Integration Point

Integration point (Turkish: entegrasyon noktası) is a specific point within an element in the finite element method (Finite Element Method - FEM) where physical quantities such as stress strain and energy density are numerically computed. In software such as ANSYS and similar finite element programs these points are used to enhance solution accuracy at the element level.

Node and Integration Point (generated by artificial intelligence)

Definition and Function

Integration points are used in finite element analysis for the numerical integration of internal element quantities. For this purpose Gauss-Legendre (Gauss quadrature) like numerical integration methods are commonly preferred. In these methods the value of an integral over a continuous domain is approximated as a weighted sum of function values at specific points. These points are called integration points.

Application and Characteristics

At each integration point quantities such as stress strain plastic deformation and energy dissipation within the element are evaluated. These points are typically located at positions different from the element’s knot nodes and their number varies according to the element geometry and the chosen integration order.

For example:

• In a two-dimensional quadrilateral element using 2x2 Gauss integration there are a total of four integration points.
• In a three-dimensional hexahedral element applying 2x2x2 integration yields eight integration points.

Nodal and Integration Point Results

In ANSYS software stress and strain results obtained after solving are by default computed at the integration points. However to visualize these results they may need to be transferred to the nodal points. Such a transfer is performed using interpolation or averaging methods. Therefore results directly obtained from integration points generally provide higher accuracy accuracy.

Technical Importance

Integration points enable more accurate and localized solutions particularly in regions of high strain such as areas where plastic deformation begins. Consequently evaluating integration point data is critical for correctly identifying stress concentrations in engineering analyses.