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2 results on '"uniformly valid plate theory"'

1. A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates.

Author

Wang, Fan-Fan, Dai, Hui-Hui, and Giorgio, Ivan

Subjects
*ELASTIC plates & shells, *NAVIER-Stokes equations, *THREE-dimensional modeling, *FINITE element method
Abstract

In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations. [ABSTRACT FROM AUTHOR]

Published
2022
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2. A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

Author

Hui-Hui Dai, Fan-Fan Wang, and Ivan Giorgio

Subjects
weak formulation, numerical analysis, uniformly valid plate theory, General Mathematics, large deformations, 3d model, 02 engineering and technology, Weak formulation, Physics::Fluid Dynamics, Software, 0203 mechanical engineering, General Materials Science, Physics, business.industry, Numerical analysis, Mathematical analysis, 021001 nanoscience & nanotechnology, Finite element method, 020303 mechanical engineering & transports, Mechanics of Materials, finite-element method, Plate theory, Compressibility, 0210 nano-technology, business
Abstract

In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations.

Published
2021

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