Non-classical dual methods in equilibrium problems for thin elastic plates

Edge layers in thin elastic plates

Monique DAUGE and Isabelle GRUAIS Abstract. This paper deals with the asymptotics of the displacement of a thin elastic plate when it is submitted to various boundary conditions on its lateral face: namely, hard and soft clamped conditions, and hard support. Of particular interest is the in uence of the edges of the plate where boundary conditions of di erent types meet. The singular perturbati...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Non-Classical Problems in the Theory of Elastic Stability

When a structure is put under an increasing compressive load, it may become unstable and buckle. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that inherently exist in real systems. The techniques ...

Meshfree Particle Methods for Thin Plates

For thin plate problems, using the Kirchoff hypothesis, the three dimensional elasticity equations are reduced to a fourth order PDE for the vertical displacement. Conventional FEM has difficulties with this because the basis functions are required to have continuous partial derivatives. Meshfree methods have the advantage of constructing smooth approximation functions, but have difficulties in...

Thermoelastic Relaxation in Elastic Structures, with Applications to Thin Plates

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal...