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Journal articles on the topic 'Statics of thin shells'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Chen, Zhen, Hsiao-Yu Chen, Danny M. Kaufman, Mélina Skouras, and Etienne Vouga. "Fine Wrinkling on Coarsely Meshed Thin Shells." ACM Transactions on Graphics 40, no. 5 (2021): 1–32. http://dx.doi.org/10.1145/3462758.

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We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude

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2

Nemat-Nasser, Sia, Jeom Yong Choi, Jon B. Isaacs, and David W. Lischer. "Quasi-Static and Dynamic Buckling of Thin Cylindrical Shape-Memory Shells." Journal of Applied Mechanics 73, no. 5 (2005): 825–33. http://dx.doi.org/10.1115/1.2165241.

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To investigate the buckling behavior of thin and relatively thick cylindrical shape-memory shells, uniaxial compression tests are performed at a 295K initial temperature, using the CEAM/UCSD’s modified split Hopkinson bar systems and an Instron hydraulic testing machine. The quasi-static buckling response of the shells is directly observed and recorded using a digital camera with a close-up lens and two back mirrors. To document the dynamic buckling modes, a high-speed Imacon 200 framing camera is used. The shape-memory shells with an austenite-finish temperature of Af=281K, buckle gradually a

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3

Ayaz, Osman, Ahmad Reshad Noorı, Burkay Sivri, and Beytullah Temel. "STATIC ANALYSIS OF AXISYMMETRIC THIN CYLINDRICAL SHELL USING THE COMPLEMENTARY FUNCTIONS METHOD." Konya Journal of Engineering Sciences 13, no. 2 (2025): 510–23. https://doi.org/10.36306/konjes.1606387.

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The analysis of thin cylindrical shells is essential for a wide range of engineering applications, making it critical to understand their static behavior under various loading conditions. In this study, the static analysis of axisymmetric thin cylindrical shells is performed using the Complementary Functions Method (CFM). The research focuses on examining the static behavior of cylindrical shells made of homogeneous, isotropic, and linear elastic materials under various loading conditions. The governing differential equations for the static response of these structural elements are derived bas

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4

Viebahn, Nils, Paulo M. Pimenta, and Jörg Schröder. "A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy." Computational Mechanics 59, no. 2 (2016): 281–97. http://dx.doi.org/10.1007/s00466-016-1343-6.

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5

Maksimyuk, V. A., E. A. Storozhuk, and I. S. Chernyshenko. "Using mesh-based methods to solve nonlinear problems of statics for thin shells." International Applied Mechanics 45, no. 1 (2009): 32–56. http://dx.doi.org/10.1007/s10778-009-0166-y.

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6

Prabu, B., N. Bujjibabu, S. Saravanan, and A. Venkatraman. "Effect of a Dent of Different Sizes and Angles of Inclination on Buckling Strength of a Short Stainless Steel Cylindrical Shell Subjected to Uniform Axial Compression." Advances in Structural Engineering 10, no. 5 (2007): 581–91. http://dx.doi.org/10.1260/136943307782417735.

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Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (L / D ∼1 and R/t = 280) stainless steel cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed usi

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7

Steele, Charles R., and Khaliq ur-Rehman Shad. "Asymptotic-Numeric Solution for Shells of Revolution." Applied Mechanics Reviews 48, no. 11S (1995): S44—S51. http://dx.doi.org/10.1115/1.3005082.

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Thin shell structures offer a challenge to the analyst. It is well known that asymptotic expansion procedures offer simple approximate solutions for a number of shell problems for which direct numerical methods are inefficient. In this paper, a “very large finite element” method (VLFEM) is offered for the axisymmetric shell. The shape functions are obtained by sufficiently accurate asymptotic approximations through numerical procedures. A number of examples in statics and vibration have been considered that demonstrate the efficiency and accuracy of the approach.

