variational asymptotic method

Three ways to derive the classical plate model

Submitted by Wenbin Yu on Fri, 04/13/2012 - 04:20

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

Three-ways to derive the Euler-Bernoulli-Saint Venant Beam Theory

Submitted by Wenbin Yu on Wed, 03/28/2012 - 16:11

variational asymptotic method

extension

After having taught graduate structural mechanics for several years, I am finally
able to write down my lecture notes (attached) for teaching the beam theory. In
the notes, we formulated the complete classical beam model
(extension/torsion/bending in two directions), which is also called
Euler-Bernoulli-Saint beam theory, in three ways: Newtonian method, variational
method, and variational asymptotic method, using 3D elasticity theory as the
starting point. Many self-contradictions of the various assumptions used in both
Newtonian method and variational method are clearly pointed out. The

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