We need to be able to support the case when the Schwarz contact Dirichlet BC when not aligned with coordinate axes. The common formulation for doing this can be found on pp. 216-218 of this book. Here equation (7.6.-1) is the global system w/o the inclined contact. The rotation matrix T in (7.6-5) must be formed and applied to the global stiffness matrix and RHS, as in equation (7.6-6). The rotation matrices comprising this matrix must be derived for 3D, which can be done using the Rodriguez formulation. An implementation of this is done in Minitensor.jl in the Norma code here.
We will need to add the following capabilities to enable inclined contact:
Capability to detect inclined contact
Routine that calculates the matrix T used to transform the stiffness matrix and load vector. For no inclined surfaces, it would just return an identity matrix.
Apply the matrix T to the stiffness and load vector, e.g. here.
Once the solve happens, we will need to transform things back by applying the inverse rotation transformation.
We are looking into alternate ways to handle inclined contact that are perhaps less intrusive.
We need to be able to support the case when the Schwarz contact Dirichlet BC when not aligned with coordinate axes. The common formulation for doing this can be found on pp. 216-218 of this book. Here equation (7.6.-1) is the global system w/o the inclined contact. The rotation matrix T in (7.6-5) must be formed and applied to the global stiffness matrix and RHS, as in equation (7.6-6). The rotation matrices comprising this matrix must be derived for 3D, which can be done using the Rodriguez formulation. An implementation of this is done in Minitensor.jl in the Norma code here.
We will need to add the following capabilities to enable inclined contact:
We are looking into alternate ways to handle inclined contact that are perhaps less intrusive.