Approximations to buckling loads and other eigenvalues via the least-squares method. (English) Zbl 0907.73031

Summary: This paper traces the relations between the variational method and several approximate analytical techniques for estimating eigenvalues such as buckling loads and fundamental frequencies of vibration. A number of simple examples have been solved to corroborate some of the author’s statements concerning the upper and lower bounds. The numerical results obtained have been compared with the exact solutions.


74G60 Bifurcation and buckling
74H55 Stability of dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics