Finiteelementmodellering

Finiteelementmodellering, or finite element modelling (FEM), is a numerical method for approximating solutions to boundary value problems in engineering and physics. It subdivides a complex domain into smaller, simpler elements connected at nodes, enabling the solution of partial differential equations that describe physical fields such as displacement, temperature, or pressure.

The modelling process typically includes discretization of the domain into a mesh of elements (one-, two-, or three-dimensional), selection of interpolation (shape) functions, and formulation of governing equations in weak form. The local element equations are assembled into a global system, which is solved for the unknown nodal quantities. Boundary conditions and loads are applied to reflect real-world constraints.

Time-dependent problems use dynamic analysis with mass and damping terms and may employ implicit or explicit time integration. Nonlinear problems arising from large deformations, nonlinear materials, or contact require iterative solvers.

Mesh quality and refinement influence accuracy; practitioners perform mesh convergence studies and may employ adaptive refinement.

FEM is used across disciplines: structural mechanics, heat conduction, fluid-structure interaction, acoustics, electromagnetism, and biomechanics, among others. It supports linear and nonlinear, static and dynamic analyses, and steady-state as well as transient simulations.

Software tools range from commercial packages to open-source frameworks. Validation and verification are standard practices to ensure models reflect physical behavior, while calibration against experiments improves predictive capability.

Limitations include model simplifications, numerical error, and the need for appropriate material data and boundary conditions.

Finiteelementmodellering is the Danish or Norwegian term for the same methodology used worldwide. The field continues to evolve with high-performance computing and advanced material models.