The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M -dimensional manifold in N -dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M − 1 dimensional ridge in an M = N − 1 dimensional manifold. A ridge of lin...

b Institut Français du Pétrole, 1 et 4 avenue de Bois Préau 92852 Rueil Malmaison, France c present address : Institut Français du Pétrole, 1 et 4 avenue de Bois Préau 92852 Rueil Malmaison, France, [email protected] d present address : Laboratoire LIP CNRS UMR 7623, Université Pierre et Marie Curie, Paris, France, [email protected] * corresponding author August 31, 2009 Lectur...

In this study, nonlinear bending of solid and annular functionally graded (FG) sector plates subjected to transverse mechanical loading and thermal gradient along the thickness direction is investigated. Material properties are varied continuously along the plate thickness according to power-law distribution of the volume fraction of the constituents. According to von-Karman relation for large ...

Mechanical buckling response of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The takes account transverse shear effects parabolic distribution strains through thickness plate; hence it unnecessary to use correction factors. Governing equations are derived from principle virtual displacements. nonlinear strain-displacement Von Karman re...

Abstract An investigation of dynamic behaviors a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by faces on two-parameter elastic foundation and subjected to moving load is carried out in this paper. The present solid composed porous 2D-FG covered homogenous layers. It assumed that the middle layer has micro voids dispersed uniformly unevenly ...

This paper deals with a variational model applicable to small-deformation structural analysis expressed for linearly elastic-perfectly plastic (von Mises-Hubcr-Hencky) material. The model comprises a unification of the minimum complementary energy principal, the Haar-von Karman principle for deformation elastoplasticity, and (in a sense) the lower bound theorem of Limit Analysis. Thus it corres...

A smart-skin antenna structure is investigated for active flutter control with piezoelectric sensors and actuators. The skin designed as a multilayer sandwich dielectric polymer to perform the role of or radar structures. governing equations are developed according first-order shear deformation theory, von Karman strain–displacement relationships used moderate geometrical nonlinearity. To consi...

A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing...

These notes supplement Robert Kohn’s Lecture 3 at the 2014 PCMI Graduate Summer School. For background and heuristic arguments, see the pdf of that lecture. For physicsoriented discussions of this topic see [4] and [3]. For upper and lower energy bounds similar to those presented here but using nonlinear elasticity and a rather general membrane model see [1]. We want to study deformations of a ...