By Stephen P. Timoshenko, James M. Gere, Donovan H. Young
Topics variety from theoretical motives of two- and 3D pressure and pressure to functional purposes akin to torsion, bending, thermal rigidity, and wave propagation via solids. extra topics contain beam columns, curved bars and arches, buckling of earrings, and experiments and layout formulation. rather compatible for complicated undergraduate and graduate scholars of engineering, this quantity can also be an imperative reference for professionals.
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Additional info for Theory of Elastic Stability
It is clear from equation (10) that for discretizations in Rd these products can be efficiently calculated in O(KNd+l) operations using sum-factorization methods . Additional computational efficiency can be gained by exploiting the regular structure of the spectral (intra-element) operators and recognizing that the inner most kernel of the matrix-vector product, (Dip up;), is exactly equivalent to a matrix-matrix product which can be rapidly evaluated on many vector architectures. In addition to the 0 (K Nd+l) computational effort, the direct stiffness summation will require O(KN d - 1 ) operations, corresponding to the number of degrees-of-freedom lying on the element interfaces.
Numerical results clearly demonstrate the superiority of the iterative algorithm over implicit/direct and explicit strategies. The iterative algorithm, in its present form, is not applicable to completely general nonsymmetric systems, as we assume either the diagonal entries are positive, or the nodal block-diagonal submatrices admit Cholesky factorization. However, we conjecture these properties are possessed by many finite element discretizations of well-posed physical problems of interest. Current work is focused on reducing the data base of the unassembled element file.
The value of E that was used for checking convergence of eigenvectors as in Eq. (47) and following was 10- 9 . If the determinant of the 2 X 2 mass matrix was less than E, only a single vector was included in the reduced subspace for representing the eigenvector in question. If this determinant was less than two orders of magnitude smaller than EO, the included vector was a linear combination of the present and previous iterates, found by solving the associated 2 x 2 eigenvalue problem. If the determinant was more than two orders of magnitude smaller than EO, it was assumed that the present iterate was sufficiently accurate by itself.
Theory of Elastic Stability by Stephen P. Timoshenko, James M. Gere, Donovan H. Young