Energy Quantities

Strain energy

Strain energy is the total elastic energy stored in the deformed body. It equals the work done by the applied loads:

U = ½ · F · u

where F is the applied force and u is the displacement at the load application point (for a single load).

Strain energy is useful for:

• Comparing the stiffness of design variants (lower strain energy = stiffer structure under the same load)
• Checking energy balance as a secondary plausibility check
• Identifying which regions of the model carry the most load (strain energy density)

Strain energy density

Strain energy density (energy per unit volume) shows which regions are most highly loaded. High strain energy density areas carry the most structural work and are where weight reduction is most costly — a useful guide for topology optimisation.

Energy-based error estimation

Some solvers report an energy norm error — a global measure of solution quality. A high energy norm error suggests the mesh is too coarse to resolve the stress gradients accurately. Refine the mesh in the high-error regions and re-run.