A general way of obtaining novel closed-form solutions for functionally graded columns
In this paper, we present a general methodology for solving buckling problems for inhomogeneous columns. Columns that are treated are functionally graded in axial direction. The buckling mode is postulated as the general order polynomial function that satisfies all boundary conditions. For specifici...
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| Veröffentlicht in: | Archive of applied mechanics (1991) 2017-10, Vol.87 (10), p.1641-1646 |
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| container_title | Archive of applied mechanics (1991) |
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| creator | Eisenberger, Moshe Elishakoff, Isaac |
| description | In this paper, we present a general methodology for solving buckling problems for inhomogeneous columns. Columns that are treated are functionally graded in axial direction. The buckling mode is postulated as the general order polynomial function that satisfies all boundary conditions. For specificity, we concentrate on the boundary conditions of simple support, and employ the second-order ordinary differential equation that governs the buckling behavior. A quadratic polynomial is adopted for the description of the column’s flexural rigidity. Satisfaction of the governing differential equation leads to a set of nonlinear algebraic equations that are solved exactly. In addition to the recovery of the solutions previously found by Duncan and Elishakoff, several new solutions are arrived at. |
| doi_str_mv | 10.1007/s00419-017-1278-1 |
| format | Article |
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Columns that are treated are functionally graded in axial direction. The buckling mode is postulated as the general order polynomial function that satisfies all boundary conditions. For specificity, we concentrate on the boundary conditions of simple support, and employ the second-order ordinary differential equation that governs the buckling behavior. A quadratic polynomial is adopted for the description of the column’s flexural rigidity. Satisfaction of the governing differential equation leads to a set of nonlinear algebraic equations that are solved exactly. 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Columns that are treated are functionally graded in axial direction. The buckling mode is postulated as the general order polynomial function that satisfies all boundary conditions. For specificity, we concentrate on the boundary conditions of simple support, and employ the second-order ordinary differential equation that governs the buckling behavior. A quadratic polynomial is adopted for the description of the column’s flexural rigidity. Satisfaction of the governing differential equation leads to a set of nonlinear algebraic equations that are solved exactly. In addition to the recovery of the solutions previously found by Duncan and Elishakoff, several new solutions are arrived at.</description><subject>Boundary conditions</subject><subject>Buckling</subject><subject>Classical Mechanics</subject><subject>Columns (structural)</subject><subject>Differential equations</subject><subject>Engineering</subject><subject>Functionally gradient materials</subject><subject>Mathematical analysis</subject><subject>Nonlinear equations</subject><subject>Ordinary differential equations</subject><subject>Original</subject><subject>Polynomials</subject><subject>Theoretical and Applied Mechanics</subject><issn>0939-1533</issn><issn>1432-0681</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAURYMoOI7-AHcB19G8JG2a5TD4BYIbdRuSNCkdOs2YtMr8ezOMCzeuHhfOvTwOQtdAb4FSeZcpFaAIBUmAyYbACVqA4IzQuoFTtKCKKwIV5-foIucNLXjF6AJ9rHDnR5_MgL_NHseAo51MP_Zjh8f45Qfshph9S0JMW5zjME99HDMuEYd5dIdkhmGPu2Ra32JXiO2YL9FZMEP2V793id4f7t_WT-Tl9fF5vXohjkM9EVk78MpIIZTwFVPOBytap5xQTVvXnIEVDWsaGipjbKDWNpJbYQNzraqt4Ut0c9zdpfg5-zzpTZxT-ShrUEJWQlKpCgVHyqWYc_JB71K_NWmvgeqDPn3Up4s-fdCnoXTYsZMLO3Y-_Vn-t_QDsdhziQ</recordid><startdate>20171001</startdate><enddate>20171001</enddate><creator>Eisenberger, Moshe</creator><creator>Elishakoff, Isaac</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20171001</creationdate><title>A general way of obtaining novel closed-form solutions for functionally graded columns</title><author>Eisenberger, Moshe ; Elishakoff, Isaac</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-76c1e9a74494e529cefb4dc9c498d66321b482880f5aabf0bb873b4bf2cd96ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Boundary conditions</topic><topic>Buckling</topic><topic>Classical Mechanics</topic><topic>Columns (structural)</topic><topic>Differential equations</topic><topic>Engineering</topic><topic>Functionally gradient materials</topic><topic>Mathematical analysis</topic><topic>Nonlinear equations</topic><topic>Ordinary differential equations</topic><topic>Original</topic><topic>Polynomials</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Eisenberger, Moshe</creatorcontrib><creatorcontrib>Elishakoff, Isaac</creatorcontrib><collection>CrossRef</collection><jtitle>Archive of applied mechanics (1991)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Eisenberger, Moshe</au><au>Elishakoff, Isaac</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A general way of obtaining novel closed-form solutions for functionally graded columns</atitle><jtitle>Archive of applied mechanics (1991)</jtitle><stitle>Arch Appl Mech</stitle><date>2017-10-01</date><risdate>2017</risdate><volume>87</volume><issue>10</issue><spage>1641</spage><epage>1646</epage><pages>1641-1646</pages><issn>0939-1533</issn><eissn>1432-0681</eissn><abstract>In this paper, we present a general methodology for solving buckling problems for inhomogeneous columns. 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| ispartof | Archive of applied mechanics (1991), 2017-10, Vol.87 (10), p.1641-1646 |
| issn | 0939-1533 1432-0681 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Boundary conditions Buckling Classical Mechanics Columns (structural) Differential equations Engineering Functionally gradient materials Mathematical analysis Nonlinear equations Ordinary differential equations Original Polynomials Theoretical and Applied Mechanics |
| title | A general way of obtaining novel closed-form solutions for functionally graded columns |
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