Distributed traction and edge loads

The analyses in this section test the traction load labels TRVEC and TRSHR using distributed element-based and surface loads. One-element and two-element tests are performed to verify the loading options on all the faces of supported elements. In both Abaqus/Standard and Abaqus/Explicit tests, the elements are held fixed by kinematic coupling constraints as each face of each element is loaded with a combination of distributed general tractions and shear tractions. The resultant forces at the kinematic reference nodes are output to verify that distributed loads are properly applied to each element.

The analyses in this section test the edge load labels EDLD, EDNOR, EDSHR, and EDTRA using distributed element-based and surface loads. One-element and two-element tests are performed to verify the loading options on all the edges of supported shell elements. In both Abaqus/Standard and Abaqus/Explicit tests, the elements are held fixed by kinematic coupling constraints as each edge of each element is loaded with a combination of distributed edge loads. The resultant forces at the kinematic reference nodes are output to verify that distributed loads are properly applied to each element.

The analyses in this section test the traction load labels TRVEC and TRSHR using distributed element-based and surface loads in geometrically nonlinear analyses. Tests include models under large rigid body rotations and large deformations. In the tests where elements undergo large rigid body rotations, one facet is coupled to a kinematic coupling reference node. A traction load is applied to another face. This load is kept constant as the elements are rotated by the kinematic coupling reference node. The reaction forces at the kinematic reference node are used to verify that the loads are properly applied and rotated with the element. Different combinations of the follower and non-follower surface loads and constant resultants are also used. Some of the models in the tests have cylindrical geometry. General traction or shear loadings are applied on the cylindrical surface by defining a local cylindrical coordinate system.

The analyses in this section test the edge load labels EDLD, EDNOR, EDSHR, and EDTRA using distributed element-based and surface loads in geometrically nonlinear analyses. One facet is coupled to a kinematic coupling reference node. A traction load is applied to another face. This load is kept constant as the elements are rotated by the kinematic coupling reference node. The reaction forces at the kinematic reference node are used to verify that the loads are properly applied and rotated with the element. Different combinations of the follower and non-follower surface loads and constant resultants are also used.

This section provides basic verification of using constant resultants in a dead load analysis. The constant resultant method has certain advantages when a traction is used to model a distributed load with a known constant resultant.

If you choose not to have a constant resultant, the traction vector is integrated over the surface in the current configuration, a surface that in general deforms in a geometrically nonlinear analysis. The most common example of a traction that should be integrated over the current configuration is a live pressure load defined as $\mathbf{t}=-p\mathbf{n}$, where $\mathbf{n}$ is the normal in the current configuration. The total resultant due to a pressure load depends on the surface area in the current configuration. A live uniform normal surface traction integrated over the current surface is equivalent to applying a uniform pressure load. By default, the traction vector is integrated over the surface in the current configuration.

If you choose to have a constant resultant, the traction vector is integrated over the surface in the reference configuration, which is constant.

The analysis in this section consists of a unit planar membrane structure that is held fixed at the edges by a kinematic coupling constraint. The normal of the flat structure is in the $\left(1,0,1\right)$ direction. A uniform dead traction load (of magnitude 4) is applied in the negative ${\mathbf{e}}_3$-direction. This could be considered a simple model of a sloped roof with a snow load.

Let $S_o=1$ and S denote the total surface area of the plate in the reference and current configurations, respectively. With no constant resultant, the total integrated load on the plate, $\mathbf{f}$, is

In this case a uniform traction leads to a resultant load that increases as the surface area of the plate increases, which is not consistent with a fixed snow load. With the constant resultant method, the total integrated load on the plate is

In the first step the load is applied without a constant resultant. In the second step the structure is unloaded. In the third step the load is applied with a constant resultant.