Conservative Numerical Methods for the Full von Kármán Plate Equations

Dynamic response of various von-Kármán non-linear plate models and their 3-D counterparts

Dynamic von-Kármán plate models consist of three coupled non-linear, time-dependent partial differential equations. These equations have been recently solved numerically [Kirby, R., Yosibash, Z., 2004. Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method. Comp. Meth. Appl. Mech. Eng. 193 (6–8) 575–599 and Yosibash, Z., Kirby, R., Gottlieb, D., 2004. Pseudo-sp...

Finite element approximations of the von Kármán equations

— We analyse a général technique in order to prove the convergence and optimal error boundsfor suitable finite element approximations of the von Kârmân plate bending équations.

Mechanics of Materials and Structures SOLUTIONS OF THE VON KÁRMÁN PLATE EQUATIONS BY A GALERKIN METHOD, WITHOUT INVERTING THE TANGENT STIFFNESS MATRIX

The Von Kármán Equations for Plates with Residual Strain

We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three dimensional equations of elasticity to the low-dimensional des...

Existence of solutions to a dynamic contact problem for a thermoelastic von Kármán plate

We study a dynamic contact problem for a thermoelastic von Kármán plate vibrating against a rigid obstacle. Dynamics is described by a hyperbolic variational inequality for deflections. The plate is subjected to a perpendicular force and to a heat source. The parabolic equation for a thermal strain resultant contains the time derivative of the deflection. We formulate a weak solution of the sys...