Convergence insights of closed-form and approximate solutions for functionally graded material columns

Author Type

Faculty

Co-Author Type 1

Faculty

Co-Author Type 2

Faculty

Co-Author Type 3

Outside Researcher

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

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