Stress-strained state and the stability of a spherical segment under the influence of a load with a flat base

Paper


Ermakov, A. M.. 2013. "Stress-strained state and the stability of a spherical segment under the influence of a load with a flat base." Logg, Anders, Mardal, Kent-Andre and Massing, Andre (ed.) 26th Nordic Seminar on Computational Mechanics. Oslo, Norway 23 - 25 Oct 2013 Oslo, Norway.
Paper/Presentation Title

Stress-strained state and the stability of a spherical segment under the influence of a load with a flat base

Presentation TypePaper
Authors
AuthorErmakov, A. M.
EditorsLogg, Anders, Mardal, Kent-Andre and Massing, Andre
Journal or Proceedings TitleProceedings of the 26th Nordic Seminar on Computational Mechanics
Number of Pages4
Year2013
Place of PublicationOslo, Norway
ISBN9788292593127
Web Address (URL) of Paperhttp://cbc.simula.no/pub/data/nscm26-proceedings.pdf
Conference/Event26th Nordic Seminar on Computational Mechanics
Event Details
26th Nordic Seminar on Computational Mechanics
Event Date
23 to end of 25 Oct 2013
Event Location
Oslo, Norway
Abstract

In this paper the problem of the buckling of the transversal-isotropic segment of spherical shell with the different thicknesses under the influence of the load with a flat base is studied. The spherical segment has a rigid support on the edge and previously has been loaded by internal pressure. The solution of this problem is based on the theory of the shell of moderate thickness by Paly-Spiro. This theory takes into account the influence of the cross-section shear and change of the shell thickness. For modelling such large deformations, the method of consequent loading is used. In this method, due to the use of linear physical relations, it is possible to trace the non-linear problem at each separate stage to the solution of a linear system. The comparison of the results which were obtained with the use of the method of linearization of non-linear equilibrium equations and the method of minimization of elastic potential of the shell has been done. The problems of stress-strain state of soft and close to soft shells that are under the influence of a load with a flat base are important for analysing the data related to measuring a very important in ophthalmology characteristic of intraocular pressure.

Keywordsnonlinear shell theory, stability, load with a flat base
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
420701. Biomechanics
401707. Solid mechanics
Public Notes

c. 2013 The authors.

Byline AffiliationsSaint Petersburg State University, Russia
Institution of OriginUniversity of Southern Queensland
Permalink -

https://research.usq.edu.au/item/q3q93/stress-strained-state-and-the-stability-of-a-spherical-segment-under-the-influence-of-a-load-with-a-flat-base

Download files


Published Version
2013 NSCM.pdf
File access level: Anyone

  • 1532
    total views
  • 114
    total downloads
  • 0
    views this month
  • 0
    downloads this month

