Choosing Beam, Shell & Solid Elements

The First Idealisation Decision

Before meshing a single surface, the analyst must decide how to represent the structure: as a collection of beams, a collection of shells, a collection of solids, or a mixture of all three. This is the element type decision, and it is the first idealisation decision in FEA. It determines what the model can capture — which stress components, which failure modes, which load paths — and what it cannot. It determines the computational cost, the meshing effort, and the complexity of the model. And it is a decision that cannot be undone easily — changing element types means rebuilding the model from the geometry up. The right choice is not always obvious, and it depends on the structure, the failure mode, and the analysis objective. But the principle is simple: use the simplest element type that captures the physics of interest.

1D Beam Elements

Beam elements are 1D elements — a line in space with section properties assigned to it. The line represents the centroidal axis of the member, and the section properties (area, second moment of area, torsion constant) define the cross-sectional behaviour. Beam elements capture axial force, bending in two planes, shear in two directions, and torsion — all six internal forces of a slender member. They are the most efficient element type for slender members — members whose length is much greater than their cross-sectional dimensions (typically length > 10× the largest cross-section dimension). A beam model of a frame or truss can have thousands of members and solve in seconds, because each element has only 2 nodes and 12 DOFs. Beam elements do not capture local stress distributions — the stress at a hole, at a fillet, at a joint — because the cross-section is represented by properties, not by geometry. For local stress, a beam model must be supplemented by a shell or solid submodel.

• 1D line element with section properties — area, I, J
• Captures: axial, bending (2 planes), shear (2 directions), torsion — all 6 internal forces
• Efficient: 2 nodes, 12 DOFs per element — thousands of members solve in seconds
• Appropriate: slender members (length > 10× cross-section dimension) — frames, trusses, beams
• Does not capture: local stress at holes, fillets, joints — requires submodel

Beam Section Properties

The beam element captures the cross-sectional behaviour through section properties, not through geometric modelling. The key properties are the cross-sectional area A (for axial stiffness), the second moments of area Iy and Iz (for bending stiffness), the torsion constant J (for torsional stiffness), and the shear areas Ay and Az (for transverse shear stiffness). These are computed from the cross-section geometry and assigned to the beam element. The beam element computes the internal forces and recovers the stress at the extreme fibres using the section properties. The stress recovery is based on beam theory — linear stress distribution across the section — and is accurate for compact sections but not for thin-walled sections with warping or distortion. For thin-walled sections, a shell model of the cross-section may be more appropriate.

• A: cross-sectional area — axial stiffness
• Iy, Iz: second moments of area — bending stiffness in two planes
• J: torsion constant — torsional stiffness
• Stress recovery: beam theory — linear across the section, accurate for compact sections

2D Shell Elements

Shell elements are 2D elements — a surface in space with a thickness assigned to it. The surface represents the mid-surface of the wall, and the thickness defines the through-thickness behaviour. Shell elements capture two types of behaviour: membrane behaviour (in-plane stretching, compression, and shear) and bending behaviour (out-of-plane bending, transverse shear). They are the standard element type for thin-walled structures — structures whose thickness is much smaller than their other dimensions (typically thickness < 1/10 of the other dimensions). Panels, skins, vessels, plates, and thin brackets are all shell structures. A shell model captures the membrane and bending stress distribution across the surface, including stress concentrations at holes, fillets, and junctions — but it does not capture the through-thickness stress variation beyond the linear assumption of plate theory. For thick walls where through-thickness stress is important, solid elements are required.

• 2D surface element with thickness — mid-surface and through-thickness behaviour
• Captures: membrane (in-plane) + bending (out-of-plane) + transverse shear
• Efficient: 3 or 4 nodes (or 6/8 for second-order), 6 DOFs per node
• Appropriate: thin-walled structures (thickness < 1/10 of other dimensions)
• Does not capture: through-thickness stress variation beyond linear plate theory

Shell Membrane and Bending Behaviour

Shell elements combine two behaviours: membrane and bending. Membrane behaviour is the in-plane response — the shell stretches, compresses, and shears in its own plane. Bending behaviour is the out-of-plane response — the shell bends and twists under transverse load. The two are coupled at curved surfaces (a curved shell carries pressure by a combination of membrane and bending action) and at junctions. The relative importance depends on the geometry: a flat plate under pressure is bending-dominated; a curved dome under pressure is membrane-dominated. The shell element captures both, and the analyst must understand which is governing to interpret the results. A thin shell under pressure that is bending-dominated is likely to buckle; the same shell in a membrane-dominated configuration is much more stable.

