曲梁在彎－剪耦合條件下之非彈性應力分析

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曲梁在弯－剪耦合条件下之非弹性应力分析

Inelastic Stress Analysis of Curved Beams under Bending and Shear Coupling

黄诗乔 , 硕士　　导师：王彦博　　

繁体中文

封闭式类椭圆阻尼器；弹性力学；应变－谐合方程式；非线弹性分析；边界值问题； in-Plane Oval Damper ； elasticity ； strain-compatibility ； inelastic stress analysis ； boundary-valued problem

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摘要 │ 参考文献 (15) │ 国际计量

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An analytical and experimental study on the proposed in-plane flexural damper has been conducted in this thesis, which includes development of the inelastic stress analysis of curved beams with bending and shear coupling, as well as component test of in-Plane Oval Damper. Experimental results indicate that the proposed in-plane flexural damper in closed-form performs in a more stable manner than the previous one in terms of the ultimate strength and energy dissipation capacity among others. In addition, the characteristics of the damper are found to be related to the product of the average radius of the arched segment with the arm length, providing for a design reference. If the stiffness ratio is known as a priori, ANSYS can be used to effectively simulate the hysteretic behavior and mechanical characteristic of the in-Plane dampers. However, the bilinear stress-strain model does not reflect the stiffness softening characteristic in large deformation, and leads to deviation of the analytical prediction from its test counterpart. In this study, an analytical model for inelastic stress analysis has been developed based on the classical theory of elasticity on curved beams in conjunction with the generalized Hook’s law under plane stress condition and plastic strains defined using the total deformation theory. The inelastic stress analysis of curved beams under bending and shear coupling is further advanced from the numerical method by Eraslan and Arslan developed for pure bending only. The numerical algorithm is to first transform the boundary-value problem into a two-stage initial-value problem following by an iterative process in solving the ODE. The yielding state is determined by von Mises’ yielding criterion, and the swift-type hardening law is considered as the stress-strain relationship of the material in plastic stage. When the load is within the elastic limit, numerical results predicted by the proposed method agree perfectly with their analytical counterparts given by the theory of elasticity, regardless of pure bending, end shear, or bending and shear coupling, suggesting adequacy of the proposed algorithm. The inelastic force-displacement relationship of the damper under monotonically increasing (or decreasing) loads can be regarded as the backbone curve of hysteresis loop, and the hysteresis loops can be reconstructed by adopting Masing’s rule. This serves as the basis of characterizing the mechanical properties of the damper and in turn for design. The inelastic stress analysis for straight beams, however, has not yet been completed in this study. The in-plane oval damper can be fully assessed after completion of the related theoretical development.

参考文献 ( 15 ) 〈TOP〉

2.王为元 (2014)，「面内挠曲式拱形阻尼器之材料力学理论与试验」，国立交通大学土木工程学系，硕士論文。
连结：
3.梁诚伟 (2014)，「面内挠曲式拱形阻尼器之弹性力学理论与试验」，国立交通大学土木工程学系，硕士論文。
连结：
5.A.N. Eraslan, E. Arslan (2008), “A Concise Analytical Treatment of Elastic-Plastic Bending of a Strain Hardening Curved Beam,” ZAMM, Vol. 88, No. 8, pp. 600-616.
连结：
7.E. Arslan, A.N. Eraslan (2010), “Analytical Solution to the Bending of a Nonlinearly Hardening Wide Curved Bar,” Acta Mechanica, Vol. 210, pp.71-84.
连结：
8.E. Arslan, A.N. Eraslan (2013), “Bending of graded curved bars at elastic limits and beyond,” International Journal of Solids and Structures, Vol. 50, pp.806-814.
连结：

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使用DOI作为永久连结

引用含有DOI的文献

DOI可强化引用精确性、增强学术圈连结，并给予使用者跨平台的良好使用经验，目前在全世界已有超过五千万个对象申请DOI。 如想对DOI的使用与概念有进一步了解，请参考 （ ） 。

DOI可强化引用精确性、增强学术圈连结，并给予使用者跨平台的良好使用经验，目前在全世界已有超过五千万个对象申请DOI。如想对DOI的使用与概念有进一步了解，请参考（）。