CosmosWorks算法验证文件 9 (Buckling Analysis)

tigerdak

.
提示：屈曲分析（特征值法）。
. \, j/ u/ F6 L
# w$ o8 E( r$ pTitle      Buckling of a Bar with Hinged Ends (Line Elements)

8 C) ?7 A) O7 @7 P* m0 uOverview
+ q1 `# V& a# t( C9 {5 W( i2 }/ N
. K3 v# ~( C6 \

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 * Z  f$ E7 M0 }) m# W* L& K

Test Case

" N3 b. y0 B8 G, t  |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.

; L; B& D0 e4 L! G9 |1 y9 H6 p% bFigure 127.1  Buckling Bar Problem Sketch
% u! f& B! R- Z


8 d$ L0 Q/ f9 ^# t) v- X5 X9 Z3 f

Material Properties E = 30E6 psi

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

Loading F = 1 lb

: i9 [; ^, b$ u; w$ |$ F, J8 Y; p9 f/ pAnalysis 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 .

5 Z  C2 @$ g5 t, NResults Comparison

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

5 p4 p7 }+ H2 Z- G1 d) i

• Fcr = Load Factor (1st mode).

[ 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。

4 z7 [9 w: k) U5 Y8 q. |1 R. p# P1. 在杆的中间点加上1e-9 lb 初始扰动的非线性屈曲分析
1 q3 i2 S" ~7 R
/ Z' q* E, h! B' v$ I

+ s  {! [" R! P$ t5 m
  l; U/ I8 E; }2 `9 t2. 在杆的中间点加上1e-3 lb 初始扰动的非线性屈曲分析
; P  m. _& y- [' v+ @/ I0 \. R
; w+ M; H2 r! L7 _; D

' ^- P9 H3 T& v6 S% T[ 本帖最后由 tigerdak 于 2007-11-8 12:44 编辑 ]

tigerdak

对比CosmosWorks的计算结果
* X; w6 o% {2 I# _' @3 R, m1 U
/ W* g( Y0 X7 H4 g) e' m1. 特征值方法，即扭曲研究

Load＝38.553 lb

+ \$ h3 s7 k8 [* k

4 U+ M2 t9 l9 L) q0 M( @
. {7 |+ m6 |( L6 e* x( @# P  {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

+ Z& M) F+ V, l. s5 m( f
% b9 U+ r1 J7 ^6 }% x