• Membrane: in-plane stretching, compression, shear — carries load through axial stiffness
• Bending: out-of-plane bending, twisting — carries load through bending stiffness
• Flat plate under pressure: bending-dominated
• Curved shell under pressure: membrane-dominated — more efficient, more stable

Shell Thickness Definition

The shell thickness is a property, not a geometric dimension — the element is a 2D surface, and the thickness is assigned as a scalar (uniform) or a function (varying). The thickness defines the through-thickness behaviour: the bending stiffness is proportional to t³, the membrane stiffness is proportional to t. A small error in thickness produces a large error in bending stiffness — a 10% thickness error produces a 33% bending stiffness error (1.1³ = 1.33). This is why the thickness must be the as-designed thickness, not a nominal or rounded value. For laminated composites, the thickness is defined ply by ply — each ply has its own thickness, material, and orientation, and the shell element computes the laminate stiffness from the ply stack.

• Thickness is a property — uniform, varying, or ply-by-ply for composites
• Bending stiffness ∝ t³ — a 10% thickness error gives a 33% bending stiffness error
• Membrane stiffness ∝ t — less sensitive to thickness error
• Use the as-designed thickness, not a nominal or rounded value

3D Solid Elements

Solid elements are 3D elements — a volume in space with full 3D stress state. They capture all six stress components — three normal, three shear — at every integration point. They are the most general element type, capable of representing any geometry and any stress state, but they are also the most expensive. A solid model of a structure that could be modelled with shells requires many more elements — a shell model with one element through the thickness requires 3–5 solid elements through the thickness to achieve the same bending accuracy. Solid elements are necessary when the through-thickness stress is important — thick walls, contact regions, load introduction zones, and 3D stress concentrations. They are not necessary for thin walls, where shells are more accurate and more efficient.

• 3D volume element — full 3D stress state, all 6 stress components
• Captures: through-thickness stress, contact, 3D stress concentrations
• Expensive: 3 DOFs per node (translations only), but many more elements needed
• Appropriate: thick geometry, contact, load introduction, 3D stress concentrations
• Not appropriate: thin walls — shells are more accurate and more efficient

element-types

Comparison: Beam vs Shell vs Solid

The three element types represent different levels of idealisation, and each has its strengths and weaknesses. The table below compares them across the key dimensions that drive the element type decision.

When to Use Each Element Type

The element type decision should be driven by the physics, not by the geometry or the software defaults. The following guidance captures the practical considerations for the most common structural forms.

• Beams: slender members (length > 10× cross-section) — frames, trusses, beams, stiffeners in a shell model
• Shells: thin-walled structures (thickness < 1/10 of other dimensions) — panels, skins, vessels, thin brackets
• Solids: thick geometry, contact regions, load introduction, local submodels with boundary loads from a global model
• Mixed: beams for slender members, shells for panels, solids for joints — with carefully modelled connections

Mixed-Dimensional Models

Many real structures are best modelled with a mixture of element types — beams for the slender members, shells for the panels, solids for the joints and load introductions. A mixed-dimensional model combines the efficiency of beams and shells for the global structure with the accuracy of solids for the local details. The challenge is the connection between element types: a beam connected to a shell, a shell connected to a solid. The connection must transfer the correct forces and moments without introducing artificial stiffness or stress concentrations. A beam-to-shell connection must transfer the beam's bending moment into the shell's membrane and bending forces — usually through a rigid link or a coupling. A shell-to-solid connection must transfer the shell's bending moment into the solid's stress — usually through a constraint that ties the shell edge to the solid surface. These connections are critical — a poorly modelled connection introduces errors that can dominate the result.

• Beams for slender members, shells for panels, solids for joints — mixed model
• Efficient globally, accurate locally — the best of both approaches
• Beam-to-shell: rigid link or coupling distributes beam force to shell nodes
• Shell-to-solid: constraint ties shell edge to solid surface

Mixed-dimensional models combine efficiency with local detail, but the connections between element types are critical. A beam-to-shell or shell-to-solid connection that does not correctly transfer the forces and moments introduces artificial stiffness or stress concentrations that can dominate the result. Model the connections deliberately, and verify them with hand calculations.

