CosmosWorks算法验证文件 9 (Buckling Analysis)

tigerdak

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9 G6 S; x7 d% s+ c3 w提示：屈曲分析（特征值法）。
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7 T0 m' _. X4 o5 k0 P  ?  KTitle      Buckling of a Bar with Hinged Ends (Line Elements)
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Overview
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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 $ k9 o' B9 S( I# ?2 d

5 Q) C8 D; h7 L, STest Case
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6 E8 F) d" K8 K# o1 ZDetermine 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 r5 w4 m, c) M! nFigure 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

  I; n& }: D+ A) t9 EAnalysis 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

• Fcr = Load Factor (1st mode).

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[ 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。
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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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1 f! D& _6 F0 |9 W. F* n* E5 A2. 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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3 S5 R" X1 i7 [7 S; O1. 特征值方法，即扭曲研究
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" y- l8 Z- T/ K( |Load＝38.553 lb

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7 }! M9 ^: o& h" J) ]1 B) q) F6 {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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