Variational Method in Limit Load Analysis—A Review

This paper reviews the literature on variational method in limit load analysis and presents both analytical and numerical approaches. One of the most successful applications of variational method in theory of plasticity is limit load analysis. The main objective of the limit load analysis is to estimate the load at the impending plastic limit state of a body. However, for complicated problems it may be very difficult to find the exact limit load. Therefore, based on the extremum principles of limit load analysis, the lower-bound theorem or the upper bound theorem is employed to estimate the limit load directly without considering the entire loading history. In general, limit load analysis plays an important role in design and fitness-for-service assessment of pressurized vessels and piping.