Shell model
The shell connection model consists of two plates with a uniform thickness of 10 mm, a width of 100 mm, and a length of 250 mm. The horizontal member is subjected to a tensile force of 150 kN, while the vertical members experience compression forces of 150 kN. The plates are welded together using butt welds.
Fig. 01) Model with loads
Fig. 02) Shell model and uniform mesh
The maximal Von-Mises stress occurs at the edge of the horizontal member, where it intersects with the vertical member. The stress reaches around 204 MPa.
Fig. 03) Von-Misses stress on the shell
If we examine the stress tensor more closely, we can see that Sigma ZZ (S33) equals zero. It is a basic assumption of shell elements that the stress across the thickness is equal to zero.
Fig. 04) Von-Misses hand-calculation
Solid model
The solid model has identical geometry and load setups. There are five elements over the thickness to capture the entire stress field on the model and mainly in the critical region.
Fig. 05) Solid model and mesh
The critical plate is located near the intersection, where the stress across the thickness is significantly high. The Von-Mises stress reached 235 MPa, indicating the onset of plasticity.
Fig. 06) Von-Misses stress on the solid
The Sigma ZZ (S22) stress indicates the stress across the thickness of a horizontal member, reaching a value of -162 MPa. This suggests that the stress in these types of connections cannot be ignored, as it contributes to an increase in Von Mises stress.
Fig. 07) Von-Misses hand-calculation
Conclusion
To ensure accurate stress assessments in structures, especially at complex connection regions, both shell and solid models provide valuable insights under identical loading conditions. The shell model, while simpler, highlights peak stresses at critical connection edges effectively and aligns with shell theory assumptions (with zero through-thickness stress, Sigma ZZ). This makes it useful for a broad, efficient analysis in steel connection models where computational resources may be limited.
However, the solid model demonstrates a more comprehensive stress distribution, especially through thickness, which is vital in high-stress areas prone to plastic deformation, as seen with the higher Von Mises stress (235 MPa) and non-zero Sigma ZZ values. This in-depth view is crucial for identifying potential issues such as plasticity or failure initiation, which may be underestimated by shell models.
Using both shell and solid models together can provide a balanced approach. The shell model can be applied to efficiently evaluate global behavior, while the solid model can focus on critical regions where stress concentration and through-thickness effects are essential. This combined strategy ensures a reliable assessment without overly burdening computational resources.
Suggested Solutions
- Hybrid Modeling Approach: Implement shell elements for the majority of the structure and use solid elements in high-stress or complex connection regions. This hybrid approach balances computational efficiency and accuracy, enabling detailed stress assessment where needed without a fully solid model's computational cost.
- Stress Correction Factors: If relying on shell models in some areas, apply stress correction factors derived from detailed solid model analyses in critical zones. This allows shell models to approximate stress concentrations and through-thickness effects more accurately in critical locations.
- Validation and Calibration: Use experimental data or high-fidelity solid model results to validate shell model results, applying any necessary adjustments for more accurate predictions, especially in welded connections or critical load-bearing intersections.
- Reserve in the bearing capacity: Due to the triaxial stress state, you can allow some bearing capacity reserve and reach 80% of the plate's maximal bearing capacity to provide the remaining energy of the material for stress distribution over the thickness.
Connections of this type are infrequently addressed in structural engineering design. However, the article offers valuable insights on effectively managing these connections using IDEA StatiCa Connections. In most cases—up to 99%—a shell model proves to be a highly effective tool for simulating the structural behavior of these connections.