Thick Plate Theory (Mindlin Plate Theory)

If the thickness t of a plate is not “thin”, e.g., t / L ≥1/10 (L = a characteristic dimension of the plate), then the thick plate theory by Mindlin should be applied. This theory accounts for the angle changes within a cross section, that is,

γ xz ≠ 0, γ yz ≠ 0.

This means that a line which is normal to the mid surface before the deformation will not be so after the deformation.

w

∂w x

∂x

New independent variables:

θx and θy : rotation angles of a line, which is normal to the

mid surface before the deformation, about x- and y-axis, respectively.

New relations:

γxz = ∂∂wx +θy ,

γyz = ∂∂wy −θx .

Note that if we imposed the conditions (or assumptions)

that

then we can recover the relations applied in the thin plate theory.

Main variables: w(x, y),θx (x, y)andθy (x, y) .

The governing equations and boundary conditions can be established for thick plate based on the above assumptions.