The displacement of three-dimensional linearly elastic plate-like domains can be expanded as a compound power series asymptotics, when the thickness parameter tends to zero. The leading term in this expansion is the well-known Kirchhoff-Love displacement field, which is the solution to the limit plane-stress and bending models. Herein we focus our discussion on plate-like domains with either clamped or free lateral boundary conditions, and characterize the loading conditions for which this leading term vanishes. In these situations the first non-zero term in the expansion appears at rank 2, 3 or 4 and is denoted as higher-order response of order 2, 3 or 4 respectively. The mathematical analysis for higher-order responses (see also the notes on clamped and free plates) is backed-up by numerical simulation using the p-version finite element method.
Rennes, Stuttgart, Beer Sheva, Sept. 1999
International Journal for Numerical Methods in Engineering 53, 2002, 1353-1376.
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