Transverse shear for shear-flexible shells

The model consists of a composite plate with a length of 10.0, width of 1.0, and thickness of 1.5. Plane strain conditions are imposed in the y-direction (parallel to the unit width), the end at $x=$ 0 is fixed, and various boundary conditions are applied to the remaining degrees of freedom (refer to input files). A single shell element is used to model the plate. The plate has three layers of equal thickness (0.5) defined using a composite shell section or a composite general shell section. Three integration points are specified in each layer for a total of nine points through the thickness.

Orthotropic elasticity in a plane stress is used to define an orthotropic material with $E_1=$ 25 × 10⁶, $E_2=$ 1 × 10⁶, ${\nu }_{12}=$ 0.25, $G_{13}=$ 0.5 × 10⁶ and $G_{23}=$ 0.2 × 10⁶. The material orientation is specified such that the local 1-direction for layers 1 and 3 is parallel to the x-axis, and the local 1-direction for layer 2 is parallel to the y-axis. A user-defined material that has equivalent behavior to the linear elastic material is also tested.

A section orientation is used with the general shell section tests such that the 1-direction is parallel to the y-axis and the 2-direction is parallel and opposite to the x-axis. This section orientation only changes local directions for the section forces and section strains.

Gauss integration is used for the shell cross-section for elements S4, S4R, and S8R.

Two groups of tests are performed; all forces are applied at $x=$ 10.

Static tests:

Step 1, uniaxial tension: total force of 20000 in the x-direction.

Step 2, transverse shear: total force of 20000 in the z-direction.

Step 3, pure bending: total moment of 20000 about the y-axis.

Static and dynamics tests:

(The first two static steps are performed to correlate (closely) with the eigenmode results of the frequency step.)

Step 1, static, transverse shear: $u_z=$ 1 at the $x=$ 10 edge.

Step 2, static, uniaxial tension: $u_x=$ 1 at the $x=$ 10 edge.

Step 3, frequency: extract four lowest eigenmodes.

Step 4, steady-state dynamics: total force of 20000 in the z-direction.

Step 5, steady-state dynamics, direct: total force of 20000 in the z-direction.

Step 6, modal dynamic: total force of 20000 in the z-direction.

Step 7, response spectrum.