Summary
Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.
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Received 10 January 2002; accepted for publication 16 April 2002
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Kienzler, R. On consistent plate theories . Archive of Applied Mechanics 72, 229–247 (2002). https://doi.org/10.1007/s00419-002-0220-2
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DOI: https://doi.org/10.1007/s00419-002-0220-2