Abstract
A framework for the asymptotic derivation of plate models from three-dimensional elasticity theory is reviewed and extended. This is shown to subsume the pure membrane and bending limits that have been derived via gamma convergence or alternative asymptotic methods, and to incorporate Koiter’s model for finite deformations with small midsurface strains. A model that accommodates large midsurface strains and which satisfies the relevant Legendre-Hadamard necessary condition for energy minimizers is also proposed.
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We gratefully acknowledge the support of the US National Science Foundation through grant CMMI-1538228.
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Shirani, M., Steigmann, D.J. (2019). Asymptotic Derivation of Nonlinear Plate Models from Three-Dimensional Elasticity Theory. In: Altenbach, H., Chróścielewski, J., Eremeyev, V., Wiśniewski, K. (eds) Recent Developments in the Theory of Shells . Advanced Structured Materials, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-030-17747-8_30
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