The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacem...

We show that mode jumping in the buckling of a rectangular plate may be explained by a secondary bifurcation as suggested by Bauer et al. [1] when "clamped" boundary conditions on the vertical displacement function are assumed. In our analysis we use the singularity theory of mappings in the presence of a symmetry group to analyse the bifurcation equation obtained by the Lyapunov-Schmidt reduct...

The flow of a thin layer of power-law fluid on a porous inclined plane is considered. The unsteady equations of motion are depth-integrated according to the von Karman momentum integral method. The variation of the velocity distribution with the depth is accounted for, and it is furthermore assumed that the flow through the porous medium is governed by the modified Darcy’s law. The stability co...

A nonlinear transmisson problem for an elastic full von Karman beam is considered here. We prove that the system possesses a compact global attractor.

The morphology of telephone-cord buckles of elastic thin films can be used to evaluate the initial residual stress and interface toughness of the filmsubstrate system. The maximum out-of-plane displacement δ, the wavelength λ and amplitude A of the wave buckles can be measured in physical experiments. Through δ, λ, and A, the buckle morphology is obtained by an annular sector model established ...

fiber/ metal laminates (fmls) are hybrid composites consisting of alternating thin layers of metal sheets and fiber reinforced epoxy laminates. in this study, the effect of fiber orientation on impact properties of fml plates is investigated both analytically and experimentally. two groups of specimens were prepared and tested in two different levels of impactor energy. the indentation depth an...

The Bénard-von Karman vortex shedding instability in the wake of a cylinder is perhaps the best known example of a supercritical Hopf bifurcation in fluid dynamics. However, a simplified physical description that accurately accounts for the saturation amplitude of the instability is still missing. Here we present a simple self-consistent model that provides a clear description of the saturation...

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically,...

The plant hormone auxin is fundamental for plant growth, and its spatial distribution in plant tissues is critical for plant morphogenesis. We consider a leading model of the polar auxin flux, and study in full detail the stability of the possible equilibrium configurations. We show that the critical states of the auxin transport process are composed of basic building blocks, which are isolated...