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8

Chen, Xuwen, Xingyu Ni, Bo Zhu, Bin Wang, and Baoquan Chen. "Simulation and optimization of magnetoelastic thin shells." ACM Transactions on Graphics 41, no. 4 (2022): 1–18. http://dx.doi.org/10.1145/3528223.3530142.

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Magnetoelastic thin shells exhibit great potential in realizing versatile functionalities through a broad range of combination of material stiffness, remnant magnetization intensity, and external magnetic stimuli. In this paper, we propose a novel computational method for forward simulation and inverse design of magnetoelastic thin shells. Our system consists of two key components of forward simulation and backward optimization. On the simulation side, we have developed a new continuum mechanics model based on the Kirchhoff-Love thin-shell model to characterize the behaviors of a megnetolelast

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9

Rubín de Celis, Emilio, Cecilia Tomasini, and Claudio Simeone. "Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach." International Journal of Modern Physics D 27, no. 01 (2017): 1750171. http://dx.doi.org/10.1142/s0218271817501711.

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Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.

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10

Krivenko, Olha, Yurii Vorona, and Andrii Kozak. "Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures." Strength of Materials and Theory of Structures, no. 107 (October 29, 2021): 20–34. http://dx.doi.org/10.32347/2410-2547.2021.107.20-34.

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Thin-walled shell-type structures are widely used in various branches of technology and industry. Such structures under operating conditions are usually exposed to various loads, including thermomechanical ones. Real shell structures, as a rule, have a complex shapes. To increase reliability, reduce material consumption, for technological reasons, they are designed as inhomogeneous systems in thickness. This causes a great and constant interest of engineers and designers in the problems of investigating the behavior of elastic thin-walled shell structures. The work is devoted to the meth

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11

MAMIEVA, I. A., and V. V. KARNEVICH. "GEOMETRY AND STATIC ANALYSIS OF THIN SHELLS WITH RULED MIDDLE SURFACES OF THREE SUPERELLIPSES AS MAIN FRAME." Building and reconstruction 105, no. 1 (2023): 16–27. http://dx.doi.org/10.33979/2073-7416-2023-105-1-16-27.

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The possibility of generating three different translational surfaces of velarodial type by having the same main frame of the surface is proved and illustrated. Using these three different ruled surfaces as middle surfaces of thin shells allows to extend the number of architectural forms in construction practice. Static analysis of the shells with the middle surfaces under consideration is performed using the SCAD standard finite element software. The results of the analysis of different ruled shells with oval-shaped base, but of the same main frame, imply that the stress, moment and displaceme

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12

Liu, Xiaobin, Jian Zhang, Ming Zhan, Xilu Zhao, Wenwei Wu, and Kaiwei Xu. "Wrinkling of Toroidal Shells in Free Hydroforming." Journal of Marine Science and Engineering 12, no. 1 (2024): 89. http://dx.doi.org/10.3390/jmse12010089.

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In this study, we investigated toroidal shell wrinkling in free hydroforming. We specifically focused on toroidal shells with a regular hexagonal cross-section. Membrane theory was used to examine the distribution of stress and yield load in both preform and toroidal shells. The wrinkling moment was then predicted using an empirical formula of shell buckling. In addition, the wrinkling state was investigated using a general statics method, and the free hydroforming of toroidal shells was simulated using the Riks method. Subsequently, nonlinear buckling and equilibrium paths were analyzed. A to

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13

Krivenko, Olga P., Petro Lizunov, and Oleksandr Kalashnikov. "The influence of geometrical shape on the buckling of thin-walled axisymmetric shells." Management of Development of Complex Systems, no. 57 (March 29, 2024): 102–6. http://dx.doi.org/10.32347/2412-9933.2024.57.102-106.

