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2D Face Loads

Face loads can be constant or varying across the face of an element. For a point load on the face the load vector is

rs=hTfs\mathbf{r}_{s} = \mathbf{h}^{T}f_{s}

This can be generalised for the distributed case giving the load vector as

rs=∫shTfsdS\mathbf{r}_{s} = \int_{s}^{}{\mathbf{h}^{T}\mathbf{f}_{s}dS}

where integration is over the surface of the element. Using Gaussian integration this can be expressed as

rs=∑iαihiTfs,idet⁡Js,i\mathbf{r}_{s} = \sum_{i}^{}\alpha_{i}{\mathbf{h}_{i}}^{T}\mathbf{f}_{s,i}\det J_{s,i}

Where α\alpha are the Gaussian weights and det⁡J\det J is the determinant of the Jacobian.

Note: In GSA, loads can be applied to a list of members or elements. Any loads applied onto members will be automatically expanded into the appropriate elements loads in the solver in order to analyse the model.