Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A successive bounding method to find the exact eigenvalues of transcendental stiffness matrix formulations
AU - Ye, Jianqiao
AU - Williams, F. W.
PY - 1995/3/30
Y1 - 1995/3/30
N2 - An alternative algorithm for finding exact natural frequencies or buckling loads from the transcendental, e.g. dynamic, stiffness matrix method is presented in this paper and evaluated by using the plate assembly testbed program VICONOPT. The method is based on the bounding properties of the eigenvalues provided by either linear or quadratic matrix pencils on the exact solutions of the transcendental eigenvalue problem. The procedure presented has five stages, including two accuracy checking stages which prevent unnecessary calculations. Numerical tests on buckling of general anisotropic plate assemblies show that significant time savings can be achieved compared with an earlier multiple determinant parabolic interpolation method.
AB - An alternative algorithm for finding exact natural frequencies or buckling loads from the transcendental, e.g. dynamic, stiffness matrix method is presented in this paper and evaluated by using the plate assembly testbed program VICONOPT. The method is based on the bounding properties of the eigenvalues provided by either linear or quadratic matrix pencils on the exact solutions of the transcendental eigenvalue problem. The procedure presented has five stages, including two accuracy checking stages which prevent unnecessary calculations. Numerical tests on buckling of general anisotropic plate assemblies show that significant time savings can be achieved compared with an earlier multiple determinant parabolic interpolation method.
KW - bounding exact
KW - transcendental eigenproblems
U2 - 10.1002/nme.1620380612
DO - 10.1002/nme.1620380612
M3 - Journal article
VL - 38
SP - 1057
EP - 1067
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 6
ER -