Export as

Related outputs

Development of rigorous methods in fluid mechanics and theory of water waves
Ermakov, Andrei. 2019. Development of rigorous methods in fluid mechanics and theory of water waves. PhD Thesis Doctor of Philosophy. University of Southern Queensland. https://doi.org/10.26192/ez1n-g463
Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry
Ermakov, Andrei and Stepanyants, Yury. 2020. "Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry." Pure and Applied Geophysics. 177 (3), pp. 1675-1693. https://doi.org/10.1007/s00024-019-02259-4
Soliton interaction with external forcing within the Korteweg–de Vries equation
Ermakov, Andrei and Stepanyants, Yury. 2019. "Soliton interaction with external forcing within the Korteweg–de Vries equation." Chaos: an interdisciplinary journal of nonlinear science. 29 (1). https://doi.org/10.1063/1.5063561
Local stability of a plate with a circular inclusion under tensile stress
Bauer, Svetlana, Ermakov, Andrei, Kashtanova, Stanislava and Morozov, Nikita. 2018. "Local stability of a plate with a circular inclusion under tensile stress." Pietraszkiewicz, Wojciech and Witkowski, Wojciech (ed.) Shell structures: theory and applications, vol. 4. London, United Kingdom. CRC Press. pp. 199-202
Wave scattering in spatially inhomogeneous currents
Churilov, Semyon, Ermakov, Andrei and Stepanyants, Yury. 2017. "Wave scattering in spatially inhomogeneous currents." Physical Review D. 96 (6), p. 064016. https://doi.org/10.1103/PhysRevD.96.064016
Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current
Churilov, Semyon, Ermakov, Andrei, Rousseaux, Germain and Stepanyants, Yury. 2017. "Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current." Physcial Review Fluids. 2 (9), p. 094805. https://doi.org/10.1103/PhysRevFluids.2.094805
On the stability of the cylindrical shell under the axial compression with use of non-classical theories of shells
Ermakov, A. M.. 2012. "On the stability of the cylindrical shell under the axial compression with use of non-classical theories of shells." Holzapfel, Gerhard (ed.) 8th European Solid Mechanics Conference (ESMC-2012) . Graz, Austria 09 - 13 Jul 2012 Graz, Austria.
Stress--strain state of the sclera and cornea as orthotropic non-uniform conjugated spherical shells
Ermakov, A. M.. 2008. "Stress--strain state of the sclera and cornea as orthotropic non-uniform conjugated spherical shells." Russian Journal of Biomechanics. 13 (1), pp. 47-58.
Tonometric estimation of mechanical properties of a cornea and sclera
Voronkova, E., Bauer, S. and Ermakov, A.. 2009. "Tonometric estimation of mechanical properties of a cornea and sclera." 2009 Association for Research in Vision and Ophthalmology Annual Meeting (ARVO 2009). Fort Lauderdale, United States of America 03 - 07 May 2009 United States. Association for Research in Vision and Ophthalmology (ARVO).
Biomechanical analysis of parameters influencing pressure-volume relationship in the human eye
Bauer, S. M., Ermakov, A. M., Kotliar, K. E. and Voronkova, E. B.. 2010. "Biomechanical analysis of parameters influencing pressure-volume relationship in the human eye." 2010 Association for Research in Vision and Ophthalmology Annual Meeting (ARVO 2010). Fort Lauderdale, United States of America 02 - 06 May 2010 Association for Research in Vision and Ophthalmology (ARVO).
The models of nonclassical anisotropic spherical shells
Ermakov, A.. 2012. "The models of nonclassical anisotropic spherical shells." Pecherski, Ryszard, Rojek, Jerzy and Kowalczyk, Piotr (ed.) 38th Solid Mechanics Conference. Warsaw, Poland 27 - 31 Aug 2012 Warsaw, Poland.
Buckling of a spherical segment under the flat base load
Bauer, Svetlana and Ermakov, Andrei. 2013. "Buckling of a spherical segment under the flat base load." Lellep, J. and Puman, E. (ed.) 2nd International Conference on Optimization and Analysis of Structures (OAS 2013). Tartu, Estonia 25 - 27 Aug 2013 Tartu, Estonia.
Description of vortical flows of incompressible fluid in terms of quasi-potential function
Ermakov, A. M. and Stepanyants, Y. A.. 2016. "Description of vortical flows of incompressible fluid in terms of quasi-potential function." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.
Mathematical modelling of applanation tonometry for intraocular pressure measurements
Ermakov, Andrei M. and Bauer, Svetlana M.. 2016. "Mathematical modelling of applanation tonometry for intraocular pressure measurements." 55th ASMR National Scientific Conference: Next Generation Healthcare - Merging Biology and Technology . Gold Coast, Australia 13 - 15 Nov 2016
Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes
Bauer, S. M., Ermakov, A. M., Kashtanova, S. V. and Morozov, N. F.. 2011. "Application of nonclassical models of shell theory to study mechanical parameters of multilayer nanotubes." Vestnik: Mathematics (St. Petersburg University). 44 (1), p. Article 13. https://doi.org/10.3103/S1063454111010055
Evaluation of the mechanical parameters of nanotubes by means of nonclassical theories of shells
Bauer, Svetlana M., Ermakov, Andrei M., Kashtanova, Stanislava V. and Morozov, Nikita F.. 2011. "Evaluation of the mechanical parameters of nanotubes by means of nonclassical theories of shells." Altenbach, Holm and Eremeyev, Victor A. (ed.) Shell-like structures. Heidelberg, Germany. Springer. pp. 519-530
Nonclassical models in the shell theory with applications to multilayered nanotubes
Bauer, Svetlana M., Ermakov, Andrei M., Kashtanova, Stanislava V. and Morozov, Nikita F.. 2011. "Nonclassical models in the shell theory with applications to multilayered nanotubes." Papadrakakis, Manolis, Fragiadakis, Michalis and Plevris, Vagelis (ed.) 3rd ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2011). Corfu, Greece 25 - 28 May 2011 Dordrecht, Netherlands. https://doi.org/10.1007/978-94-007-6573-3
Numerical and analytical modeling of the stability of the cylindrical shell under the axial compression with the use of the non-classical theories of shells
Ermakov, Andrei M.. 2013. "Numerical and analytical modeling of the stability of the cylindrical shell under the axial compression with the use of the non-classical theories of shells." Lecture Notes in Computer Science (Book series). 8236, pp. 279-286. https://doi.org/10.1007/978-3-642-41515-9_30