Chang-Yong Lee (1,2) and Dewey H. Hodges (3)
(1) Interdisciplinary Program of Biomedical Engineering, Pukyong National University, Busan 608–737, Republic of Korea
(2) Department of Mechanical Engineering, Pukyong National University, Busan 608–739, Republic of Korea
(3) Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0150, USA
“Hybrid energy transformation to generalized Reissner-Mindlin model for laminated composite shells”, International Journal of Engineering Science, Vol. 122, pp 30-55, January 2018, https://doi.org/10.1016/j.ijengsci.2017.09.006
ABSTRACT: By using the variational-asymptotic method, a two-dimensional mechanical model for laminated composite shells is established from a mathematical perspective, having the energy functional asymptotically correct up to the desired order in the small parameters. However, it is not in a practical form from an engineering perspective because of the appearance of partial derivative terms, which bring unnecessary mathematical complexity and obscure physical interpretation of mechanical boundary conditions in the shell modeling. Therefore, one more procedure is inevitably required – a so-called energy transformation procedure, which constructs a mathematical link between the energy functional derived herein and a simpler engineering model, such as a generalized Reissner–Mindlin model. In a different manner from previous works, this article introduces a hybrid energy transformation procedure composed of two successive steps: an equilibrium transformation via a linear algebraic approach, and an energy transformation via a perturbation approach. During this procedure, the first step is to transform the two-dimensional equilibrium equations from a hyper-static system into an isostatic system by augmenting them with the two-dimensional compatibility equations. Then, for obtaining a generalized Reissner–Mindlin model, the second step is to introduce initial curvature/twist as small parameters (in the sense of perturbations) into the constitutive law. The coupling stiffness terms between the transverse shear generalized strain measures and the remaining generalized Reissner–Mindlin strain measures are shown to be identically zero for laminated composite plates/shells (in contrast to the analogous terms of a similarly constructed generalized Timoshenko model for composite beams). Several examples are presented to demonstrate the capability and accuracy of this new approach.
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