Assessment of the consistent second-order plate theory for isotropic plates from the perspective of the three-dimensional theory of elasticity

Reinhold Kienzler* (Corresponding Author), Maria Kashtalyan

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In this paper, the consistent second-order plate theory for isotropic plates is validated against the three-dimensional elasticity theory using a well-known benchmark problem of a simply-supported rectangular plate subjected to symmetric transverse sinusoidal loading. The choice of the benchmark problem is based on the fact that it allows for an exact three-dimensional elasticity solution to be derived in closed-form. In the paper, two equivalent closed-form solutions are employed for validation purposes, one of which is specifically derived for this study. Once the equivalence of the two closed-form analytical solutions is established, they are expanded into a power-law series with respect to the non-dimensionalised plate thickness. This enables a direct term-by-term comparison with the consistent second-order plate theory solution and provides a valuable mechanism to validate the consistent plate theory in purely analytical form. The term-by term comparison reveals that the first terms of the above power-law series coincide exactly with the expressions of the consistent second-order plate theory. In addition to the analytical validation, a parametric study is carried out with a view to establish the range of applicability of the consistent second-order plate theory in terms of the thickness-to-length ratio. It is demonstrated that the consistent plate theory can predict displacements and stresses in thick plates with very high degree of accuracy, such that even for very thick plates with thickness-to-length ratio of 1/2, the deviation from the three-dimensional elasticity solution is less than 1%.
Original languageEnglish
Pages (from-to)257-271
Number of pages15
JournalInternational Journal of Solids and Structures
Volume185-186
Early online date29 Aug 2019
DOIs
Publication statusE-pub ahead of print - 29 Aug 2019

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plate theory
Plate Theory
Elasticity
elastic properties
Three-dimensional
Term
thick plates
Power Law
Closed-form
Benchmark
rectangular plates
Series
Rectangular Plate
Elasticity Theory
Closed-form Solution
equivalence
Analytical Solution
Transverse
Deviation
Equivalence

Keywords

  • Consistent plate theory
  • Isotropic plate
  • Three-dimensional theory of elasticity
  • Closed-form solution
  • Youngdahl's displacement potentials

Cite this

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title = "Assessment of the consistent second-order plate theory for isotropic plates from the perspective of the three-dimensional theory of elasticity",
abstract = "In this paper, the consistent second-order plate theory for isotropic plates is validated against the three-dimensional elasticity theory using a well-known benchmark problem of a simply-supported rectangular plate subjected to symmetric transverse sinusoidal loading. The choice of the benchmark problem is based on the fact that it allows for an exact three-dimensional elasticity solution to be derived in closed-form. In the paper, two equivalent closed-form solutions are employed for validation purposes, one of which is specifically derived for this study. Once the equivalence of the two closed-form analytical solutions is established, they are expanded into a power-law series with respect to the non-dimensionalised plate thickness. This enables a direct term-by-term comparison with the consistent second-order plate theory solution and provides a valuable mechanism to validate the consistent plate theory in purely analytical form. The term-by term comparison reveals that the first terms of the above power-law series coincide exactly with the expressions of the consistent second-order plate theory. In addition to the analytical validation, a parametric study is carried out with a view to establish the range of applicability of the consistent second-order plate theory in terms of the thickness-to-length ratio. It is demonstrated that the consistent plate theory can predict displacements and stresses in thick plates with very high degree of accuracy, such that even for very thick plates with thickness-to-length ratio of 1/2, the deviation from the three-dimensional elasticity solution is less than 1{\%}.",
keywords = "Consistent plate theory, Isotropic plate, Three-dimensional theory of elasticity, Closed-form solution, Youngdahl's displacement potentials",
author = "Reinhold Kienzler and Maria Kashtalyan",
note = "Acknowledgement Financial support of this research by The Royal Society, United Kingdom, International Exchanges award (IE161021) is gratefully acknowledged.",
year = "2019",
month = "8",
day = "29",
doi = "10.1016/j.ijsolstr.2019.08.035",
language = "English",
volume = "185-186",
pages = "257--271",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",

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T1 - Assessment of the consistent second-order plate theory for isotropic plates from the perspective of the three-dimensional theory of elasticity

AU - Kienzler, Reinhold

AU - Kashtalyan, Maria

N1 - Acknowledgement Financial support of this research by The Royal Society, United Kingdom, International Exchanges award (IE161021) is gratefully acknowledged.

PY - 2019/8/29

Y1 - 2019/8/29

N2 - In this paper, the consistent second-order plate theory for isotropic plates is validated against the three-dimensional elasticity theory using a well-known benchmark problem of a simply-supported rectangular plate subjected to symmetric transverse sinusoidal loading. The choice of the benchmark problem is based on the fact that it allows for an exact three-dimensional elasticity solution to be derived in closed-form. In the paper, two equivalent closed-form solutions are employed for validation purposes, one of which is specifically derived for this study. Once the equivalence of the two closed-form analytical solutions is established, they are expanded into a power-law series with respect to the non-dimensionalised plate thickness. This enables a direct term-by-term comparison with the consistent second-order plate theory solution and provides a valuable mechanism to validate the consistent plate theory in purely analytical form. The term-by term comparison reveals that the first terms of the above power-law series coincide exactly with the expressions of the consistent second-order plate theory. In addition to the analytical validation, a parametric study is carried out with a view to establish the range of applicability of the consistent second-order plate theory in terms of the thickness-to-length ratio. It is demonstrated that the consistent plate theory can predict displacements and stresses in thick plates with very high degree of accuracy, such that even for very thick plates with thickness-to-length ratio of 1/2, the deviation from the three-dimensional elasticity solution is less than 1%.

AB - In this paper, the consistent second-order plate theory for isotropic plates is validated against the three-dimensional elasticity theory using a well-known benchmark problem of a simply-supported rectangular plate subjected to symmetric transverse sinusoidal loading. The choice of the benchmark problem is based on the fact that it allows for an exact three-dimensional elasticity solution to be derived in closed-form. In the paper, two equivalent closed-form solutions are employed for validation purposes, one of which is specifically derived for this study. Once the equivalence of the two closed-form analytical solutions is established, they are expanded into a power-law series with respect to the non-dimensionalised plate thickness. This enables a direct term-by-term comparison with the consistent second-order plate theory solution and provides a valuable mechanism to validate the consistent plate theory in purely analytical form. The term-by term comparison reveals that the first terms of the above power-law series coincide exactly with the expressions of the consistent second-order plate theory. In addition to the analytical validation, a parametric study is carried out with a view to establish the range of applicability of the consistent second-order plate theory in terms of the thickness-to-length ratio. It is demonstrated that the consistent plate theory can predict displacements and stresses in thick plates with very high degree of accuracy, such that even for very thick plates with thickness-to-length ratio of 1/2, the deviation from the three-dimensional elasticity solution is less than 1%.

KW - Consistent plate theory

KW - Isotropic plate

KW - Three-dimensional theory of elasticity

KW - Closed-form solution

KW - Youngdahl's displacement potentials

UR - http://www.mendeley.com/research/assessment-consistent-secondorder-plate-theory-isotropic-plates-perspective-threedimensional-theory

U2 - 10.1016/j.ijsolstr.2019.08.035

DO - 10.1016/j.ijsolstr.2019.08.035

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EP - 271

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

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