Examining Eigenvalues and Eigenvectors of Stiffness

Examining Eigenvalues and Eigenvectors of Stiffness

Matrix The eigenvalues and eigenvectors of the stiffness matrix have some physical meanings. An eigenvalue and its associated eigenvector can be interpreted as a strain energy and corresponding displacement mode, respectively. On the basis of this physical meaning, an eigenvector can be graphically visualized as a displacement mode which results in the strain energy relevant to the associated eigenvalue as exemplified in the figure below. The images of the displacement modes are overlaid on the undeformed images of the model. They can also be visualized in the form of animation. For a 3-dimensional model, the view may be transformed freely without interruption of display or animation.
The set of an eigenvalue and associated eigenvector is termed “eigen mode. ”There are as many eigen modes as the number of free d.o.f. in the model, which may consist of a single element, a number of selected elements, or the whole system. The model may or may not include the boundary constraints, which are reflected in eigen modes. The integration rules as well as the element properties assigned to the model are also reflected in the displayed eigen modes. This educational function is useful in teaching or understanding the meaning of eigenvalues and eigenvectors, and their consequences in relation to element characteristics. This function may also be used for more practical purposes such as diagnosing the validity and the efficiency of the element. This function is available for all types of structural models supported in VisualFEA/CBT, but not for heat transfer models.

< Graphically visualized eigenvalues and eigenvectors >