Deformation Decomposition Based on the Elemental Eigen-Deformation Shapes

The eigenvalues and eigenvectors decomposed from elemental stiffness matrix are related to the elemental characteristic parameters. By associating the eigenvectors with node-displacement vector, the elemental eigen-deformation shapes are defined. Each eigen-deformation shape is characterized by the cross-sectional characteristic parameters of EA, EI and GA etc. The first order Timoshenko beam element is used for illustration in this paper. The elemental stiffness matrix is decomposed to define the eigen-deformation shapes, including the axial, bending and the shear. The total deformation of each element is formulated as the weighted summation of the elemental eigen-deformation shapes together with given rigid body modes. The weights corresponding to the eigen-deformation shapes indicate the elemental deformation characteristic.The sensors to monitor the bending and shear strain are sorted and located based on the weights distribution in structure. Numerical examples are presented to illustrate the proposed method and its application.