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The most economical for long span structures are thin-walled covering consisting of shell elements. These include shells of cylindrical, spherical, conical and other shapes. Buckling analysis of thinwalled structures is important in the design of buildings and structures. In this case, the geometric shape of the shell used has a great effect on the critical load. A comparative analysis of the geometrically nonlinear deformation, buckling, and postbuckling behavior of rotation panels of the same v olume under static thermomechanical loading is carried out. Spherical and conical shells having th

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14

Tzou, H. S., W. K. Chai, and S. M. Arnold. "Structronics and Actuation of Hybrid Electrostrictive/Piezoelectric Thin Shells." Journal of Vibration and Acoustics 128, no. 1 (2005): 79–87. http://dx.doi.org/10.1115/1.2149397.

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Certain ferroelectric materials possess dual electrostrictive and piezoelectric characteristics, depending on their specific Curie temperatures. The nonlinear electro-mechanical effect of electrostrictive materials provides stronger actuation performance as compared with that of piezoelectric materials. Due to the complexity of the generic ferroelectric actuators, micro-electromechanics, structure-electronic (structronic) coupling and control characteristics of hybrid electrostrictive/piezoelectric dynamic systems deserve an in-depth investigation. In this study, dynamic electro-mechanical sys

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15

Krivenko, Olga, and Petro Lizunov. "Vibrations of launch vehicle fairings with conical shape." Strength of Materials and Theory of Structures, no. 109 (November 11, 2022): 66–71. http://dx.doi.org/10.32347/2410-2547.2022.109.66-71.

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Vibrations of launch vehicle conical fairings are investigated. Fairings are simulated using thin conic shells. The modal analysis of a thin elastic shell is based on the use of the developed finite element model of an inhomogeneous shell. In general, the technique makes it possible to investigate the geometrically nonlinear deformation, stability, and post-buckling behavior of a wide class of thin elastic shells. The modal analysis of the structure is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest vib

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16

Godin, Oleg A. "Sound scattering and radiation suppression by pressurized spherical shells." Journal of the Acoustical Society of America 154, no. 5 (2023): 3223–36. http://dx.doi.org/10.1121/10.0022416.

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Thin-shell models offer important insights into the complex process of sound-structure interaction but are found to be inconsistent with the rigorous thick-shell theory for fluid-loaded spherical shells. Here, linearized equations of motion of fluid-loaded, thin, spherical shells are re-derived from the first principles. The shell may be prestressed due to the difference in the static pressures in the internal and external fluids. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived of th

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17

Krivoshapko, S. N., and G. L. Gbaguidi-Aisse. "Geometry, Static, Vibration and Bucking Analysis and Applications to Thin Elliptic Paraboloid Shells." Open Construction and Building Technology Journal 10, no. 1 (2016): 576–602. http://dx.doi.org/10.2174/1874836801610010576.

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A large number of references dealing with the geometry, static, vibration and buckling analysis of elliptic paraboloid shells exist in the literature. This review work attempts to organize and summarize the extensive published literature on the basic achievements in investigations of thin-walled structures in the form of elliptic paraboloids. Possibilities of elliptic paraboloids with reference to machine-building and construction designs and to the apparatuses used in theoretical physics are briefly considered. The geometric part of the review is extended due to consideration of optimization

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18

ARIK, METIN, and OZGUR DELICE. "TRAPPING PHOTONS BY A LINE SINGULARITY." International Journal of Modern Physics D 12, no. 06 (2003): 1095–112. http://dx.doi.org/10.1142/s0218271803003475.

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We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin shell and the line singularity is discussed. It is also shown that thick shells containing mostly radiation are possible in a numerical solution.

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19

Lepikhin, P. P., V. A. Romaschenko, and S. O. Tarasovs’ka. "Peculiarities of Strengthening of Spherical Composite Pressure Vessels with Thin Metal Shells Under Static and Dynamic Loads. Part 1. Statics." Strength of Materials 53, no. 3 (2021): 388–94. http://dx.doi.org/10.1007/s11223-021-00298-8.

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20

Bakshi, Kaustav, and Dipankar Chakravorty. "Static and Dynamic Characteristics of Composite Conoidal Shell Roofs." Advances in Acoustics and Vibration 2013 (December 3, 2013): 1–9. http://dx.doi.org/10.1155/2013/539817.

