Three ways to derive the classical plate model
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Attached is part of my lecture notes for a graduate structural mechanics. In
the notes, we derived the classical plate theory, which is also called
the Kirchhoff plate theory, in three ways: Newtonian method, variational
method, and variational asymptotic method, using 3D elasticity theory as the
starting point. The self-contradictions of Kirchhoff assumptions and plane-stress assumptions used in both
Newtonian method and variational method are clearly pointed out. The
variational asymptotic method does not rely on any ad hoc assumptions, ending
in a self-consistent theory. It can be considered as a theoretical
tutorial for VAPAS, a general-purpose tool for modeling composite plates.