We derive the Euler-Lagrange equation corresponding to 'non-Euclidean' convex constrained von Kármán theories.

In the present work, we consider a one-dimensional Von kármán beam with infinite memory, establish well-posedness of system using semigroup theory and prove exponential stability under some conditions on kernel memory term.

This paper develops a computational model for nonlinear bending analysis of functionally graded (FG) plates using a four-node quadrilateral element SQ4T within the context of the first order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations are based on Total Lagrangian approach in which the motion at the present state compared with the initia...

We propose a Newton-GMRES type algorithm to solve the discrete von Kármán problem. We show that this algorithm is efficient both in memory and computation time and robust in the neighborhood of the singular points of the bifurcation diagrams. Placing ourselves in the context of the Schaeffer and Golubitsky theory, we use this algorithm to study the post-buckling behavior of a rectangular plate ...

The present study is concerned with thin isotropic shallow shells interacting with inviscid fluid flow of constant velocity. It is assumed that the dynamic behaviour of the shells is governed by the Marguerre–von Kármán equations. The influence of the fluid flow is taken into account by introducing additional differential and external load terms in the shell equations. It is shown that the syst...

This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system...

In 1911 Theodore von Kármán first noticed the unusual alternating stream of vortices that result from fluid flowing past a cylinder. This phenomenon, now known as a von Kármán vortex street, only occurs for fluids with particular characteristics. The most important attribute, is the Reynolds number, which is the ratio of inertial forces to viscous forces in the fluid. It turns out that vortices...

Wafer made from single crystal gallium arsenide (GaAs) are used as substrate materials in microand opto-electronic devices. During the various processes of manufacturing, the wafers are subjected to mechanical loads which may lead to fracture. The characterization of the fracture strength of the wafers need bending tests and a theoretical calculation of various stress distributions within the w...

in this paper the nonlinear bending analysis of thick functionally graded plates subjected to mechanical loading is studied. the formulation is derived based on the third-order shear deformation plate theory and von kármán type non-linearity. young’s modulus is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. the principle of virtual wo...

We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a deformation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. However, for both small deflections using classical linear elastic theory and large deflections usi...