Flexure under Line Load

The graph below allows you to test the influence of different line loads/displacements and effective elastic thickness on the flexure of a plate. Just drag the sliders to modify the values. You find a short description of the governing equation below.

Young’s Modulus [GPa]:
Poisson’s Ratio:

Plate Flexure due to Line Load

Flexure, w, of an elastic plate due to a line load / end displacement, w_0, is

w = w_0{e^{ - x/\alpha }}\left( {\cos {x \over \alpha } + \sin {x \over \alpha }} \right)

If the plate is broken then the sine term is dropped.

x is the distance from the line load and \alpha is

\alpha  = {\left( {{{4D} \over {\left( {{\rho_m} - {\rho_w}} \right)g}}} \right)^{1/4}}

where D is the flexural rigidity, which is related to Young’s modulus E, Poisson’s ratio \nu, and the effective elastic thickness h through

D = {{E{h^3}} \over {12\left( {1 - {\nu ^2}} \right)}}

The other variables are the density of the mantle, \rho_m, the density of water, \rho_w, and the gravity acceleration, g.

A more detailed derivation can be found in Geodynamics by Turcotte and Schubert.