Invertible Does Not Mean Stable

That you can invert a stiffness matrix does not tell you everything about the numerical stability of a structural model built in OpenSees or any other finite element software. In fact, no finite element software actually forms the inverse of the stiffness matrix, but let's go with the misleading terminology anyway. Consider the beam shown … Continue reading Invertible Does Not Mean Stable →

Eigenvalues of the Stiffness Matrix

Students are exposed to eigenvalues and eigenvectors a few times through their structural engineering education. After the math department's obligatory treatment to sophomores with definitions, characteristic polynomials, and toy matrices, two to three years pass before students see eigenanalysis again as first year graduate students: Structural dynamics - find natural modes of vibration of a … Continue reading Eigenvalues of the Stiffness Matrix →