Mindlin, com apoio do Programa Institucional de Pesquisa nos Acervos da USP. Tendo como fio condutor a relação entre Rubens Borba de Moraes, José Mindlin e o livreiro português António Tavares de Carvalho, este texto procura gerar subsídios para compreender a formação da coleção que originou a Biblioteca Brasiliana Guita e José Mindlin, inserindo sua trajetória em um horizonte em mutação das coleções brasilianas na segunda metade do século XX. Esse quadro complexo inclui o desenvolvimento dos “estudos brasileiros” no exterior nas décadas de 1940 e 1950, que levou a uma corrida para a constituição de acervos sobre o país, mas também, num quadro doméstico, a consolidação de instituições de produção de conhecimento, como a USP e a Unb, bem como a conversão de coleções privadas em acervos públicos.

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50

Gao, X. L., and G. Y. Zhang. "A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 2016): 20160275. http://dx.doi.org/10.1098/rspa.2016.0275.

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A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived.

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