1.1.3 Composite shells in cylindrical bending

Products: ABAQUS/Standard  ABAQUS/Explicit  

This example provides verification of the transverse shear stress calculations in ABAQUS for multilayer composite shells and demonstrates the use of the plane stress orthotropic failure measures. A discussion of the transverse shear stresses obtained by composite solids in ABAQUS/Standard is also included. The problem consists of a two- or three-layer plate subjected to a sinusoidal distributed load, as described by Pagano (1969). The resulting transverse shear and axial stresses through the thickness of the plate are compared to two existing analytical solutions by Pagano (1969). The first solution is derived from classical laminated plate theory (CPT), while the second is an exact solution from linear elasticity theory.

Problem description

Failure measures

The plane stress orthotropic failure measures are defined in Plane stress orthotropic failure measures, Section 17.2.3 of the ABAQUS Analysis User's Manual. To demonstrate their use, let the limit stresses and limit strains be given as follows (defined with *FAIL STRESS and *FAIL STRAIN):


Stress Values:S
(GPa)2.07 × 10–4–8.28 × 10–53.45 × 10–6–1.03 × 10–56.89 × 10–6
(lb/in2)30.0–12.00.5–1.51.0
Strain Values:
 17. × 10–2–7. × 10–25. × 10–2–1.3 × 10–211. × 10–2

The scaling factor for the Tsai-Wu coefficient is 0.0. These values are chosen such that failure occurs under the stress-based failure criteria for the given loading in the two-layer case with  4.

Results and discussion

Input files

Reference

Figures

Figure 1.1.3–1 Composite plate subject to distributed loading.

Figure 1.1.3–2 Maximum deflection of two- and three-layer plates with various span-to-thickness ratios; ABAQUS/Standard analysis.

Figure 1.1.3–3 Transverse shear stress distribution through the thickness of a two-layer plate (4); ABAQUS/Standard analysis.

Figure 1.1.3–4 Axial stress distribution through the thickness of a two-layer plate (4); ABAQUS/Standard analysis.

Figure 1.1.3–5 Transverse shear stress distribution through the thickness of a three-layer plate (4); ABAQUS/Standard analysis.

Figure 1.1.3–6 Axial stress distribution through the thickness of a three-layer plate (4); ABAQUS/Standard analysis.

Figure 1.1.3–7 Comparison of the elasticity solution of the transverse shear stress distribution in a three-layer plate to the output variable SSAVG4 with 24 SC8R elements stacked through the thickness; ABAQUS/Standard analysis.

Figure 1.1.3–8 Comparison of the elasticity solution of the transverse shear stress distribution in a three-layer plate to the output variable CTSHR13 with 3 SC8R elements stacked through the thickness; ABAQUS/Standard analysis.

Figure 1.1.3–9 Comparison of the elasticity solution of the transverse shear stress distribution in a two-layer plate to the output variable CTSHR13 with 2 SC8R elements stacked through the thickness; ABAQUS/Standard analysis.

Figure 1.1.3–10 Transverse shear stress distribution through the thickness of a three-layer plate (4): shells versus solid elements; ABAQUS/Standard analysis.

Figure 1.1.3–11 Transverse shear stress distribution through the thickness of a three-layer plate (10); ABAQUS/Standard analysis.

Figure 1.1.3–12 Axial stress distribution through the thickness of a three-layer plate (10); ABAQUS/Standard analysis.

Figure 1.1.3–13 Maximum stress theory and Tsai-Wu theory (0.0) failure indices as a function of normalized distance from the midsurface. Two-layer plate, 4; ABAQUS/Standard analysis.

Figure 1.1.3–14 Maximum stress theory and Tsai-Wu theory (0.0) failure indices as a function of normalized distance from the midsurface. Three-layer plate, 4; ABAQUS/Standard analysis.

Figure 1.1.3–15 Transverse shear stress distribution through the thickness of a two-layer plate; ABAQUS/Explicit analysis.

Figure 1.1.3–16 Axial stress distribution through the thickness of a two-layer plate; ABAQUS/Explicit analysis.

Figure 1.1.3–17 Transverse shear stress distribution through the thickness of a three-layer plate; ABAQUS/Explicit analysis.

Figure 1.1.3–18 Axial stress distribution through the thickness of a three-layer plate; ABAQUS/Explicit analysis.

Figure 1.1.3–19 Maximum stress theory and Tsai-Wu theory failure indices as a function of normalized distance from the midsurface. Two-layer plate; ABAQUS/Explicit analysis.

Figure 1.1.3–20 Maximum stress theory and Tsai-Wu theory failure indices as a function of normalized distance from the midsurface. Three-layer plate; ABAQUS/Explicit analysis.