Integration Point

In the Finite Element Method (FEM), an integration point refers to a specific location within an element where physical quantities such as stress, strain, and energy density are numerically calculated. These points are used in finite element software such as ANSYS to enhance the accuracy of solutions at the element level.

Node and Integration Points (Generated by AI)

Definition and Function

Integration points are used for numerical integration of quantities within finite elements. Methods such as Gauss quadrature are commonly employed for this purpose. In such methods, the integral of a continuous field over an element is approximated by a weighted sum of function values at specific locations—these are the integration points.

Application and Characteristics

At each integration point, quantities such as stress, strain, plastic deformation, and energy dissipation are evaluated. These points are usually located differently from the element’s nodes, and their number varies depending on the element type and the selected degree of integration.

Examples:

• For a 2D quadrilateral element with 2x2 Gauss integration, there are 4 integration points.
• For a 3D hexahedral element with 2x2x2 Gauss integration, there are 8 integration points.

Nodal vs. Integration Point Results

In ANSYS, results such as stress and strain are, by default, computed at the integration points. However, to visualize these results, they often need to be extrapolated or averaged to the nodes. This transfer can be done through interpolation or averaging techniques. Therefore, results obtained directly from integration points are generally more accurate.

Technical Significance

Integration points allow for more precise and localized results, especially in high-strain regions such as areas undergoing plastic deformation. For this reason, evaluating data at integration points is critically important for accurately determining stress concentrations in engineering analyses.