DO NOT USE SOLIDS JUST BECAUSE THEY LOOK MORE REALISTIC

The most common element selection error is using solid elements for thin-walled structures because they look more realistic. A solid model of a thin panel, with multiple elements through the thickness, is not more accurate than a shell model — it is less accurate, because the solid elements must capture the bending through the thickness with multiple elements, and first-order solid elements are notoriously poor at bending (they suffer from shear locking). A single second-order shell element through the thickness captures the bending accurately with a fraction of the computational cost. The belief that solids are more accurate because they are more "3D" is a misconception — the accuracy depends on whether the element type captures the physics, not on whether it looks like the real structure. A shell model of a thin panel is more accurate, more efficient, and more appropriate than a solid model. Solids are the right choice for thick geometry and local 3D stress, not for thin walls.

A solid model of a thin wall is not more accurate than a shell model — it is less accurate and more expensive. Shell elements capture thin-wall bending with a single element through the thickness; solid elements need many, and first-order solids suffer from shear locking. Use shells for thin walls, solids for thick geometry. Do not confuse visual realism with physical accuracy.

Shear Locking and Hourglassing

Shear locking is a numerical artefact that affects first-order solid and shell elements in bending. The element's shape functions cannot represent the curved displacement field of pure bending, so they introduce artificial shear strain. This makes the element artificially stiff in bending — the bending deformation is underpredicted. Shear locking is cured by using second-order elements or by using reduced-integration elements with hourglass control. Hourglassing is the opposite problem — reduced-integration elements are too flexible in certain zero-energy modes, and they can deform without generating stress. Hourglassing is cured by hourglass control — artificial stiffness that suppresses the zero-energy modes. Both errors are numerical, not physical, and they produce results that look reasonable but are wrong. The remedy is to use the right element formulation: second-order elements for bending, reduced-integration with hourglass control for efficiency, and always verify against a known solution.

• Shear locking: first-order elements are too stiff in bending — artificial shear strain
• Hourglassing: reduced-integration elements are too flexible in zero-energy modes
• Both produce plausible-looking but wrong results
• Remedy: second-order elements for bending, reduced-integration with hourglass control

Practical Selection Guidance

The element type decision should be driven by the physics, not by the geometry or the software defaults. The following checklist captures the key decisions for the most common structural forms.

• Is the member slender (length > 10× cross-section)? — Use beams — efficient, captures axial/bending/shear/torsion
• Is the wall thin (thickness < 1/10 of other dimensions)? — Use shells — captures membrane and bending, stress concentrations
• Is the geometry thick or is through-thickness stress important? — Use solids — captures full 3D stress, contact, load introduction
• Is the structure a mixture of slender, thin, and thick? — Use a mixed-dimensional model — beams, shells, solids with careful connections
• Is the analysis a global load path analysis? — Use beams or shells — efficient, captures the global behaviour
• Is the analysis a local stress analysis? — Use solids — refined, captures the local 3D stress state
• Are you using solids because they look realistic? — Reconsider — shells may be more accurate and more efficient for thin walls

Key takeaways

• Beam elements model slender members — axial, bending, shear, torsion — with a 1D line and section properties. Efficient for frames, trusses, and long members.
• Shell elements model thin-walled structures — membrane, bending, and transverse shear — with a 2D surface and a thickness. Efficient for panels, skins, and vessels.
• Solid elements model full 3D stress states — all six stress components — with a 3D volume. Necessary for thick geometry, contact, and local load introduction, but expensive.
• The right element type is the one that captures the physics of interest at the minimum computational cost. Solids for everything is not the right answer.
• Mixed-dimensional models — beams, shells, and solids in one model — combine efficiency with local detail, but the connections between element types must be modelled carefully.
• Shells can be more accurate than solids for thin structures, because a single shell element through the thickness captures the bending that would require multiple solid elements to resolve.
• DO NOT USE SOLIDS JUST BECAUSE THEY LOOK MORE REALISTIC — a solid model of a thin panel is not more accurate than a shell model. It is more expensive, and it may be less accurate.