2. Define boundary conditions

A Pattern object is a mesh datastructure that describes the topology of the structure. Several additional layers of information regarding the boundary conditions need to be added in order to give the Pattern a structural meaning: identification of the supports; treatment of the openings and open edges; and defining the loading condition.

Identify Supports

In RV2, a support is defined as a vertex of the structure that is fixed, and can have external horizontal reactions. By definition then, only the vertices on the boundary of a Pattern can be defined as supports.

The vertices can be selected using these modes:

• AllBoundaryVertices : all boundary vertices

• Corners : all corner vertices

• ByContinuousEdges : all vertices on the selected boundary edge (corner to corner)

• Manual : manual selection by the user

Update Boundaries

An opening is a chain of edges at the boundary of a Pattern, in between two support vertices. In general, openings in TNA cannot be straight, unless there are no internal forces in the non-boundary edges at the openings (i.e. barrel vault or cross vault).

This feature relaxes the Pattern using the force density method, resulting in curved openings. For each opening, the amount of curvature is defined by using the sag , which is calculated based on the percentage of the length of the opening. The $q$s for the boundary edges are automatically calculated based on the target sag values, which are then used for the force density method.

Although this feature is optional, the user should be aware that the treatment of the openings are very much dependent on the type of vault that is being investigated. In some applications where openings may already have some curvature, the relaxation will make the Pattern more "equilibrated" and optimal for the horizontal equilibrium solver later on.

Define Loads

This feature is currently under construction.

In TNA, externally applied loads can only be vertical. The user can define how the self-weight of the structure is calculated:

• ByFace : the self-weight at each vertex is calculated by the tributary area of all the faces at the vertex (i.e. continuous shell), times the density and thickness, which are defined in the global settings

• ByEdge : the self-weight at each vertex is calculated by the tributary lengths of all the edges at the vertex (i.e. grid shell), times the density and thickness, which are defined in the global settings

• PointLoad : vertical point loads of can be applied to any vertices