Verification of section forces for shells

Elements tested

S4R

S4R5

S8R

S8R5

S9R5

STRI3

STRI65

Problem description

Material:

Linear elastic, $E_{11} = $ 2.00313 × 10⁷, $E_{22} = $ 5.00783 × 10⁵, $E_{12} = $ 1.25296 × 10⁵, $G_{13} = $ 0.5 × 10⁵, $G_{23} = $ 0.5 × 10⁵.

Boundary conditions:

Nodes along edge $A D$ are clamped.

Loading:

$F_{z} = $ 0.5 at nodes B and C.

Orientations

90° in the first layer and 0° in the second layer, with respect to the x-axis, rotated about the z-axis.

There are two elements with identical geometries in the model. The first element is defined using a composite shell section and uses a local coordinate system. The second element is defined using a general shell section, with the section stiffness matrix input directly, and is equivalent to the two-layer model presented above.

The section stiffness is:

D = [\begin{matrix} 0.2053 \times 10^{7} & 0.2506 \times 10^{5} & 0.0 & 0.9765 \times 10^{5} & 0.0 & 0.0 \\ 0.2053 \times 10^{7} & 0.0 & 0.0 & - 0.9765 \times 10^{5} & 0.0 \\ Symmetric & 0.5 \times 10^{5} & 0.0 & 0.0 & 0.0 \\ 0.6844 \times 10^{4} & 0.8346 \times 10^{2} & 0.0 \\ 0.6844 \times 10^{4} & 0.0 \\ 0.1667 \times 10^{3} \end{matrix}]

Reference solution

Stress resultants: Moment = −1.0(10.0 − x).

Results and discussion

All elements yield acceptable solutions. Local coordinate directions are requested in the input file with element type S8R5 (es58s2sc.inp).

Input files

ese4s2sc.inp: S4 elements.
esf4s2sc.inp: S4R elements.
es54s2sc.inp: S4R5 elements.
es68s2sc.inp: S8R elements.
es58s2sc.inp: S8R5 elements.
es59s2sc.inp: S9R5 elements.
es63s2sc.inp: STRI3 elements.
es56s2sc.inp: STRI65 elements.