prismelement

Prismelement, or prism element, is a three-dimensional finite element type used in finite element analysis. A triangular prism is formed by extruding a triangle along a perpendicular direction, yielding a polyhedron with two parallel triangular faces and three rectangular side faces. The simplest linear prism has six nodes (three on each triangular face) and uses six shape functions to interpolate displacement within the element. Higher-order variants exist, such as the 15-node quadratic triangular prism, which includes mid-edge nodes to increase interpolation accuracy.

In finite element formulations, prism elements employ isoparametric mapping, with the same shape functions used to approximate geometry and field variables. Numerical integration is typically performed with Gauss quadrature appropriate for the element order. Prism elements can be combined with other element types in a mesh to fill three-dimensional domains, and are particularly suited to meshes that include layered or anisotropic regions because their triangular bases can conform to curved surfaces while maintaining a regular medial axis.

Common applications include geotechnical and civil engineering problems involving soils and sediments, structural analysis of laminated composites, and fluid–structure interaction problems where a layered meshing strategy is advantageous. Compared with tetrahedral elements, prism elements can offer better accuracy for boundary layers and interfaces with less distortion in layered geometries, but they are less flexible for filling arbitrary complex geometries and may require more careful mesh generation.

Variants include linear prisms (6-node) and quadratic prisms (15-node), among others.