The stiffness matrix
\(K\) is \(N \times N\) where \(N\) is the number of DOF
\(K\) is symmetric
\(K\) is sparse (has many zeros)
\(K\) is singular until appropriate constraints are applied (ie it can float in space, non-unique solution)
\(K\) typically has a “band” of non-zero values.
Boundary conditions are enforced on the nodes
Force (general) boundary conditions are added to the loading vector.
Displacement boundary conditions are enforced on the nodal displacement vector.
“Elimination method/Matrix Partitioning”
“Penalty method”
The “cost” of solving the problem scales exponentially with \(N\) (and bandwidth)
18.4 Comments on the matrices
The stiffness matrix
\(K\) is \(N \times N\) where \(N\) is the number of DOF
\(K\) is symmetric
\(K\) is sparse (has many zeros)
\(K\) is singular until appropriate constraints are applied (ie it can float in space, non-unique solution)
\(K\) typically has a “band” of non-zero values.
Boundary conditions are enforced on the nodes
Force (general) boundary conditions are added to the loading vector.
Displacement boundary conditions are enforced on the nodal displacement vector.
“Elimination method/Matrix Partitioning”
“Penalty method”
The “cost” of solving the problem scales exponentially with \(N\) (and bandwidth)