Estimating Lower Bound Limit Loads for Structures Subjected to Multiple Loads

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It is shown that the extended variational theorem of Mura et al. (1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) can be applied to structures subjected to more than one load and be used to compute lower bound limit load multipliers. In particular, the multiplier proposed by Simha and Adibi-Asl (2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207), which can be computed using an elastic stress field, is shown to be a lower bound. Furthermore, it is demonstrated that lower bound limit load for cracked structures may also be computed using a subvolume selection method. No iterations or elastic modulus adjustment are required. Several analytical and numerical examples that illustrate the procedure are presented.