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A thorough review of the existing literature reflects that forced vibration studies of laminated composite conoidal shells with complicated boundary conditions are missing. Hence, the present paper aims to fill the lacuna. A finite element code utilizing eight-noded doubly curved elements together with modified Sanders’ first approximation theory for thin shells is used to study the forced vibration behavior of moderately thin laminated composite conoidal shells subjected to three different uniformly distributed time-dependent forces. Newmark’s direct time integration method is used to solve t

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21

Panteleienko, V. I., S. O. Karpushyn, and A. L. Chervonoshtan. "Interaction of conical monolithic thin-walled reinforced concrete shells with the soil of the foundation." IOP Conference Series: Earth and Environmental Science 1254, no. 1 (2023): 012058. http://dx.doi.org/10.1088/1755-1315/1254/1/012058.

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Abstract Conical monolithic thin-walled reinforced concrete blocks (shells) can be used as foundations for frame structures and buildings with load-bearing walls. As an analogue of columnar foundations, this type has the advantage of the speed of installation. It almost wholly excludes earthwork and formwork from the technological process, provided that the physical and mechanical properties of the soil base are improved. Shells are immersed in the supporting soil base with the help of dynamic or static loading. Additional soil base compaction occurs due to interaction with the conical outer s

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22

Agapov, Vladimir P., and Alexey S. Markovich. "Investigation of the accuracy and convergence of the results of thin shells analysis using the PRINS program." Structural Mechanics of Engineering Constructions and Buildings 17, no. 6 (2021): 617–27. http://dx.doi.org/10.22363/1815-5235-2021-17-6-617-627.

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The theoretical foundations of compatible finite elements construction for static and dynamic analysis of single-layer and multilayer shells are discussed. These finite elements are implemented in the PRINS computer program. The paper presents verification tests to investigate the accuracy and convergence of the results of calculating various shells using these finite elements. Shell structures are widely used in various fields of technology - construction, mechanical engineering, aircraft construction, shipbuilding, etc. Specialists on the design and calculation of such structures need a reli

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23

GAO, SIJIE, and JOSÉ P. S. LEMOS. "COLLAPSING AND STATIC THIN MASSIVE CHARGED DUST SHELLS IN A REISSNER–NORDSTRÖM BLACK HOLE BACKGROUND IN HIGHER DIMENSIONS." International Journal of Modern Physics A 23, no. 19 (2008): 2943–60. http://dx.doi.org/10.1142/s0217751x08041402.

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The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner–Nordström black hole in d space–time dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First, a derivation of the equation of motion of such a shell in a d-dimensional space–time is given. Then, a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is deri

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24

Vendhan, Chiruvai P., and Subroto Kumar Bhattacharyya. "A New Approach to Linear Buckling of Thin Circular Cylindrical Shells." Journal of Ship Research 34, no. 04 (1990): 311–16. http://dx.doi.org/10.5957/jsr.1990.34.4.311.

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Adopting an end-problem approach to static displacement equations of thin circular cylindrical shells, a type of coupled eigenvalue problem is developed which integrates the eigenvalue problem of bending as well as that of linear buckling. This is shown to provide an alternative mathematical criterion of linear bifurcation buckling. In addition, it provides new insight into the nature of Saint Venant effects. Numerical illustrations for an isotropic shell are worked out to demonstrate the structure of the proposed eigenvalue problem.

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25

Combescure, Alain. "Static and dynamic buckling of large thin shells." Nuclear Engineering and Design 92, no. 3 (1986): 339–54. http://dx.doi.org/10.1016/0029-5493(86)90130-5.

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26

Godin, Oleg A. "Vibrations of a thin, prestressed, fluid-loaded spherical shell forced by a point sound source." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A53. http://dx.doi.org/10.1121/10.0018137.

