This paper develops a model for evolving wrinkles in a bilayer thin film consisting of an elastic layer and a viscoelastic layer. The elastic layer is subjected to a compressive residual stress and is modeled by the nonlinear von Karman plate theory. A thin-layer approximation is developed for the viscoelastic layer. The stability of the bilayer and the evolution of wrinkles are studied first b...

A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving surface. The method is applied to three problems in nonlinear elasticity: the bulging of a thin plate under pressure (the original motivation for Föppl-von Karma...

The branching of un,symmetric equilibrium states from axisymmetric equilibrium states for clamped circular plates subjected to a uniform edge thrust and a uniform lateral pressure is analyzed in this paper. The branching process is called wrinkling and the loads at which branching occurs are called wrinkling loads. The nonlinear von Karman plate theory is employed. The wrinkling loads are deter...

We study the linearized Föpl – von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2α. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness σ and the bending angle. We show that the minimum energy scales as σα. This scaling is in sharp contrast with previously obtained results for the linearized theory of ...

In this study, the buckling response of homogeneous circular plates with variable thickness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal thickness distribution over the plate with respect to buckling is presented. In order to determine the distr...

Abstract Current design approaches to determine the capacity of plates in local buckling are based on empirical equations, particular widely used Winter equation. In contrast, this research presents a novel analytical approach, focusing outstand steel plates. The derivation method is rooted Föppl‐von Karman which first simplified by making number basic mechanical assumptions about post‐buckling...

in the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. the basic assumption is that the class of functions that we investigate here, except the verification of dirichlet's principles, is concurrently able to be expanded in taylor's representation, over a particular interval o...