Summary
Classical and refined plate theories derived from linear continuum mechanics lead to correct results only if the transverse deflection of the plate is small compared to its thickness. In the case of large deflections, geometrical nonlinearities have to be incorporated. For the classical Kirchhoff plate theory, a suitable extension for moderate rotations has been presented by von Kármán in 1911.
Starting from the three-dimensional equations of nonlinear continuum mechanics, a family of von Kármán-type plate theories is deduced. For the derivation, the kinematical variables are replaced by a series representation and the principle of virtual displacements is used. It can be shown that most plate theories can be obtained from this type of theory and that the kinematical assumptions must fulfill certain conditions to obtain a solvable system of equations.
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Meenen, J., Altenbach, H. A consistent deduction of von Kármán-type plate theories from three-dimensional nonlinear continuum mechanics. Acta Mechanica 147, 1–17 (2001). https://doi.org/10.1007/BF01182348
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DOI: https://doi.org/10.1007/BF01182348