Abstract
Kirchhoff’s classical theory of bending of elastic plates is widely used in mechanical engineering for the mathematical modeling of structures consisting of thin elements. Since most of the solutions in such problems are found computationally, it is very useful to have a tool that provides tight a priori estimates for the error. In this chapter, we construct an algorithm that generates such estimates by means of what is called a dual functional. The argument is constructed variationally and is illustrated by means of a numerical example.
Similar methods for the plate model with transverse shear deformation have been developed in [ChCoKo00] and [ChEtAl06]. A full mathematical study of the static and dynamic bending within the framework of this model can be found in [ChCo00] and [ChCo05], respectively.
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References
Timoshenko, S., Woinowsky-Krieger, S.: Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York (1987).
Chudinovich, I., Constanda, C., Koshchii, A.: The classical approach to dual methods for plates. Quart. J. Mech. Appl. Math., 53, 497-510 (2000).
Chudinovich, I., Constanda, C., Doty, D., Koshchii, A.: Non-classical dual methods in equilibrium problems for thin elastic plates. Quart. J. Mech. Appl. Math., 59, 125-137 (2006).
Chudinovich, I., Constanda, C.: Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation, Chapman & Hall/CRC, Boca Raton, FL (2000).
Chudinovich, I., Constanda, C.: Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes, Springer, London (2005).
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Chudinovich, I., Constanda, C., Doty, D., Koshchii, A. (2010). Solution Estimates in Classical Bending of Plates. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 2. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4897-8_10
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DOI: https://doi.org/10.1007/978-0-8176-4897-8_10
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