핵심 개념
The authors present an asymptotically accurate and shear-locking-free finite element implementation of the first-order shear deformation theory (FSDT) for linear-elastic homogeneous plates.
초록
The key highlights and insights of the content are:
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The authors formulate the FSDT for plates in rescaled coordinates and rotation angles, which makes the problem independent of the plate thickness and inherently shear-locking-free.
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They develop a finite element implementation of the rescaled FSDT using isogeometric analysis with NURBS shape functions, which ensures C1-continuity of the solution and achieves asymptotic accuracy.
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Numerical simulations of circular and rectangular plates are performed, showing complete agreement between the analytical solution, the numerical solution based on the 2D FSDT, and the numerical solution of the 3D elasticity theory.
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The rescaled formulation and the use of isogeometric elements eliminate the need for high-order interpolation schemes and sophisticated integration techniques, significantly improving the computational efficiency.
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The proposed approach provides a simple and effective way to avoid the shear-locking effect, which is a common issue in the numerical implementation of FSDT for plates.
통계
The authors provide the following key figures and equations to support their analysis:
Equation (9): The rescaled variational formulation of the FSDT for plates.
Equation (12): The expression for the true average displacement of the plate.
Equations (48)-(51): The analytical solution for the bending of a rectangular plate with one clamped edge and three free edges.
Equations (52)-(53): The solution based on the classical Kirchhoff plate theory.
인용구
"The goal of this paper is therefore twofold. First, we give the formulation of the FSDT for plates in the rescaled coordinates and rotation angles. This formulation occurs naturally when the coordinates in the mid-plane are scaled by the plate thickness h (thus becoming dimensionless), while the rotation angles are multiplied by h, resulting in equal and finite orders of the bending and shear stiffnesses as well as the scaled rotation angles and bending measures."
"Since this formulation is independent of the plate thickness and inherently shear-locking-free, no high-order interpolation scheme and/or sophisticated integration technique is required for the discretization and FE-implementation, so the computational efficiency can be significantly improved."