# Shear deformable plate elements based on exact elasticity solution

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**Shear deformable plate elements based on exact elasticity solution.** / Karttunen, Anssi T.; von Hertzen, Raimo; Reddy, J. N.; Romanoff, Jani.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Computers and Structures*, vol. 200, pp. 21-31. https://doi.org/10.1016/j.compstruc.2018.02.006

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*Computers and Structures*,

*200*, 21-31. https://doi.org/10.1016/j.compstruc.2018.02.006

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TY - JOUR

T1 - Shear deformable plate elements based on exact elasticity solution

AU - Karttunen, Anssi T.

AU - von Hertzen, Raimo

AU - Reddy, J. N.

AU - Romanoff, Jani

PY - 2018/4/15

Y1 - 2018/4/15

N2 - The 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin (i.e., first-order plate theory), Levinson (i.e., a third-order plate theory), and Full Interior plate finite elements. The general plate solution is defined by a biharmonic mid-surface function, which is chosen for the thick plate elements to be the same polynomial as used in the formulation of the well-known nonconforming thin Kirchhoff plate element. The displacement approximation that stems from the biharmonic polynomial satisfies the static equilibrium equations of the 2-D plate theories at hand, the 3-D Navier equations of elasticity, and the Kirchhoff constraints. Weak form Galerkin method is used for the development of the finite element model, and the matrices for linear bending, buckling and dynamic analyses are obtained through analytical integration. In linear buckling problems, the 2-D Full Interior and Levinson plates perform particularly well when compared to 3-D elasticity solutions. Natural frequencies obtained suggest that the optimal value of the shear correction factor of the Mindlin plate theory depends primarily on the boundary conditions imposed on the transverse deflection of the 3-D plate used to calibrate the shear correction factor.

AB - The 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin (i.e., first-order plate theory), Levinson (i.e., a third-order plate theory), and Full Interior plate finite elements. The general plate solution is defined by a biharmonic mid-surface function, which is chosen for the thick plate elements to be the same polynomial as used in the formulation of the well-known nonconforming thin Kirchhoff plate element. The displacement approximation that stems from the biharmonic polynomial satisfies the static equilibrium equations of the 2-D plate theories at hand, the 3-D Navier equations of elasticity, and the Kirchhoff constraints. Weak form Galerkin method is used for the development of the finite element model, and the matrices for linear bending, buckling and dynamic analyses are obtained through analytical integration. In linear buckling problems, the 2-D Full Interior and Levinson plates perform particularly well when compared to 3-D elasticity solutions. Natural frequencies obtained suggest that the optimal value of the shear correction factor of the Mindlin plate theory depends primarily on the boundary conditions imposed on the transverse deflection of the 3-D plate used to calibrate the shear correction factor.

KW - Boundary layer

KW - Eigenvalues

KW - Finite element

KW - Galerkin's method

KW - Interior plate

UR - http://www.scopus.com/inward/record.url?scp=85042403510&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2018.02.006

DO - 10.1016/j.compstruc.2018.02.006

M3 - Article

VL - 200

SP - 21

EP - 31

JO - Computers & Structures

JF - Computers & Structures

SN - 0045-7949

ER -

ID: 18269717