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This paper investigates vibrations of and sound scattering by a thin elastic spherical shell when static pressures are different in the fluids inside and outside the shell. The work is motivated by stratospheric balloons being employed to carry acoustic sensors and by the proposed use of large, encapsulated gas bubbles for passive suppression of underwater sound [O. A. Godin and A. B. Baynes, J. Acoust. Soc. Am., 143, EL67–EL73 (2018)]. Linearized equations of motion of thin, prestressed shells are derived from first principles. Differences in the fluid-loading terms from previously proposed a

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27

ZLOSHCHASTIEV, KONSTANTIN G. "BAROTROPIC THIN SHELLS WITH LINEAR EOS AS MODELS OF STARS AND CIRCUMSTELLAR SHELLS IN GENERAL RELATIVITY." International Journal of Modern Physics D 08, no. 04 (1999): 549–55. http://dx.doi.org/10.1142/s0218271899000389.

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The spherically symmetric thin shells of the barotropic fluids with the linear equation of state are considered within the frameworks of general relativity. We study several aspects of the shells as completely relativistic models of stars, first of all the neutron stars and white dwarfs, and circumstellar shells. The exact equations of motion of the shells are obtained. Also we calculate the parameters of the equilibrium configurations, including the radii of static shells. Finally, we study the stability of the equilibrium shells against radial perturbations.

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28

Vahid Yousefi Ramandi. "Evaluation the Reverse Crashing Characteristics of Thin-Walled Shells that are Packed with FGM Foam and Forecast the Energy Absorption Through the Use of Artificial Neural Networks." Power System Technology 48, no. 1 (2024): 2045–73. https://doi.org/10.52783/pst.478.

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The present research investigates the reverse crashing behavior of thin-walled shells filled with functionally graded foam (FGF). The study employs a combination of nonlinear finite element analysis and artificial neural networks (ANN) to predict the energy absorption capacity of the shells. Three types of foam properties distributions are examined for aluminum porous core foam under quasi-static vertical loading. The impact parameters, including specific energy absorption, are evaluated by analyzing the geometrical parameters of the shell and the mechanical properties of the foam core. The re

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29

Krivenko, Olha, and Yurii Vorona. "Comparative Analysis of Nonlinear Deformation and Buckling of Thin Elastic Shells of Step-Variable Thickness." Strength of Materials and Theory of Structures, no. 108 (May 30, 2022): 107–18. http://dx.doi.org/10.32347/2410-2547.2022.108.107-118.

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A comparative analysis of finite element models and methods for solving complex problems of geometrically nonlinear deformation, buckling and post-buckling behavior of thin shells of stepwise variable thickness is carried out. An approach based on the use of the moment scheme of finite elements is considered. The features of using the software suite LIRA and integrated software system SCAD for solving the assigned problems are also provided. Thin and medium thickness shells are considered. They can have different geometric features in thickness and be under the action of static thermomechanica

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30

Nwoji, C. U., D. G. Ani, O. A. Oguaghamba, and V. T. Ibeabuchi. "Static Bending of Isotropic Circular Cylindrical Shells Based on the Higher Order Shear Deformation Theory of Reddy and Liu." International Journal of Applied Mechanics and Engineering 26, no. 3 (2021): 141–62. http://dx.doi.org/10.2478/ijame-2021-0041.

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Abstract In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analy

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31

Nam, Vu Hoai, Nguyen Thi Phuong, Dao Huy Bich, and Dao Van Dung. "Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation." Vietnam Journal of Mechanics 36, no. 1 (2014): 27–47. http://dx.doi.org/10.15625/0866-7136/36/1/3470.

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This paper presents an analytical approach to investigate the nonlinear buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression and surrounded by an elastic foundation. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, initial geometrical imperfection, the smeared stiffeners technique and Pasternak’s two-parameter elastic foundation, the governing equations of eccentrically stiffened functionally graded cylindrical shells are derived. The functionally graded cylindric

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32

Krivoshapko, S. N. "Static Analysis of Shells With Developable Middle Surfaces." Applied Mechanics Reviews 51, no. 12 (1998): 731–46. http://dx.doi.org/10.1115/1.3098985.

