Base Vector System
Define a Base Vector System () using a set of base vectors to form a coordinate system. The system does not necessarily need to be orthonormal, but when it is, declaring it orthonormal and linear enables simplifications that improve performance.
A vector F is represented by its contravariant components [F1, F2, F3]T in the base of the new base vector system defined by the base vectors u1, u2, and u3 on the form F = F1uF2u2 + F3u3. Expressing the base vectors as components in another system (for example, the global spatial system [ex, ey, ez]) gives the transformation matrix between bases:
where the last equality holds when the base vector system is orthonormal.
Note that you specify the base vectors as components in the default global coordinate system, which is context-dependent. The base vector system is therefore a relative coordinate system whose interpretation depends on the interpretation of the global system in the current context.
If this coordinate system is added as a subnode to a Combined System node, define where it will be active using a selection in the Geometric Entity Selection section. Also, the Name and Coordinate names fields are not available in this case.
Settings
Coordinate names
In the Coordinate names table, the default names are entered — x1, x2, and x3. In planar 2D models, x1 and x2 are typically the in-plane coordinates, and x3 is the out-of-plane coordinate. Note that these coordinate names are only used as indices for vector and tensor variable names, and cannot be evaluated as variables.
Base vectors
Define the Base vectors in terms of the global Cartesian coordinates (typically x, y, and z); one base vector on each row (two for 2D and three for 3D).
For 1D models, select which basis vector is parallel to the 1D geometry. Select an option from the In-plane index list. The default is 1.
For 2D models, select which basis vector to compute as the cross product of the two in-plane vectors specified. Select an option from the Out-of-plane index list. The defaults are 3 for a plane 2D model and 2 for an axisymmetric 2D model. For example, to map the first vector, x1, to the direction defined by y = x in 2D, enter 1 in the fields under x and y on the x1 row.
Simplifications
For some applications, only orthonormal coordinate systems can be used. Since the base vectors entered in a Base Vector System node are not necessarily orthonormal, these systems are by default not allowed in contexts requiring orthonormality. To make the coordinate system available in such contexts, select either the Assume orthonormal check box or the Make orthonormal check box. The former instructs automatic variable transforms to use the entered Base vectors directly, but treat them as orthonormal — if they are not, results will be incorrect. The Make orthonormal check box enables a polar decomposition of the base vector matrix into a rotation matrix and a stretch matrix. The rotation matrix — which is orthonormal — is kept, while the stretch matrix is discarded. This procedure is computationally more expensive than assuming orthonormality but guarantees a truly orthonormal transformation matrix that will behave correctly in subsequent variable transforms.
Relative to System from Geometry
This section is available in 3D, if you have added any work plane to the geometry.
From the Work plane list, select xy-plane (the default, for a standard global Cartesian coordinate system) or select any work plane in the geometry sequence. If you choose a work plane, the work plane’s coordinates xw, yw, and zw are used for the definition of the base vector.
Go to Name for information about the Settings window Label and Name. Also see Settings and Properties Windows for Feature Nodes.
If you have the Nonlinear Structural Materials Module, see Pressurized Orthotropic Container: Application Library path Nonlinear_Structural_Materials_Module/Plasticity/orthotropic_container.
If you have the Structural Mechanics Module, see Piezoelectric Shear-Actuated Beam: Application Library path Structural_Mechanics_Module/Piezoelectric_Effects/shear_bender.