Convergence insights of closed-form and approximate solutions for functionally graded material columns
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
International Journal for Computational Methods in Engineering Science and Mechanics
Publication Status
Version of Record
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.
First Page
31
Last Page
55
DOI
10.1080/15502287.2024.2445000
Publication Date
1-1-2025
Recommended Citation
Suttin, Zachary; Elishakoff, Isaac; and Stewart, Kristopher, "Convergence insights of closed-form and approximate solutions for functionally graded material columns" (2025). Faculty Scholarship. 155.
https://digitalcommons.fau.edu/faculty_papers/155