The paper proposes a method of incremental loading for solving nonlinear problems of shell theory. A feature of this method is that the same algorithm is used before buckling, at the limit point, and after buckling. The method is based on the assumption that all the unknowns, including the load parameter, are on an equal footing. It is shown that the method can be used to solve algebraic equations with Cramer's rule involved to avoid numerical instability in the neighborhood of the limit point. Test problems confirm the validity of the approach
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 85–93, September 2008.
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Semenyuk, N.P., Trach, V.M. & Zhukova, N.B. Incremental analysis of the nonlinear behavior of thin shells. Int Appl Mech 44, 1025–1031 (2008). https://doi.org/10.1007/s10778-009-0114-x
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DOI: https://doi.org/10.1007/s10778-009-0114-x