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This review article is devoted to an analysis of the literature on the stress-strain state of shells with developable middle surfaces. Wide choices of design methods for the developable surfaces provide not only the necessary shapes and special properties; they also prove to be convenient to apply. Representative examples are given for the static analysis of thin elastic shells by both analytic and numerical methods. Generally, the curvilinear non-orthogonal conjugate coordinates of the developable middle surface are used. Lines of principal curvatures are used as coordinates only for the stre

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33

Ziolkowski, Marcin, Marek Ziolkowski, and Stanislaw Gratkowski. "Optimal parameters of a nonmagnetic conducting cylindrical double-shell shield rotating in a static magnetic field." International Journal of Applied Electromagnetics and Mechanics 69, no. 3 (2022): 401–10. http://dx.doi.org/10.3233/jae-210208.

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This paper first presents an analytical model for calculating the shielding effectiveness of static magnetic fields using a rotating double-shell cylindrical shield with electromagnetically thin layers made of non-magnetic conducting material. Then a procedure is given for finding the optimum distance between the shells and their thickness for maximum mass reduction compared to a thick single shield for a given shielding factor.

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34

Babenkova, E., and J. Kaplunov. "Radiation conditions for a semi-infinite elastic strip." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2056 (2005): 1163–79. http://dx.doi.org/10.1098/rspa2004.1402.

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High-frequency vibrations of a semi-infinite elastic strip with traction-free faces are considered. The conditions on end data that are derived do not allow non-radiating in Sommerfeld's sense of polynomial modes at thickness resonance frequencies. These represent a high-frequency analogue of the well-known decay conditions in statics that agree with the classical Saint-Venant principle. The proposed radiation conditions are applied to the construction of boundary conditions in the theories of high-frequency long-wave vibrations describing slow-varying motions in the vicinity of thickness reso

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35

Dzhabrailov, Arsen, Anatoly Nikolaev, and Natalya Gureeva. "Calculation of thin-walled axisymmetrically loaded structures of the AIC taking into account FEM-based physical nonlinearity." BIO Web of Conferences 17 (2020): 00199. http://dx.doi.org/10.1051/bioconf/20201700199.

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The article describes an algorithm for calculating an axisymmetrically loaded shell structure with a branching meridian, taking into account elastic-plastic deformations when loading based on the deformation theory of plasticity without assuming that the material is incompressible during plastic deformations. The correct relations which determine the static conjugation conditions of several revolution shells in the joint assembly are used. A comparative analysis of finite element solutions is presented for various options plasticity matrix development at the loading stage.

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36

Tokuda, N., and Y. Sakata. "Application of Static Condensation Method to Vibration Analysis of Thin Cylindrical Shells." Journal of Pressure Vessel Technology 111, no. 3 (1989): 275–84. http://dx.doi.org/10.1115/1.3265675.

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A simple formula is proposed, by which the error in the natural frequencies introduced by using the static condensation method can be evaluated prior to the numerical computation, though its effective applicability is found in simple structures such as plates and shells. The effectiveness of the proposed formula is examined in the vibration analysis of thin cylindrical shells having freely supported ends by using various reduction patterns. Not only the accuracy of natural frequencies, but also that of modal displacements and the corresponding modal stresses are investigated by comparing with

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37

Fernandes, Susana C. F., Jesus Cuartero, and Antonio J. M. Ferreira. "Using Collocation with Radial Basis Functions in a Pseudospectral Framework for a New Layerwise Shallow Shell Theory." Journal of Composites Science 8, no. 11 (2024): 448. http://dx.doi.org/10.3390/jcs8110448.

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This work presents radial basis function collocation methods in pseudospectral form for forecasting the static deformations and free vibration characteristics of thin and thick cross-ply laminated shells. This method utilizes an innovative layerwise shallow shell theory that integrates both translational and rotational degrees of freedom. A collection of numerical examples illustrates the precision and efficacy of the suggested numerical method, highlighting its capability in resolving static and vibrational issues.

