Abstract
Based on the approximation theory adopting non-kirchhoff-Love assumption for three dimensional elastic plates with arbitrary shapes[1],[2], the author derives a functional of generalized variation for three dimensional elastic circular plates, thereby obtains a set of differential equations and the relate boundary conditions to establish a first order approximation theory for elastic circular plate with fixed boundary and under uniform loading on one of its surface. The analytical solution of this problem will present in another paper.
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References
Chien Weizang, Approximation theory of three dimensional elastic plates and its boundary conditions without using Kirchhoff-Love assumptions,Applied Mathematics and Mechanics,16, 3 (1995), 203–224.
Chien Weizang, The second order approximation theory of three dimensional elastic plates- and its boundary conditions without using Kirchhoff-Love Assumptions,Applied Mathematics and Mechanics,16, 5 (1995), 405-427.
Chien Weizang, Further study of generalized variational principles in elasticity,Advance of Applied Mathematics and Mechanics in China, Edited by Chien, W. Z. and Fu. Z. Z., 1 (1987), 1–10
Chien Weizang, Incompatible elements and generalized variational principles,Advances in Applied Mechanics, U. S. A.,14 (1984), 93–153.
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Weizang, C. The first order approximation of non-Kirchhoff-Love theory for elastic circular plate with fixed boundary under uniform surface loading (I). Appl Math Mech 18, 1–18 (1997). https://doi.org/10.1007/BF02457496
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DOI: https://doi.org/10.1007/BF02457496