On the first order and buckling behaviour of thin-walled regular polygonal tubes

Abstract Mirror error compensation is usually employed to improve the machining precision of thin-walled parts. However, this zero-order method may result in inadequate error compensation, due to the time-varying cutting condition of thin-walled parts. To cope with this problem, an on-line first-order error compensation method is proposed for thin-walled parts. With this context, firstly, the time-varying cutting condition of thin-walled parts is defined with its in-process geometric and physical characteristics. Based on it, a first-order machining error compensation model is constructed. Then, during the process planning, the theory geometric and physical characteristic of thin-walled parts are respectively obtained with CAM software and structure dynamic modification method. After process performing, the real geometric characteristic of thin-walled parts is measured, and it is used to calculate the dimension error of thin-walled parts. Next, the error compensated value is evaluated based on the compensation model, from which, an error compensation plane is constructed to modify the tool center points for next process step. Finally, the machining error is compensated by performing the next process step. A milling test of thin-walled part is employed to verify the proposed method, and the experiment results shown that the proposed method can significantly improve the error compensation effect for low-stiffness structure, and thickness precision of thin-walled parts is improved by 71.4 % compared with the mirror error compensation method after machining.

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On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars

Acta Mechanica ◽

10.1007/s00707-020-02849-7 ◽

2020 ◽

Author(s):

T. Lewiński ◽

S. Czarnecki

Keyword(s):

Cross Sections ◽

Transverse Shear ◽

Explicit Construction ◽

Effective Characteristics ◽

Warping Function ◽

Torsional Buckling ◽

Lateral Buckling ◽

First Order ◽

Thin Walled ◽

Scientific Tool

Abstract By endowing El Fatmi’s theories of bars with first-order warping functions due to torsion and shear, a family of theories of bars, of various applicability ranges, is effectively constructed. The theories thus formed concern bars of arbitrary cross-sections; they are reformulations of the mentioned theories by El Fatmi and theories by Kim and Kim, Librescu and Song, Vlasov and Timoshenko. The Vlasov-like theory thus developed is capable of describing the torsional buckling and lateral buckling phenomena of bars of both solid and thin-walled cross-sections, which reflects the non-trivial correspondence, noted by Wagner and Gruttmann, between the torsional St.Venant’s warping function and the contour-wise defined warping functions proposed by Vlasov. Moreover, the present paper delivers an explicit construction of the constitutive equations of Timoshenko’s theory; the equations linking transverse forces with the measures of transverse shear turn out to be coupled for all bars of asymmetric cross-sections. The modeling is hierarchical: the warping functions are numerically constructed by solving the three underlying 2D scalar elliptic problems, providing the effective characteristics for the 1D models of bars. The 2D and 1D problems are indissolubly bonded, thus forming a unified scientific tool, deeply rooted in the hitherto existing knowledge on elasticity of elastic straight bars.

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Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

Continuum Mechanics and Thermodynamics ◽

10.1007/s00161-019-00847-2 ◽

2019 ◽

Vol 32 (5) ◽

pp. 1347-1356 ◽

Cited By ~ 1

Author(s):

Czesław Szymczak ◽

Marcin Kujawa

Keyword(s):

Sensitivity Analysis ◽

Cross Section ◽

Torsional Vibration ◽

Volume Fraction ◽

Fibre Volume Fraction ◽

Vibration Frequencies ◽

Cross Sectional ◽

First Order ◽

Thin Walled ◽

Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

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GBT formulation to analyse the first-order and buckling behaviour of thin-walled members with arbitrary cross-sections

Thin-Walled Structures ◽

10.1016/j.tws.2008.09.007 ◽

2009 ◽

Vol 47 (5) ◽

pp. 583-600 ◽

Cited By ~ 64

Author(s):

R. Gonçalves ◽

P.B. Dinis ◽

D. Camotim

Keyword(s):

Cross Sections ◽

First Order ◽

Thin Walled

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A New Thin-Walled Beam-Column Element Using First-Order Beam Theory

Civil Engineering and Urban Planning 2012 ◽

10.1061/9780784412435.007 ◽

2012 ◽

Author(s):

Jing Jiang ◽

Zhaoqiang Wang

Keyword(s):

Beam Theory ◽

First Order ◽

Thin Walled ◽

Column Element

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