Hi friends,
I wrote an essay about Sophie Germain and her work in uncovering the role that geometry in plays in the mechanics of plates and shells. I'm excited to share the essay with this community of mechanicians.
Abstract:
Transverse wrinkles commonly occur in a uniaxially tensile elastic membrane and can vanish upon excess stretching. The wrinkling direction is usually perpendicular to the stretching direction under isotropic elasticity. Here, we show that wrinkles are orientable by material anisotropy, such as in fiber-reinforced or fibrous films, and the wrinkling orientation can be tuned by varying the stiffness and direction of fibers.
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
