Using the stiffness method of matrix structural analysis, you build up the stiffness matrix. Is this matrix positive definite ? I know it is symmetrical and usually banded and when the support restraints are not excluded, also singular, but is it positive definite too ?
Google with: stiffness-matrix structural-analysis positive-definite
If it is "stable", yes. It is not required to be stable by the formalism of the mathematics, no.
David A. Smith
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