The element library: when to use 2D or 3D?

In Finite Element Analysis (FEA), one of the most common mistakes among beginner analysts is trying to model every structure directly in 3D “because the physical part is three-dimensional”. In professional simulation engineering, however, computational efficiency is just as critical as the accuracy of the results.

Understanding the element library and knowing when to apply a dimensional reduction (going from a 3D solid to a 2D shell or planar model) is what separates an agile, accurate analysis from a clumsy, heavy, inefficient simulation.

The concept of dimensional reduction: why not always use 3D?

The goal of dimensional reduction is to simplify the equations that govern the problem by replacing physical geometric dimensions with numerical parameters.

For example, when a sheet-metal part is represented with 2D shell elements, the mesh is built only on the mid-surface (mid-plane), and the thickness (t) is given to the solver as a mathematical property attached to the element.

The maths behind the computational cost

This geometric abstraction has a huge impact on hardware resources:

• The RAM needed to store the stiffness matrix scales in proportion to the square of the number of nodes (N²).
• The computation time needed to solve the system of equations scales roughly with the cube of the number of nodes (N³).

If you try to model a thin 1 mm sheet with 3D solid elements, you will need at least 3 or 4 elements through the thickness to capture bending properly and avoid shear locking. That generates millions of unnecessary degrees of freedom (DoF), pushing run time from minutes to hours or days without adding any accuracy.

When to use 2D planar elements and shells

Two-dimensional elements fall conceptually into two large groups: planar (2D) elements and shell elements.

Planar 2D elements: plane stress, plane strain and axisymmetry

They are used when the three-dimensional problem can be collapsed entirely into a plane (special stress states have their own article):

• Plane stress: for very thin structures loaded exclusively in their own plane, where the out-of-plane stresses are zero (σ_z = τ_xz = τ_yz = 0). Example: metal plates, spanners or thin gear discs.
• Plane strain: for very long bodies with a constant cross-section where longitudinal deformation is prevented (ε_z = γ_xz = γ_yz = 0). Example: concrete dams, tunnels or buried pipes.
• Axisymmetry: for solids of revolution whose geometry and loads are symmetric about a central axis. Example: cylindrical tanks or rotating shafts.

Shell elements

Shell elements are true “hybrids”: they sit in three-dimensional space but are formulated on a 2D surface. They combine two fundamental elastic behaviours:

1. Membrane: responds to loads contained in the plane of the element (2 translational DoF u_x, u_y).
2. Plate (bending): responds to loads perpendicular to the plane (1 out-of-plane translational DoF u_z + 2 rotational DoF θ_x, θ_y).

Each node of a shell element has 5 degrees of freedom (3 translations + 2 rotations).

Typical applications: aircraft fuselages and wing skins, car bodies, thin-walled pressure vessels, stamped profiles and tubes. Their formulation is covered in Shell elements: the FEA hybrids.

When 3D solid elements are mandatory

There are scenarios where dimensional reduction is physically impossible and inaccurate. In those cases, volumetric three-dimensional elements are strictly mandatory.

The most common 3D solid elements are tetrahedra (TET4 / TET10) and hexahedra (HEX8 / HEX20), compared in 3D solid elements: hexahedra vs. tetrahedra. A defining trait of 3D solids is that they have only 3 translational degrees of freedom per node (u, v, w) and no rotational DoF at all.

Use 3D solid elements whenever any of the following conditions holds:

1. Three comparable dimensions (massive or bulky structures): the part has no dimension significantly smaller than the other two.
2. Complex triaxial stress state: when the three normal stresses (σ_x, σ_y, σ_z) and the three shear stresses (τ_xy, τ_yz, τ_zx) are of a similar order of magnitude and none can be neglected.
3. No mid-plane can be extracted: in parts with irregular geometry, abrupt and continuous thickness changes, or solid blocks where defining a homogeneous scalar thickness would be geometrically false.
4. Specific manufacturing processes: components made by casting, forging or single-piece machining.

Typical applications: engine crankcases and blocks, suspension knuckles, tow hooks, bulky gears, turbine supports, high-integrity fittings and moulding tools.

Quick selection criteria for the analyst

Summary for decision-making

Before you start meshing, ask yourself these questions in order:

1. Can I define the part by a mid-surface with a constant or thinly varying thickness? Yes → use shell elements (preferably Q4 or Q8 quadrilaterals).
2. Is the geometry massive, with complex cast or machined volumes where bending acts on thick blocks? Yes → use 3D solid elements (preferably HEX8/HEX20 hexahedra, or quadratic TET10 tetrahedra).
3. Is the problem a very thin sheet loaded only in its plane, or an infinitely long body? Yes → use a planar 2D formulation (plane stress or plane strain).

Mastering element selection lets you build models that are computationally light, numerically stable and highly reliable for design decision-making.