plate theory

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