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）。

$ p( A. R1 j% A3 v: a. q( ATitle      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 Static , }+ y, }) F* |. V/ ~: S

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.
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Figure 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

  F5 U# L3 x' O) X, O; IAnalysis 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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Results Comparison

	Target	ANSYS	Ratio
Fcr, lb	38.553	38.553 [1]	1.000

• Fcr = Load Factor (1st mode).

" V, V4 ]; F1 p; T3 H* u[ 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
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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
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' ~6 e" O6 e, d5 ~1. 特征值方法，即扭曲研究

Load＝38.553 lb
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2. 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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