Machine Design

Designers introduction to FEA

Most introductory classes in finite-element analysis probably breeze over the details that would explain exactly what the software is doing and why.

An industrial robot and car engine (engine block not shown) are both mechanisms.

The chart classifies FEA problems in solid mechanics.

The base plate of an elliptic trammel mechanism (left) is a structure. The elliptic trammel — the base plate, sliders, and the connecting link (right) — is a mechanism. No deformation of any component is required to move the mechanism.

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For instance, FEA programs calculate stresses after finding displacements. Because most FEA images show stresses, readers think that's all it finds.

Modern FEA programs simulate static, dynamic, linear, nonlinear, thermal, modal, and random vibrations, and more. "But these names do not follow standard engineering terminology, and that leads to confusion," says Design Generator President Paul Kurowski. "To decide what analysis is needed for a particular project, it's useful to first classify FEA capabilities."

FEA solves many different problems out of which structural and thermal problems are most common for mechanical engineers. "Structural analysis finds deformations, strains, and stresses caused by structural loads such as force, pressure, and gravity. Supports and contact also add to loads," he says.

Thermal analysis finds temperatures, temperature gradients, and heat flow caused by thermal loads such as heat flux or heat power. Boundary conditions such as prescribed temperatures and convection coefficients also affect results. Structural and thermal analyses share many analogies. The most important is between displacements and temperatures. Other analogies are consequences of this one," says Kurowski.

"Let's start with what is calculated in each analysis. Structural analysis first calculates the mesh's node displacements. Displacements are vectors and so must have directions and magnitudes. Describing nodal displacements in 2D models takes two components, and in 3D models meshed with solid elements, it takes three. And for a 3D model meshed with shell elements, nodal displacements take six components, displacements in the X, Y, and Z directions and rotations about each. Each displacement component is a degree of freedom constituting an unknown that must be found. After finding displacement components for the nodes, they are interpolated across elements to calculate a displacement field in the model. Displacement fields are then differentiated to find strains. Finally, stresses are calculated based on strains and material elasticity," says Kurowski.

The primary unknowns in thermal analysis are nodal temperatures. "These scalar entities need only one component or one degree of freedom — a temperature. This is true whether the model is 2D or 3D, and regardless of element type. Temperatures are then interpolated over elements to calculate a temperature field," he says. The field is differentiated to find a temperature gradient. FEA then calculates a heat flux or flow based on that gradient and material conductivity. Thermal analysis is less computationally intensive than structural analysis because there are fewer unknowns.

Loads versus boundary conditions

What is the difference between loads and boundary conditions? "The terms are often used inconsistently and that confuses some FEA users," says Kurowski.

"Mathematically speaking, a boundary condition is anything defined on the boundary (called faces by CAD users) of a model prepared for FEA. That means forces, pressures, and supports are boundary conditions in structural analysis. Furthermore, forces and pressures are force boundary conditions and supports are displacement boundary conditions. Only so-called volume loads such as gravity or inertia are not boundary conditions because they are not defined on model boundaries but over the entire volume. In thermal analysis, thermal loads, prescribed temperatures, convection coefficients, and radiation emissivity are boundary conditions. Only a volume heat load is not," he says.

The terminology used in everyday practice often differs. "For example, the phrase 'apply loads and boundary conditions,' when used in structural analysis uses 'loads' as forces or pressures on both model boundary and volume, while boundary conditions are understood as supports. 'Loads' in thermal analysis means thermal loads on both the model boundary and volume, while boundary conditions mean prescribed temperatures, convection coefficients, and radiation emissivities," he says.

Rigid bodies don't deform

A structure is a firmly supported solid body. It may remain motionless or vibrate about a position of equilibrium, but cannot move as a rigid body. Any motion of a structure must be accompanied by deformation.

The base plate in the accompanying image is a structure because it has fixed support and, consequently, no rigidbody motions. "An assembly of the same base plate with two sliders and a connecting link is a mechanism because the sliders and link can move without deforming," says Kurowski. They move as rigid bodies. An industrial robot and a four-cylinder engine are both mechanisms. Their motion may also take place without component deformations."

Structural Thermal

Displacement (m)

Temperature (K)
Strain (m/m) Temperature gradient (K/m)
Stress (N/m2) Heat flux (W/m2)
Volume load (N/m3) Heat power (W/m3)
Prescribed displacement (m) Prescribe temperature (K)
Elastic support Convection coefficient
Static analysis Steady-state analysis
Vibration (dynamic) analysis Transient analysis


Steps Structural analysis Thermal analysis
1 Displacements Temperatures
2 Strains Temperature gradients
3 Stresses Heat flux

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