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Plate Models: Validation and Verification
https://orcid.org/https://orcid.org/0000-0002-6502-0198
We here study the plate models as 2D extension of the beam models. We don’t start with the classical theory of the so-called Kirchhoff plates as 2D generalization of the Euler beam, often referred to as a ‘thin’ plate model that does not account for shear deformation. Such model requires the continuity of second derivatives of transverse displacement field that is not easy to achieve for distorted elements. Hence, we present an alternative model in terms of the Reissner-Mindlin plate as 2D generalization of the Timoshenko beam, yet referred to as a ‘thick’ plate model that can take into account the shear deformation. The variational formulation now requires the inter-element continuity of only the first derivatives of transverse displacement and (independent) rotations, but again lead to locking phenomena in finite element discrete approximations. We present several Reissner-Mindlin plate elements with non-conventional interpolations that can handle locking. We also show how to recover the discrete approximation of the Kirchhoff plate model in terms of the discrete Kirchhoff plate finite element. The plate models presented in this chapter are further used to illustrate typical goals of adaptivity procedure in structural engineering that pertain to model selection or validation, as well as to discrete approximation quality or verification.
Plate Models: Validation and Verification
https://orcid.org/https://orcid.org/0000-0002-6502-0198
We here study the plate models as 2D extension of the beam models. We don’t start with the classical theory of the so-called Kirchhoff plates as 2D generalization of the Euler beam, often referred to as a ‘thin’ plate model that does not account for shear deformation. Such model requires the continuity of second derivatives of transverse displacement field that is not easy to achieve for distorted elements. Hence, we present an alternative model in terms of the Reissner-Mindlin plate as 2D generalization of the Timoshenko beam, yet referred to as a ‘thick’ plate model that can take into account the shear deformation. The variational formulation now requires the inter-element continuity of only the first derivatives of transverse displacement and (independent) rotations, but again lead to locking phenomena in finite element discrete approximations. We present several Reissner-Mindlin plate elements with non-conventional interpolations that can handle locking. We also show how to recover the discrete approximation of the Kirchhoff plate model in terms of the discrete Kirchhoff plate finite element. The plate models presented in this chapter are further used to illustrate typical goals of adaptivity procedure in structural engineering that pertain to model selection or validation, as well as to discrete approximation quality or verification.
Plate Models: Validation and Verification
https://orcid.org/https://orcid.org/0000-0002-6502-0198
We here study the plate models as 2D extension of the beam models. We don’t start with the classical theory of the so-called Kirchhoff plates as 2D generalization of the Euler beam, often referred to as a ‘thin’ plate model that does not account for shear deformation. Such model requires the continuity of second derivatives of transverse displacement field that is not easy to achieve for distorted elements. Hence, we present an alternative model in terms of the Reissner-Mindlin plate as 2D generalization of the Timoshenko beam, yet referred to as a ‘thick’ plate model that can take into account the shear deformation. The variational formulation now requires the inter-element continuity of only the first derivatives of transverse displacement and (independent) rotations, but again lead to locking phenomena in finite element discrete approximations. We present several Reissner-Mindlin plate elements with non-conventional interpolations that can handle locking. We also show how to recover the discrete approximation of the Kirchhoff plate model in terms of the discrete Kirchhoff plate finite element. The plate models presented in this chapter are further used to illustrate typical goals of adaptivity procedure in structural engineering that pertain to model selection or validation, as well as to discrete approximation quality or verification.
Plate Models: Validation and Verification
Lect.Notes in Applied (formerly:Lect.Notes Appl.Mechan.)
Ibrahimbegovic, Adnan (author) / Mejia-Nava, Rosa-Adela (author)
2023-02-24
92 pages
Article/Chapter (Book)
Electronic Resource
English
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