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38

Bazhenov, Viktor, Olga Krivenko, and Andrii Kozak. "Modal analysis of a complex shell structure under operational loads." Strength of Materials and Theory of Structures, no. 106 (May 24, 2021): 5–13. http://dx.doi.org/10.32347/2410-2547.2021.106.5-13.

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The results of calculation of a complex shell structure under the action of operational loads are presented. A three-section cooling tower, called a three-petal cooling tower, is regarded as a complex-shaped structure. Three variants of loads on the shell are considered: wind pressure, heating and load combination. The design model of a shell of a complex shape is based on the developed universal spatial finite element. The universal spatial finite element allows one to take into account the geometric features of structural elements for a thin shell (constant or varying thickness, knees, ribs,

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39

Han, Yueyang, Xiang Zhu, Tianyun Li, Yunyan Yu, and Xiaofang Hu. "Free Vibration and Elastic Critical Load of Functionally Graded Material Thin Cylindrical Shells Under Internal Pressure." International Journal of Structural Stability and Dynamics 18, no. 11 (2018): 1850138. http://dx.doi.org/10.1142/s0219455418501389.

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An analytical approach for predicting the free vibration and elastic critical load of functionally graded material (FGM) thin cylindrical shells filled with internal pressured fluid is presented in this study. The vibration of the FGM cylindrical shell is described by the Flügge shell theory, where the internal static pressure is considered as the prestress term in the shell equations. The motion of the internal fluid is described by the acoustic wave equation. The natural frequencies of the FGM cylindrical shell under different internal pressures are obtained with the wave propagation method.

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Krivenko, Olga, Petro Lizunov, Anton Polianskyi, and Oleksandr Kalashnikov. "Modal analysis of a thin coupled composite shell." Strength of Materials and Theory of Structures, no. 113 (November 29, 2024): 75–80. https://doi.org/10.32347/2410-2547.2024.113.75-80.

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The results of the study of natural vibrations of a coupled shell of revolution are presented. The shell is a spherically biconical structure that has sharp bends in the mid-surface at the junction of different shapes. The material is a unidirectional fibrous carbon/epoxy composite. The shell structure, by its geometric shape and material parameterss, is an approximate model of the fairing of the launch vehicle. The modal analysis of a thin elastic shell is based on the use of a finite element model of a inhomogeneous shell and the application of a universal 3D finite element. The governing fi

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Makowski, J., and W. Pietraszkiewicz. "Work-Conjugate Boundary Conditions in the Nonlinear Theory of Thin Shells." Journal of Applied Mechanics 56, no. 2 (1989): 395–402. http://dx.doi.org/10.1115/1.3176096.

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Work–conjugate boundary conditions for a class of nonlinear theories of thin shells formulated in terms of displacements of the reference surface are discussed. Applying theorems of the theory of differential forms it is shown that many of the sets of static boundary conditions which have been proposed in the literature do not possess work–conjugate geometric counterparts. The general form of four geometric boundary conditions and their work–conjugate static boundary conditions is constructed and three particular cases are analyzed. The boundary conditions given here are valid for unrestricted

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Tang, Zhiping, and Dan Li. "Quasi-static axial buckling behavior of NiTi thin-walled cylindrical shells." Thin-Walled Structures 51 (February 2012): 130–38. http://dx.doi.org/10.1016/j.tws.2011.10.007.

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Giani, Stefano, and Harri Hakula. "On effective material parameters of thin perforated shells under static loading." Computer Methods in Applied Mechanics and Engineering 367 (August 2020): 113094. http://dx.doi.org/10.1016/j.cma.2020.113094.

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Ross, C. T. F. "The buckling of thin-walled shells under static free-flood conditions." Thin-Walled Structures 21, no. 4 (1995): 359–63. http://dx.doi.org/10.1016/0263-8231(95)93620-2.

