Products: ABAQUS/Standard ABAQUS/Explicit
For the general shell, membrane, and continuum shell elements the model consists of a tapered plate of length 100 and width 20, as shown in Figure 2.3.13–1. The plate is clamped at one end, and the thickness varies linearly across the plate from 3 at the clamped end to 1 at the free end. The model consists of 10 elements along the length and 2 across the width. For the model using continuum shell elements the thickness is defined by the nodal geometry.
For the axisymmetric elements the model consists of a tapered cylinder, with a radius of 1 × 106 and a length of 100, as shown in Figure 2.3.13–2. The cylinder is clamped at one end, and the thickness varies linearly along the length of the cylinder from 3 at the clamped end to 1 at the free end. The radius is chosen to be very large to ensure that the effects of circumferential stresses are negligible. The cylinder is meshed with 10 elements.
A linear elastic material with a Young's modulus of 10 × 109, a Poisson's ratio of 0, and a density of 8000 is used for all the tests. The thicker ends of the plate and cylinder are fully clamped. The shell elements are loaded with a bending moment of 3 per unit length at the thin end of the shell, and the membrane elements are loaded with an in-plane force of 50 per unit length at the thin end of the membrane.
The ABAQUS/Standard results for shell and continuum shell elements are shown in Table 2.3.13–1. The ABAQUS/Explicit results for shell and continuum shell elements are shown in Table 2.3.13–2 and for membrane elements in Table 2.3.13–3. The differences in the ABAQUS/Explicit results are due to dynamic effects and mesh discretization. For the shell elements in ABAQUS/Explicit the results using a shell offset with a value of 0.5 are also shown in Table 2.3.13–2.
S3R element using *SHELL SECTION to define section properties.
S4R element using *SHELL SECTION to define section properties.
S4R element using *SHELL SECTION to define section properties. Bending moment applied with a distributed edge moment.
SC6R element using *SHELL SECTION to define section properties.
SC6R element using *SHELL GENERAL SECTION to define section properties.
SC8R element using *SHELL SECTION to define section properties.
SC8R element using *SHELL GENERAL SECTION to define section properties.
SC8R element with enhanced hourglass control using *SHELL SECTION to define section properties.
SC8R element with enhanced hourglass control using *SHELL GENERAL SECTION to define section properties.
S3R element.
S3R element and a shell offset.
S4R element.
S4R element and a shell offset.
SC6R element.
SC8R element.
SC6R element using *SHELL GENERAL SECTION to define section properties.
SC8R element using *SHELL GENERAL SECTION to define section properties.
SAX1 element.
SAX1 element and a shell offset.
M3D3 element.
M3D4R element.
COMBINED hourglass option for membrane elements included for the sole purpose of testing the performance of the code.
VISCOUS hourglass option for membrane elements included for the sole purpose of testing the performance of the code.
Table 2.3.13–1 ABAQUS/Standard shell bending results.
| Element Type | Tip Displacement ( ) | Tip Rotation |
|---|---|---|
| EXACT | 2.00 × 10–6 | 8.00 × 10–8 |
| S3R | 2.06 × 10–6 | 8.09 × 10–8 |
| S4R | 2.02 × 10–6 | 7.91 × 10–8 |
| SC6R | 1.93 × 10–6 | |
| SC6R (sgs) | 1.93 × 10–6 | |
| SC8R | 2.02 × 10–6 | |
| SC8R (sgs) | 2.02 × 10–6 | |
| SC8R* | 2.02 × 10–6 | |
| SC8R* (sgs) | 2.02 × 10–6 | |
| *ABAQUS/Standard results with enhanced hourglass control. | ||
Table 2.3.13–2 ABAQUS/Explicit shell bending results.
| Element Type | Offset Value | Tip Displacement () | Tip Rotation |
|---|---|---|---|
| EXACT | 2.00 × 10–6 | 8.00 × 10–8 | |
| SAX1 | 0 | 2.26 × 10–6 | 8.33 × 10–8 |
| SAX1 | 0.5 | 2.23 × 10–6 | 8.26 × 10–8 |
| S3R | 0 | 2.26 × 10–6 | 8.50 × 10–8 |
| S3R | 0.5 | 2.23 × 10–6 | 8.38 × 10–8 |
| S4R | 0 | 2.26 × 10–6 | 8.33 × 10–8 |
| S4R | 0.5 | 2.24 × 10–6 | 8.23 × 10–8 |
| SC6R | 1.93 × 10–6 | ||
| SC8R | 2.01 × 10–6 | ||
| SC6R (sgs) | 1.93 × 10–6 | ||
| SC8R (sgs) | 2.01 × 10–6 |
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