ABSTRACT
Note that Equation 16.33 has no solution since the global stiffness matrix has no inverse: the second row is the negative of the sum of the first and last rows. This suggests that, due to numerical errors in the load increments, the condition for static equilibrium is not satisfied numerically, and therefore that the body is predicted to accelerate indefinitely (undergo rigid-body motion). However, we also know that the configuration under incremental loads is symmetric, implying a constraint du2=0. This constraint permits “condensation,” that is, reducing Equation 16.33 to a system with two unknowns by eliminating rows and columns associated with the middle incremental displacement:
(16.34)
The condensed matrix is now proportional to the identity matrix, and the system has a solution. In general, stiffness matrices can easily be singular or nearly singular (with a large condition number) unless constraints are used to suppress “rigid-body modes.”
