Kirchhoff-Mindlin circular plate under uniform transverse pressure

Bending of a clamped circular plate under uniform transverse pressure. The analytical benchmark combines the classical Kirchhoff thin-plate flexural solution with the Mindlin first-order shear deformation correction (Reissner-Mindlin plate theory).

Tolerance:

5%

Problem statement

Geometry

Circular plate of radius R = 1000 mm, thickness t = 20 mm (R/t = 50, slender-to-moderately thick plate), modeled with shell finite elements.

Material

Isotropic linear elastic material: Young's modulus E = 210 GPa (210000 MPa), Poisson's ratio nu = 0.3, shear modulus G = E / [2*(1+nu)] = 80769.23 MPa, shear correction factor kappa = 5/6.

Boundary conditions

Fully clamped boundary along outer edge r = R (all translational and rotational DOFs fixed); quarter-symmetry boundary conditions on x = 0 and y = 0 planes; uniform transverse pressure q = 0.01 MPa (10 kPa) applied across the surface.

Measured quantity

Central vertical deflection w_center against analytical Kirchhoff-Mindlin reference: w_center = q*R^4/(64*D) + q*R^2/(8*kappa*G*t) = 1.016554 mm, where D = E*t^3/[12*(1-nu^2)] = 1.538462e8 N*mm.

WebCAE Terminal

units mm
material E=210000 nu=0.3
sketch points=0,0,0,1000,0,0,1000,1000,0,0,1000,0 as=face
section shell t=20
mesh shell size=40 element=quad pattern=structured
fix edge number 1
fix edge number 2 component=x
fix edge number 4 component=y
load surface number 1 pressure=0.01
solve
probe displacement_magnitude at=0,0,0

Results comparison

Updated: 2026-10-19 · WebCAE solver