CosmosWorks算法验证文件 9 (Buckling Analysis)

tigerdak

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提示：屈曲分析（特征值法）。
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Title      Buckling of a Bar with Hinged Ends (Line Elements)
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Reference:	S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 148, article 29.
Analysis Type(s):	Buckling Analysis ) w  U2 k6 F  f8 r, N: VStatic

Test Case
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Determine the critical buckling load of an axially loaded long slender bar of length L with hinged ends. The bar has a cross-sectional height h, and area A.

5 T) u" R3 N% j8 [8 w5 m3 Y- N! YFigure 127.1  Buckling Bar Problem Sketch
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Material Properties E = 30E6 psi

Geometric Properties l = 200 in A = 0.25 in2 h = 0.5 in

Loading F = 1 lb

! h+ @2 F) X& \3 j) E% K8 qAnalysis Assumptions and Modeling NotesOnly the upper half of the bar is modeled because of symmetry. The boundary conditions become free-fixed for the half symmetry model. A total of 10 master degrees of freedom in the X-direction are selected to characterize the buckling mode. The moment of inertia of the bar is calculated as I = Ah2/12 = 0.0052083 in4 .
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	Target	ANSYS	Ratio
Fcr, lb	38.553	38.553 [1]	1.000

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• Fcr = Load Factor (1st mode).

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: f& V9 D- O' R5 C[ 本帖最后由 tigerdak 于 2007-11-8 18:44 编辑 ]

tigerdak

屈曲分析方法分两种：特征值法和非线性分析法。特征值法偏向于纯理论计算，不考虑零件的缺陷和环境影响，所以非线性分析方法更准确。以下方法在杆的中间点加上微小力来模拟零件缺陷或环境影响。一般会比理论计算值低。

1. 在杆的中间点加上1e-9 lb 初始扰动的非线性屈曲分析




# f. E$ |4 c5 s9 X# Z. ?2. 在杆的中间点加上1e-3 lb 初始扰动的非线性屈曲分析

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[ 本帖最后由 tigerdak 于 2007-11-8 12:44 编辑 ]

tigerdak

对比CosmosWorks的计算结果

4 z, F" O# y& g. ~1. 特征值方法，即扭曲研究
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Load＝38.553 lb
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/ T. `; d/ s$ s2. 加 FX＝0.001 lb 初始扰动的非线性分析，从图中可看到在0.732996秒发生扭曲，此时Load＝36.65 lb
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