Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 420, Issue 1, Pages 48-65Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.05.016
Keywords
Bimodulus; Biparametric perturbation method; Combined load; Generalized displacement; von Karman equations
Categories
Funding
- Natural Science Foundation of Chongqing [cstc2013jcyjA30012]
- National Natural Science Foundation of China [51178485]
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The large deflection condition of a bimodular plate may yield a dual nonlinear problem where the superposition theorem is inapplicable. In this study, the bimodular Foppl-von Karman equations of a plate subjected to the combined action of a uniformly distributed load and a centrally concentrated force are solved using a biparametric perturbation method. First, the deflection and radial membrane stress were expanded in double power series with respect to the two types of loads. However, the biparametric perturbation solution obtained exhibited a relatively slow rate of convergence. Next, by introducing a generalized load and its corresponding generalized displacement, the solution is expanded in a single power series with respect to the generalized displacement parameter, thereby leading to the better convergence on the solution. A numerical simulation is also used to verify the correctness of the biparametric perturbation solution. The introduction of a bimodular effect will modify the stiffness of the plate to some extent. In particular, the bearing capacity of the plate will be strengthened further when the compressive modulus is greater than the tensile modulus. (C) 2014 Elsevier Inc. All rights reserved.
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