A dynamic formulation for the analysis of thick elastic plates by the boundary element method

Free Vibration Analysis of Very Large Rectangular Floating Structures

“…and 11 = ℎ ∬ 22 = 33 = ℎ 3 12 ∬ (18) where in Eqs. (17) and (18) integrations are over the element area. The rectangular plate is discretized by 20×7=140 elements.…”

Dynamic stiffness formulation for isotropic and orthotropic plates with point nodes

“…Levy type solution for simply supported plates has been suitably extended to cover anisotropic plates [9] and there are also some refined plate theories in the published literature [10][11][12]. Clearly, for the case of a simply supported plate, there exists an exact solution for the free transverse vibration in the form of a trigonometric series whereas for other boundary conditions, there are approximate methods such as Rayleigh-Ritz [13][14][15], extended Kantorovich [16], Galerkin [17,18], differential quadrature [19] and boundary element [20,21] amongst a few other methods. Using the Levy type solution one can build an accurate, if not exact, analytical relationship between the amplitudes of forces and displacements at the plate boundaries which are basically the sides or edges of the plate.…”

Stability of E. Reyssner’s plates on the elastic non-winkler foundation

“…For this we represent the desired solution as the sum of two independent solutions -potential and vortex. It is easy to show that the vortex solution does not solve the problem of stability of the system "plate -layer", and therefore we''ll focus only on potential solutions [9]. Let…”