Exact Solutions of Linear Buckling for a Class of FGM Columns with Varying Cross-Section

Fabiani Marco; Mentrasti Lando

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Exact Solutions of Linear Buckling for a Class of FGM Columns with Varying Cross-Section

机译：具有不同横截面的一类FGM色谱柱线性屈曲的精确解

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摘要

This paper deals with the linear buckling problem for inhomogeneous Euler-Bernoulli column having both mechanical and geometrical properties variable along its length. Four classes of longitudinally functionally graded material columns with variable cross-sections are considered. The solutions of the relevant differential equations are obtained in terms of both hypergeometric functions and elementary functions. The normalized buckling loads are computed for five typical boundary conditions and they are validated by a comparison with approximate numerical results available in literature. The proposed formulation may provide a further benchmark for the accuracy assessment of numerical and approximated solutions.

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来源
《International journal of structural stability and dynamics》 |2021年第6期|共17页
作者
Fabiani Marco; Mentrasti Lando;
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作者单位

Univ Politecn Marche DICEA Via Brecce Bianche I-60131 Ancona Italy;

Univ Politecn Marche DICEA Via Brecce Bianche I-60131 Ancona Italy;

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原文格式 PDF
正文语种 eng
中图分类应用力学;
关键词
Buckling load; functionally graded material columns; varying cross-section; exact solutions; special functions;

机译：屈曲负载;功能渐变的材料柱;不同的横截面;精确的解决方案;特殊功能;

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1. THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION [J] . 谢用九, 宁钦海, 陈明伦应用数学和力学：英文版 . 1998,第005期
2. Exact solution and dynamic buckling analysis of a beam-column system having the elliptic type loading [J] . H. S. ARTEM, L. AYDIN 应用数学和力学：英文版 . 2010,第010期
3. Exact solution and dynamic buckling analysis of a beam-column system having the elliptic type loading [J] . H.S.ARTEM, L.AYDIN 应用数学和力学（英文版） . 2010,第010期
4. Non-linear multi-mode buckling of non-symmetric FML/FGM thin-walled columns with open cross-sections under compression [J] . Teter Andrzej, Mania Radoslaw J., Kolakowski Zbigniew Composite Structures . 2017,第MAY期

机译：压缩状态下具有开放横截面的非对称FML / FGM薄壁柱的非线性多模屈曲
5. Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov's method [J] . V Kumar, SJ Singh, VH Saran, Proceedings of the Institution of Mechanical Engineers. Part L, Journal of Materials: Design and Application . 2021,第4期

机译：使用Galerkin-Vlasov方法对线性变化厚度FGM板的自由振动分析的精确解决方案
6. Influence of the coupling matrix B on the interactive buckling of FML-FGM columns with closed cross-sections under axial compression [J] . Kolakowski Zbigniew, Mania Radoslaw J. Composite Structures . 2017,第Auga期

机译：耦合矩阵B对轴向压缩下横截面为FML-FGM的圆柱交互式屈曲的影响
7. EXACT SOLUTIONS FOR THE FREE VIBRATIONS AND BUCKLING OF RECTANGULAR PLATES WITH LINEARLY VARYING IN-PLANE LOADING [C] . Arthur W. Leissa, Jae-Hoon Kang The 2001 ASME International Mechanical Engineering Congress and Exposition, 2001, Nov 11-16, 2001, New York, New York . 2001

机译：平面内线性变化的矩形板自由振动和屈曲的精确解
8. Exact and asymptotic low Reynolds, time -varying solutions for spinning rods with a comparison to experiments on the micro and macroscale. [D] . Leiterman, Terry Jo. 2006

机译：精确而渐近的低雷诺，随时间变化的纺丝杆解决方案，并与微观和宏观实验进行了比较。
9. The Study of Buckling and Post-Buckling of a Step-Variable FGM Box [O] . Leszek Czechowski, Zbigniew Kołakowski 2019

机译：阶跃可变FGM箱的屈曲和后屈曲研究
10. Exact Solutions for Vibration and Buckling of An SS-C-SS-C Rectangular Plate Loaded by Linearly Varying In-plane Stresse [O] . 2004

机译：通过线性变化的平面内应力加载SS-C-SS-C矩形板的振动和屈曲的精确解决方案
11. Stability and Instability, Exact and Approximate Solutions of Linear Differential Equations with Time Varying Coefficients [R] . Ratcliffe, A. F. 1970

机译：具有时变系数的线性微分方程的稳定性和不稳定性，精确解和近似解

Exact Solutions of Linear Buckling for a Class of FGM Columns with Varying Cross-Section

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