Abstract
This article provides a detailed accuracy study of various methods that are exposed in textbooks to for approximate evaluation of buckling loads by solving problems with known closed-form solutions. The inverse buckling problem for the inhomogeneous column is chosen with the known exact solution. The approximate methods utilized in the analysis are the Galerkin method, the finite element method (FEM), and the finite difference method (FDM). For each method, multiple boundary conditions for the columns, those being simply supported-simply supported (S-S) and clamped-clamped (C-C), are solved. These solved examples provide ample material for the interested reader to be acquainted with issues of accuracy achieved by each method. Whereas there are theorems for convergence, it is instructive to have actual demonstration of the convergence.
Published Version
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