CosmosWorks算法验证文件 9 (Buckling Analysis)

tigerdak

.
# `7 n! w8 X' Y. ~; @提示：屈曲分析（特征值法）。
% n  e1 F/ X9 J
! u" t/ n' n1 N# J! |2 `' O; yTitle      Buckling of a Bar with Hinged Ends (Line Elements)
# d; R: ]! v* _/ \! g% g  K; L0 y
Overview
* s; p/ x# [4 e% H
% o* a( h4 S4 c! N3 G; C

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   R  K8 N# W$ ?5 o7 o* fStatic

+ v0 ]% |+ z& n, J% e! V+ [! BTest Case
% e( [1 A. @" t4 r
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.

Figure 127.1  Buckling Bar Problem Sketch

. n, u* M% |0 w- T( v3 z
6 l6 U. t& P7 B" p1 K

Material Properties E = 30E6 psi

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

Loading F = 1 lb

% z" E+ H! d+ GAnalysis 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 .
- D& y* }2 U8 l0 {2 c: N
, g1 ^" \! T" g+ S9 OResults Comparison

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

& s- ?8 X/ V* x- \. T4 l, V

• Fcr = Load Factor (1st mode).

) X( U4 g) c# O, {; Z8 \' i! E
% z, o& c8 O% W' q1 ]6 m4 |: 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。

. U  t( j$ g. {1 o- k. v2 t1. 在杆的中间点加上1e-9 lb 初始扰动的非线性屈曲分析


$ }+ J' j/ U$ a5 Y  z6 O- J
' A1 f' t+ I( W! y1 Q' S8 Q
2. 在杆的中间点加上1e-3 lb 初始扰动的非线性屈曲分析
5 K) [# X; J: {, F6 l


6 i! {  {# F/ n+ E[ 本帖最后由 tigerdak 于 2007-11-8 12:44 编辑 ]

tigerdak

对比CosmosWorks的计算结果

4 Y, ?$ V2 M9 h% e1. 特征值方法，即扭曲研究

Load＝38.553 lb



3 ~% V6 ~! \( G# J# K6 W1 ^
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

4 h7 y' U# @6 W0 ?9 p  u% x! D0 w8 O

( e: r4 `  S  J) A5 }' ]* y