對稱斷面複材薄壁樑之側向挫屈分析與模擬

本研究的目的在建立具有對稱斷面的複材I 型樑的側向挫屈分析模型與有限元素模擬。在考慮樑的翹曲效應下，本文推導出I 型樑的翹曲函數的解析形式，並將此函數代入樑的應力-應變關係式，在對稱斷面及翹曲函數為奇函數的前提下，可推導出彼此獨立的合力/合力矩與位移的關係式，最後加上外力在樑變形前後座標系的幾何關係，即可得到挫屈方程式。本文並以簡支樑在純彎矩作用下及懸臂樑在自由端受到一集中力作用下的側向挫屈分析為例，求出其臨界彎矩的表示式，此表示式在等向性的假設下，經簡化後與文獻上的結果完全相符。同時，本文也建立了I 型樑的有限元素模型來進行側向挫屈的數值分析，此模型經由與文獻結果的比較來證明其正確性，之後再與理論推導的結果作一比較，相互驗證以及觀察彼此間的差異。最後，針對影響I 型樑側向挫屈行為的影響因素，例如細長比、厚度與疊層角度等，做一分析探討，以做為結構安全設計上的參考依據。關鍵詞：側向挫屈、複材I 型樑、翹曲函數、有限元素分析。

關鍵字

側向挫屈；複材I 型樑；翹曲函數；有限元素分析

並列摘要

Analytical and finite element model of lateral buckling analysis are developed for composite I-beams with symmetric cross-section. Consider the warping effect, the analytical form of the warping function is derived. Substituting this warping function into the stress-strain relationship of the composite I-beams and under the conditions that the cross-section is symmetric and the warping function is an odd function, the equations of the relations of the force/moment and displacement which are proved to be independent each other will be obtained. By adding the geometric relation between undeformed and deformed coordinate systems for the applied load will lead to the buckling equation. As illustrating examples,the lateral buckling analysis of a simple-supported beam under pure bending and a cantilever beam subjected to a concentrated force on its free end are performed, the analytical forms of the critical loads are derived, and the reduced form of the solutions for isotropic case are verified when compared to the existing literature. In addition, a finite element model of a composite I-beam is established, and the numerical results of critical loads are proved to agree well with those obtained in the literature. Then the analytical and finite element results are compared with each other to observe the deviation between these two different approaches. Finally, the factors affecting the lateral buckling behavior of a composite I-beam, such as slenderness, thickness and stacking angles of laminates, are investigated to give a better understanding for this problem. Keywords: lateral buckling, composite I-beam, warping function, finite element analysis

並列關鍵字

lateral buckling ； composite I-beam ； warping function ； finite element analysis

參考文獻

1. Chang, S. I. and Libove, C., “Shear Flows, Strains and Rate of Twist

2. Libove, C., “Stresses and Rate of Twist in Single-cell Thin-walled Beams with Anisotropic Walls”, AIAA J., 26, pp.1107-1118 (1988).

3. Wu, X. X. and Sun, C. T., “Simplified Theory for Composite Thin- walled Beams”,AIAA J., 30, pp.2945-2951 (1992).

4. Librescu, L. and Song, O., “Behavior of Thin-walled Beams Made of Advanced Composite Materials and Incorporating Non-classical Effect”, Apply Mech. Rev., 44, pp.S174-S180 (1991).

5. Librescu,L.and Song,O.,“Free Vibration and Aeroelastic Divergence

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對稱斷面複材薄壁樑之側向挫屈分析與模擬

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