Brick Elements: Gaussian Integration

Description

The number of integration points used for the assembly of the element stiffness depends on the element type and, for elements that support it, whether full or reduced integration is used.

Results such as stresses and strains are calculated at the integration points. Depending on the element type, the number of integration points and their locations can vary. For higher order elements, the number of integration points used to display stress results can be different to the actual number of integration points used for solving. To display the stress results, 2×2×2 sampling points are always used. This is summarised in the table below.

Element	Integration Points	Stress Output Points
Tetra4	1	1
Tetra10	4	4
Wedge6	3×2	3×2
Wedge15	7×3	3×2
Hex8	2×2×2	2×2×2
Hex16	3×3×2 or a reduced integration scheme	2×2×2
Hex20	3×3×3 or a reduced integration scheme	2×2×2
Pyra5	2×2×2	2×2×2
Pyra13	3×3×3	2×2×2

For the 20-node brick element (Hex20), the Gauss integration performed in the assembly of the elements can be controlled in all three natural coordinate directions. Either one, two or three Gauss points can be used in each direction. In general, for the full quadratic element, two-point integration is found to produce good quality results with reduced assembly time, subjected to the limitations of reduced integration. However three-point integration is required to fully integrate all the terms in the stiffness matrix.