Reference:

K.J. Bathe, E.N. Dvorkin. «A Formulation of General Shell Elements – The Use of Mixed Interpolation of Tensorial Components», Int. Journal for Numerical in Engineering, Vol. 22 No. 3, 1986, pg. 720.

Problem description:

Console plate is loaded by uniformly distributed bending moment along its free edge. Determine displacements w and u at free edge nodes, rotation angle θ at free edge nodes and stresses σ_x at top-layer of plate.

Problem sketch:

Type of created problem:

Spatial structure (X, Y, Z, UX, UY, UZ).

Geometric characteristics:

L = 12 mm; b = 1 mm; t = 1 mm.

Material properties:

Elastic modulus: E = 1800 N/mm²;

Poisson’s ratio: μ = 0.

Boundary conditions:

At left edge of plate: X = Y = Z = UX = UY = UZ = 0.

Loads:

М = 15.708 N·mm.

Model description:

The system is modelled via 12 4-noded geometrically nonlinear FE of tight bend shell elements (FE type is 344) with additional nodes. Automatic selection of step of loading applying for nonlinear problem solution is used.

Calculation results:

Vertical displacements distribution w, mm

Horizontal displacements distribution u, mm

Rotational displacements distribution θ, rad

Distribution of stress σ_x, МPa