4.9.3 R0031(3): Three-layer sandwich shell under normal pressure loading

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

S4R S8R SC6R SC8R

Problem description

Mesh:

One-quarter model with a 4 × 4 mesh of composite S8R elements in ABAQUS/Standard, an 8 × 8 mesh of composite S4R elements in ABAQUS/Explicit, and an 8 × 8 mesh of continuum shell elements in ABAQUS/Standard. Two types of continuum shell models are provided: (1) a single composite element and (2) three single-layer elements stacked in the thickness direction.

Material:

Face sheets: = 1.0 × 10⁷ psi, = 4.0 × 10⁶ psi, = 0.3, = 1.875 × 10⁶ psi, = 1.875 × 10⁶ psi, = 1.875 × 10⁶ psi

Core: = 10.0 psi, = 10.0 psi, = 0, = 10.0 psi, = 3.0E4 psi, = 1.2E4 psi.

Boundary conditions:

Simply supported on all four edges. The continuum shell models use an equation constraint to provide an equivalent midsurface constraint.

Loading:

Uniform normal pressure of 100 psi.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test R0031/3 from NAFEMS publication R0031, “Composites Benchmarks,” February 1995.

Results and discussion

The results are given in Table 4.9.3–1 and Table 4.9.3–2. The values enclosed in parentheses are percentage differences with respect to the reference solution. The displacements reported for the stacked continuum shell model are the average displacements of the bottom and top skins. Due to the soft core, significant pinching is observed.

Table 4.9.3–1 ABAQUS/Standard analysis.

Model	at C	at C	at C	at E
NAFEMS	–0.123	34449	13932	–5068
S8R	–0.122 (0.6%)	36272 (5.3%)	14125 (5.8%)	–5397 (6.4%)
Composite SC6R	–0.120 (–2.4%)	34687 (0.7%)	13675 (–1.8%)	–5132 (2.5%)
Stacked SC6R	–0.129 (4.8%)	35382 (2.7%)	13745 (–1.3%)	–5219 (3.0%)
Composite SC8R	–0.122 (–0.8%)	35312 (2.5%)	13805 (–0.9%)	–5237 (3.3%)
Stacked SC8R	–0.131(6.5%)	36423 (5.7%)	14009 (0.6%)	–5360 (5.8%)