ABSTRACT This paper proposes a new matrix method for calculation of critical loads and natural frequencies of circular arches with variable cross section and arbitrary forms of applied load distribution. A difference from other matrix methods is that the coefficient determinant of the corresponding characteristic equation can be reduced to one of third-order, no matter how many elements are discretized in calculation. The essential reason for the important advantage is introduction of correlation matrices associated with discrete nodes into the analysis. The method is applicable to elastic arches of arbitrary geometry.
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