Min(max)imization of horizontal and vertical displacements of a fibre-reinforced magneto-elastic cantilever rod

Asatur Zh. Khurshudyan

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Min(max)imization of horizontal and vertical displacements of a fibre-reinforced magneto-elastic cantilever rod

机译：纤维增强磁力弹性悬臂杆的水平和垂直位移的MIN（MAX）亚化

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In this brief note we suggest a procedure for extremization of horizontal and vertical displacements of a nonlinear fibre-reinforced magneto-elastic rod subjected to an oblique magnetic field and a concentrated load applied at the rod end-point. The control parameter is the angle formed by the magnetic field and the rod axis. The governing equation is nonlinear in both the unknown function and in the control parameter. The exact (implicit) solution of the governing equation is obtained. Moreover, we apply the Bubnov-Galerkin procedure and the Newton-Raphson iterative method to obtain an approximate solution to the problem. Numerical analysis of the approximate solution allows to study the influence of the magnetic field and concentrated force on the rod displacement field.

机译：在本简要说明中，我们建议一种用于经历倾斜磁场的非线性纤维增强磁弹性杆的水平和垂直位移的一个过程，以及在杆端点施加的集中负载。控制参数是由磁场和杆轴形成的角度。控制方程在未知函数和控制参数中是非线性的。获得控制方程的精确（隐式）解。此外，我们应用Bubnov-Galerkin手术和牛顿 - Raphson迭代方法，以获得对问题的近似解决方案。近似解决方案的数值分析允许研究磁场和集中力对杆位移场的影响。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2018年第11期|共6页
作者
Asatur Zh. Khurshudyan;
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作者单位

Department on Dynamics of Deformable Systems and Coupled Fields Institute of Mechanics National Academy of Sciences of Armenia 24B Baghramyan Ave. 0019 Yerevan Armenia;

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原文格式 PDF
正文语种 eng
中图分类应用数学;力学;
关键词
Bubnov-Galerkin procedure; fibre-reinforced composites; Newton-Raphson method; nonlinear magnetoelasticity; optimization;

机译：Bubnov-Galerkin手术;纤维增强复合材料;Newton-Raphson方法;非线性磁力弹性;优化;

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1. Min(max)imization of horizontal and vertical displacements of a fibre-reinforced magneto-elastic cantilever rod [J] . Asatur Zh. Khurshudyan Zeitschrift fur Angewandte Mathematik und Mechanik . 2018,第11期

机译：纤维增强磁力弹性悬臂杆的水平和垂直位移的MIN（MAX）亚化
2. A Theoretical Model to Predict Both Horizontal Displacement and Vertical Displacement for Electromagnetic Induction-Based Deep Displacement Sensors [J] . Hongjian Zhang, Hongliang Zhou, Nanying Shentu, Sensors . 2011,第1期

机译：基于电磁感应的深位移传感器预测水平位移和垂直位移的理论模型
3. A Theoretical Model to Predict Both Horizontal Displacement and Vertical Displacement for Electromagnetic Induction-Based Deep Displacement Sensors [J] . Hongjian Zhang, Hongliang Zhou, Nanying Shentu, Sensors . 2011,第1期

机译：基于电磁感应的深位移传感器预测水平位移和垂直位移的理论模型
4. Application of the Horizontal Membership Function to the Uncertain Displacement Calculation of a Composite Massless Rod Under a Tensile Load [C] . Karina Tomaszewska, Andrzej Piegat Advances Computer Systems Conference . 2015

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5. Benchmark of CFD Simulations Using Temperatures Measured Within an Enclosed Array of Heater Rods Oriented Vertically and Horizontally. [D] . Chalasani, Narayana Rao. 2010

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6. A Theoretical Model to Predict Both Horizontal Displacement and Vertical Displacement for Electromagnetic Induction-Based Deep Displacement Sensors [O] . Nanying Shentu, Hongjian Zhang, Qing Li, 2012

机译：基于电磁感应的深位移传感器预测水平位移和垂直位移的理论模型
7. A nonlinear theory for fibre-reinforced magneto-elastic rods [O] . Ciambella, Jacopo, Favata, Antonino, Tomassetti, Giuseppe 2017

机译：纤维增强磁弹性杆的非线性理论
8. Spectrum of Atmospheric Vertical Displacements and Spectrum of Conservative Scalar Passive Additives due to Quasi-Horizontal Atmospheric Motions [R] . Gage, K. S., Nastrom, G. D. 1986

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Min(max)imization of horizontal and vertical displacements of a fibre-reinforced magneto-elastic cantilever rod

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