Are Shell Elements and Plate Elements always sufficient for modelling and simulating the actual Structural Behaviour?

Are Shell Elements and Plate Elements always sufficient for modelling and simulating the actual Structural Behaviour?

Okay, straight-forward, the answer is No.

Elements Geometry in the Real World

In the real world, all geometries are inherently three-dimensional (3D). To achieve the most accurate simulation of structural elements, it is essential to model them in 3D, fully accounting for their third dimension.

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Shell and Plate Elements

When modelling slabs using shell or plate elements, the thickness is defined but assumes uniform perpendicular behaviour. This means the upper and lower faces are treated as having identical properties and responses. The meshing algorithm for these elements generates a 2D mesh on one face (the source face) and sweeps it along the length or width of the component to create the opposite face (the target face). As a result, the two faces are geometrically and behaviourally identical.

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Solid Elements

In contrast, solid elements provide a more realistic representation of 3D behaviour. These elements require specific preprocessing to meet the requirements of 3D meshing algorithms, which generate meshes throughout the volume of the element. Consequently, the results at the top face of a solid element can differ from those at the bottom face, accurately reflecting the non-uniform behaviour across the thickness of the element.

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Is it always mandatory to use a Solid element instead of Shell or plate elements for simulating structural models?

First, we need to know that the nodal degrees of freedom (DOF) vary for different element types depending on the physical behaviour they are designed to model. Here's a breakdown:

1. Plate Elements

• Purpose: Used to model bending-dominated thin structures in 2D.
• Nodal Degrees of Freedom: 3 DOF per node: Rotation about the X-axis (θx) Rotation about the Y-axis (θy) Out-of-plane displacement in Z-axis (δz)
• Key Point: Plate elements do not account for in-plane forces (like membrane action), as they are purely bending elements.

2. Membrane Elements

• Purpose: Used to model in-plane forces like tension, compression, and shear in thin structures; does not account for bending.
• Nodal Degrees of Freedom: 2 or 3 DOF per node (depending on whether it’s 2D or 3D): Translation in X-axis (δx) Translation in Y-axis (δy) (In 3D models, δz is also included for out-of-plane motion.)
• Key Point: Membrane elements do not consider rotational DOF or bending behaviour.

3. Shell Elements

• Purpose: Combines bending (plate behaviour) and in-plane (membrane behaviour) action, making it suitable for thin to moderately thick structures.
• Nodal Degrees of Freedom: 6 DOF per node: Translation in X-axis (δx) Translation in Y-axis (δy) Translation in Z-axis (δz) Rotation about the X-axis (θx) Rotation about the Y-axis (θy) Rotation about the Z-axis (θz)
• Key Point: Shell elements can handle both bending and in-plane forces, making them versatile for curved or thin to medium structures.

4. Solid Elements

• Purpose: Used to model 3D stress and deformation in thick structures, including bending, shear, and axial behaviour.
• Nodal Degrees of Freedom: 3 DOF per node: Translation in X-axis (δx) Translation in Y-axis (δy) Translation in Z-axis (δz)
• Key Point: Suitable for the thick elements (mainly thick walls and deep slabs), where the through-thickness results are desired

From the key points above, we can conclude that:

·???????? For thin plates, the shell or plate elements could be computationally sufficient and could give somehow accurate results.

·???????? For thick plates and scenarios requiring detailed analysis of stresses and strains, solid elements are suitable.

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A critical common mistake is: Modelling Transfer Slabs as Shell Element.

One of the most frequent and critical mistakes in structural analysis is incorrectly modelling transfer slabs as shell or plate elements. Transfer slabs are typically thick, and using shell or plate elements for such slabs can lead to significant inaccuracies or even structural failures. Instead, they should be modelled as solid elements. Here’s why:

1. Accurate Representation of Stress and Strain

• The Problem with Shell Elements: Shell elements are designed for thin structures and assume that stresses vary linearly through the thickness. While this is reasonable for thin slabs, it becomes invalid for thick slabs like transfer slabs. The thicker the slab, the less accurate this assumption becomes.
• Why Solid Elements Work Better: Thick slabs experience complex 3D stress and strain variations across their depth. Solid elements can capture these variations, allowing for a more realistic simulation of the slab’s behaviour. This is crucial for transfer slabs, which are subjected to not only bending but also significant shear, axial, and torsional forces.

2. Proper Modelling of Shear Deformation

• The Limitation of Shell Elements: Shell elements often oversimplify or completely ignore shear deformations, which can become significant in thick slabs. This simplification leads to inaccurate results, especially in regions near supports or high-stress areas. However, if the slab is moderately thick or if computational resources are a concern, shell elements can still provide a reasonable approximation, with some compromises in accuracy.
• How Solid Elements Excel: Solid elements naturally account for through-thickness behaviour, including shear deformations and transverse stresses, and are better for analysing local stress concentrations mainly near supports or openings, etc., which are common in transfer slabs. This makes them far more suitable for thick slabs, where these effects are critical for understanding the slab’s structural performance.

Why This Matters for Transfer Slabs

Transfer slabs play a vital role in distributing loads in structures, often supporting significant forces from columns or walls above. These slabs must be modelled accurately to ensure safety and reliability. Using shell elements for such slabs is not just an oversight—it can lead to critical design errors.

Someone could ask a question and say: Slabs are mainly bending plates, so how could solid elements capture the bending moments and deflection while it have no bending degrees of freedom?

The answer is: While solid elements do not have explicit rotational degrees of freedom or bending moments, they inherently capture bending behaviour through 2 mechanisms:

1. Stress Distribution: Solid elements compute the full 3D stress state (σx , σy, σz, and shear stresses). So, bending is captured through the distribution of stresses and strains across the element volume, and it is represented as variations in normal stresses (σx and σy) across the slab thickness, as (in bending, compressive stresses will appear on one side of the slab and tensile stresses on the other).
2. Moment Calculation via Post-Processing: After running the analysis, the bending moments can be extracted by integrating the stresses across the slab thickness. Most finite element software provides tools to calculate bending moments from stress distributions in solid elements.

Yes, there might be challenges with calculating Bending Moment: Since bending moments are not directly calculated, they must be derived from the stress distribution, which can add complexity in post-processing.

Alternative Approach: Hybrid Modelling

Hybrid modelling is a practical approach for analysing very thick slabs, especially when dealing with large structures. By combining solid and shell elements strategically, you can achieve a balance between computational efficiency and accuracy, ensuring both reliable results and manageable analysis times. I mean:

• Use solid elements near critical regions such as columns or openings and wherever detailed 3D stress analysis is required.
• Use shell elements for other areas of the slab to capture overall bending behaviour efficiently.

Conclusion:

While solid elements do not have explicit bending moments, they are capable of accurately capturing bending behaviour through stress distributions. For very thick transfer slabs, solid elements are recommended due to their ability to handle complex 3D stress states and significant shear deformations. The bending moments can be derived from the computed stress distributions during post-processing, ensuring the slab is designed correctly. In some cases, hybrid modelling with shell elements can provide a practical compromise.

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