isoparametrinen

Isoparametrinen refers to a method used in finite element analysis and computer-aided design. The core idea is to use the same set of parameters to define both the geometry of a finite element and the variation of a field within that element. These parameters are typically local coordinates, often denoted as ξ (xi) and η (eta) for two-dimensional elements, or ξ, η, and ζ (zeta) for three-dimensional elements.

In an isoparametric formulation, the shape functions used to interpolate the nodal values of the field (e.g., displacement, temperature) are identical to the shape functions used to map the local coordinates to the global Cartesian coordinates. This means that the geometry of the element is described using the same mathematical functions as the solution within the element. This approach simplifies the implementation of finite element methods, particularly for elements with curved boundaries. Instead of dealing with complex geometric transformations for each element, the calculations can be performed in a simpler, reference element (often a square or cube) in the local parameter space, and then mapped back to the physical element's geometry. This universality allows for the efficient analysis of complex shapes and structures.