1.3.16 Cantilever sandwich beam: shear flexible shells

Product: ABAQUS/Standard

Elements tested

S4 S4R S8R S8RT

Problem description

Material:

For the face a linear elastic material with Young's modulus = 1.0 × 10⁷ and Poisson's ratio = 0 is modeled. For the core the transverse shear moduli are given as 1.0 × 10⁴ and all other properties in the plane are set to negligible values, using the LAMINA definition.

Boundary conditions:

All nodes are clamped at one end.

Loading:

750.0 distributed consistently to the nodes at the free end.

Gauss integration is used for the shell cross-section for the S4R and S8R elements.

Reference solution

Displacement at the free end (Plantema, Sandwich Construction, John Wiley and Sons, Inc., 1966): = 5.5684.

Maximum bending stress at the top of the clamped end, for the case of warping prevention as enforced here: = 3.7275 × 10⁵.

Results and discussion

Element Type
S4	5.55	3.5136 × 10⁵
S4R	5.55	3.5136 × 10⁵
S8R	5.56	3.6439 × 10⁵
S8RT	5.56	3.6439 × 10⁵

Input files

S4 elements.

S4R elements.

S8R elements.

S8RT elements.