矩形截面齐次广义屈服函数及刚架极限承载力
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摘要
针对矩形截面刚架结构极限承载力分析中存在的问题,本研究通过控制性内力分析遴选了合适的矩形截面广义屈服函数,通过齐次化后建立了矩形截面刚架结构极限承载力分析的弹性模量缩减法.首先,根据回归分析和拟合误差分析建立了等效齐次广义屈服函数;其次,利用齐次广义屈服函数定义单元承载比,通过有策略地缩减高承载单元弹性模量模拟结构刚度退化,进而通过线弹性迭代分析确定矩形截面刚架结构的极限承载力;最后,根据内力占比研究了平面及空间受力刚架的控制性内力,通过对比分析遴选确定了合理的齐次广义屈服函数,并验证了本研究提出的方法的计算精度和效率.结果表明:本研究提出的方法作为线弹性迭代方法具有很高的计算精度,且克服了传统的非线性迭代方法的缺陷,能够取得更高的计算效率.
In order to solve the problems in the ultimate bearing capacity analysis of steel frames with rectangular sections,an appropriate generalized yield function of rectangular cross-section was selected through the control internal force analysis,and then the elastic modulus reduction method for the analysis of the ultimate bearing capacity of rectangular cross-section rigid frame structure was established through the homogenization.Firstly,the equiva-lent homogeneous generalized yield function was established based on regression analysis and fitting error analysis. Secondly,the element bearing ratio were defined based on the homogeneous generalized yield function,then,the elastic modulus reduction method was proposed for determining the ultimate bearing capacity of steel frame by strategically reducing the elastic modulus of the highly stressed elements to simulate the structural stiffness damage. Finally,the key internal forces of the plane and space steel frames were investigated by means of determining the internal force ratios,further,an exact homogeneous generalized yield function was determined,and the accuracy and efficiency of the proposed method was verified. The results show that the proposed method as a linear elastic ite-rative method has high accuracy and overcomes the limitations of the traditional nonlinear iterative method,which can achieve higher computational efficiency.
In order to solve the problems in the ultimate bearing capacity analysis of steel frames with rectangular sections,an appropriate generalized yield function of rectangular cross-section was selected through the control internal force analysis,and then the elastic modulus reduction method for the analysis of the ultimate bearing capacity of rectangular cross-section rigid frame structure was established through the homogenization.Firstly,the equiva-lent homogeneous generalized yield function was established based on regression analysis and fitting error analysis. Secondly,the element bearing ratio were defined based on the homogeneous generalized yield function,then,the elastic modulus reduction method was proposed for determining the ultimate bearing capacity of steel frame by strategically reducing the elastic modulus of the highly stressed elements to simulate the structural stiffness damage. Finally,the key internal forces of the plane and space steel frames were investigated by means of determining the internal force ratios,further,an exact homogeneous generalized yield function was determined,and the accuracy and efficiency of the proposed method was verified. The results show that the proposed method as a linear elastic ite-rative method has high accuracy and overcomes the limitations of the traditional nonlinear iterative method,which can achieve higher computational efficiency.
引文
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[4] FENG X,GUO S H.Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method [J].Mechanics Research Communications,2017,79:32- 42.
[5] MAHMOOD S L,SESHADRI R.Limit load evaluation using the mα-tangent multiplier in conjunction with elastic modu-lus adjustment procedure [J].Journal of Pressure Vessel Technology,2013,135(5):051203.
[6] 吕岩松.环肋轴对称组合壳塑性极限分析的弹性模量调整有限元法 [J].海军工程大学学报,2014,26(5):83- 87.Lü Yansong.Elastic modulus adjustment FEM for plastic limit analysis of ring-stiffened axisymmetric combination shell [J].Journal of Naval University of Engineering,2014,26(5):83- 87.
[7] 杨绿峰,郑健,张伟,等.钢管混凝土拱桥极限承载力分析的自适应方法 [J].中国公路学报,2017,30(3):191- 199.YANG Lufeng,ZHENG Jian,ZHANG Wei,et al.Self-adaptive approach for analysis of ultimate load bearing capacity of concrete-filled steel tubular arch bridges [J].China Journal of Highway & Transport,2017,30(3):191- 199.
[8] CHEN X H,GAO B,WANG X.Evaluation of limit load analysis for pressure vessels—part II robust methods [J].Steel & Composite Structures,2017,23(1):131- 142.
[9] MACKENZIE D,BOYLE J T,HAMILTON R.The elastic compensation method for limit and shakedown analysis:a review [J].Journal of Strain Analysis,2000,35(3):171- 188.
[10] YANG L F,YU B,QIAO Y P.Elastic modulus reduction method for limit load evaluation of frame structures [J].Acta Mechanica Solida Sinica,2009,22(2):109- 115.
[11] SANTATHADAPORN S,CHEN W F.Interaction curves for sections under combined biaxial bending and axial force [M].New York:Fritz Engineering Laboratory,1968:1- 44.
[12] DUAN L,CHEN W F.A yield surface equation for doubly symmetrical sections [J].Engineering Structures,1990,12(2):114- 119.
[13] GENDY A S,SALEEB A F.Generalized yield surface representations in the elasto-plastic three-dimensional analysis of frames [J].Computers & Structures,1993,49(2):351- 362.
[14] 杨绿峰,蒋莉芳,郑健,等.矩形钢管混凝土齐次广义屈服函数与桁架结构极限承载力 [J].土木工程学报,2017,50(11):65- 75.YANG Lufeng,JIANG Lifang,ZHENG Jian,et al.Homogenous generalized yield function and ultimate load-bearing capacity analysis of rectangular concrete-filled steel tubular trusses [J].China Civil Engineering Journal,2017,50(11):65- 75.
[15] YANG L F,YU B,JU J W.Incorporated strength capacity technique for limit load evaluation of trusses and framed structures under constant loading [J].Journal of Structual Engineering-ASCE,2015,141(11):1- 11.
[16] SHI J,BOYLE J T,MACKENZIE D,et al.Approximate limit design of frames using elastic analysis [J].Computers & Structures,1996,61(3):495- 501.