finiteelementenanalyse

Finiteelementenanalyse, eller finite element analysis (FEA), is a numerical technique used to solve boundary-value problems in engineering and physics. It works by partitioning a complex geometry into a mesh of small elements connected at nodes, and by approximating the unknown fields with simple interpolation functions within each element. Through a variational (weak) formulation, the governing partial differential equations are transformed into a system of algebraic equations that can be assembled into a global stiffness (or similar) matrix.

Typical workflow: define the geometry and material properties, create a mesh with suitable element types (lines, triangles, quadrilaterals, tetrahedra, hexahedra), specify boundary and loading conditions, choose the interpolation functions, assemble the system, apply constraints, and solve for nodal quantities such as displacements, temperatures, or pressures. Post-processing extracts derived quantities and visualizes results.

FEA covers linear static problems, nonlinear and transient analyses, dynamic and eigenvalue problems, and coupled multiphysics like thermal–structural or fluid–structure interactions. Mesh quality, element type, and material models impact accuracy and convergence. Numerical solvers—direct methods or iterative solvers—are used to handle large sparse systems.

Applications span aerospace, automotive, civil engineering, mechanical design, and bioengineering. History roots lie in the 1950s–1960s with pioneers such as Turner, Clough, Martin and Topp, and the method has since evolved into widely used commercial and open-source software.