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Alain, Bock, Krivoshapko Nikolaiv, Kouamou Arnaud, Yamb Emmanuel, and Bahel Benjamin. "Application of Curvilinear Analytical Surfaces in Forms of Architectural Objects and Machine Building Products." International Journal of Architecture, Arts and Applications 11, no. 1 (2025): 19–35. https://doi.org/10.11648/j.ijaaa.20251101.13.

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The principal achievements of science and engineering in the sphere of static and dynamic analysis of thin-walled objects, structures, and shells in the shape of analytic surfaces are used for practical needs of people. Classes of surfaces that found the application in forms of architectural erections and machine building products are considered. This is confirmed by presented illustrations of real products and erections. Classes of surfaces which did not attract the attention of architects and designers working with curvilinear forms are pointed out too. The presented materials confirm conclu

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Beltman, W. M., E. N. Burcsu, J. E. Shepherd, and L. Zuhal. "The Structural Response of Cylindrical Shells to Internal Shock Loading." Journal of Pressure Vessel Technology 121, no. 3 (1999): 315–22. http://dx.doi.org/10.1115/1.2883709.

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The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with

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Krivenko, Olga, and Petro Lizunov. "Investigation of nonlinear deformation, buckling and natural vibrations of elastic shells under thermomechanical loads using a universal three-dimensional finite element." Strength of Materials and Theory of Structures, no. 114 (April 25, 2025): 35–43. https://doi.org/10.32347/2410-2547.2025.114.35-43.

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The article presents the fundamentals and features of the method for solving static problems of nonlinear deformation, buckling, post-buckling behavior and natural vibrations of a wide class of thin elastic inhomogeneous shells of various shapes and structures under the action of thermomechanical loads. The method is developed from the unified positions of the three-dimensional geometrically nonlinear theory of thermoelasticity based on the finite element method. A universal 3D finite element is used. The distinctive feature of the finite element is the presence of its additional variable para

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Khalifa Ahmed, Mousa. "Elastic Buckling Behaviour of a Four-Lobed Cross Section Cylindrical Shell with Variable Thickness under Non-Uniform Axial Loads." Mathematical Problems in Engineering 2009 (2009): 1–17. http://dx.doi.org/10.1155/2009/829703.

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The static buckling of a cylindrical shell of a four-lobed cross section of variable thickness subjected to non-uniform circumferentially compressive loads is investigated based on the thin-shell theory. Modal displacements of the shell can be described by trigonometric functions, and Fourier's approach is used to separate the variables. The governing equations of the shell are reduced to eight first-order differential equations with variable coefficients in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential eq

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Krivenko, Olga, Petro Lizunov, Yurii Vorona, and Oleksandr Kalashnikov. "Comparative analysis of the stability and natural vibrations of shallow panels under the action of thermomechanical loads." Strength of Materials and Theory of Structures, no. 111 (November 24, 2023): 49–64. http://dx.doi.org/10.32347/2410-2547.2023.111.49-64.

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The work is a continuation of research devoted to substantiating the reliability of solutions obtained by the finite element method for the analysis of nonlinear deformation, buckling and vibrations of thin elastic shells under the action of thermomechanical loads. The method is based on geometrically nonlinear relations of the three-dimensional theory of thermoelasticity and the principles of the moment finite element scheme. A thin elastic shell of an inhomogeneous structure is modeled by a universal spatial isoparametric finite element. The modal analysis of the shell is implemented at each

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Goncharova, Tatyana. "Bionics in architecture and geometric modelling of thin shell surfaces." E3S Web of Conferences 389 (2023): 06002. http://dx.doi.org/10.1051/e3sconf/202338906002.

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In the scientific problem of design and calculation of thin elastic shells in the modern world, certain advances have already been made in mathematical and technical theory, based on hypotheses, experimental data, calculation equations and engineering calculations. Only such shells, which are designed based on calculation and used in building and technical constructions, can be referred to a small number of geometric surfaces. When designing thin shells, surfaces of rotation (sphere, torus, paraboloid, ellipsoid of rotation) and transfer surfaces (hyperbolic and elliptic paraboloid, circular t

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