曲梁在彎－剪耦合條件下之非彈性應力分析

Inelastic Stress Analysis of Curved Beams under Bending and Shear Coupling

黃詩喬

封閉式類橢圓阻尼器 ； 彈性力學 ； 應變－諧合方程式 ； 非線彈性分析 ； 邊界值問題 ； in-Plane Oval Damper ； elasticity ； strain-compatibility ； inelastic stress analysis ； boundary-valued problem

交通大學土木工程系所學位論文

2016年

碩士

王彥博

繁體中文

本研究針對面內撓曲式阻尼器進行理論分析與試驗，包括發展彎－剪耦合曲梁元件之彈塑性應力分析，以及封閉式類橢圓阻尼器之元件測試。元件測試結果顯示本研究提出之封閉式面內撓曲式阻尼器較諸先前發展的拱形阻尼器有更為穩定之性能表現，包括極限強度、消能能力等性能參數都得到提升，並找出這些性能參數與圓拱段平均半徑及力臂長度乘積之關係，可供設計參考。在勁度比已知之前提下，ANSYS可以有效模擬類橢圓阻尼器之非線性遲滯消能行為與力學特性，惟其雙線性應力－應變模型在變形較大時無法反映勁度趨緩的特徵而與試驗結果悖離。本文以曲梁彈性力學平面應力理論為基礎，結合廣義虎克定律與總變形理論所定義之塑性應變，發展出彈－塑性分析理論架構，並參考Eraslan與Arslan提出之曲梁在純彎條件下之非彈性應力分析方法，進一步發展出曲梁在彎－剪耦合作用下之非彈性應力分析法。數值計算係先將邊界值問題轉換成兩階段的初始值問題，經過迭代過程求解，降伏狀態之判斷係根據von Mises降伏指標決定，並採用Swift-type hardening law來描述材料塑性段之應力－應變關係。當載重在彈性範圍時，曲梁受純彎矩、端點剪力或彎－剪耦合之數值分析結果與彈性力學理論之解析解完全相符，支持本文理論之合理性。由單調遞增(減)載重下之彈－塑性分析結果之力－位移關係曲線可視為遲滯迴圈之背骨曲線，可遵循梅新準則推估完整的遲滯迴圈，作為建構阻尼器力學特性及設計之依據。本文尚未完成阻尼器直線段的彈塑性分析理論，相關理論完成後即能完整評估封閉式類橢圓阻尼器之力學行為。

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.

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