考虑各向同性塑性损伤的钢结构塑性区分析方法
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摘要
基于更新拉格朗日构形的增量虚位移原理和三维空间薄壁构件理论,以构件拉弯、压弯、纯弯及扭转状态下平衡微分方程的解作为形函数,详细推导了考虑截面翘曲影响的空间薄壁梁柱单元的几何非线性切线刚度矩阵;基于结构钢各向同性塑性累积损伤的本构关系,以及能反映Baus-chinger效应和屈服面扩张的Zeigler混合强化模型、Von Mises屈服准则、相关流动法则,推导了考虑材料损伤和混合强化本构关系的弹塑性刚度矩阵.算例证明文中的方法可以达到较高的精度,从而为进行空间钢框架结构考虑损伤的高等分析提供了依据.
According to the increment virtual displacement principle based on the updated Lagrange configuration and 3D space thin-walled member theory,the solutions of equilibrium equations under stretch-bending,compression-bending,pure bending and torsion,are taken as the interpolation functions,and the geometrical nonlinear stiffness matrix of space thin-walled beam-column elements considering cross-section warping effect is derived. The Von Mises yield criterion in combination with the Zeigler mixed hardening assumption which takes the Bauschinger effect and yield surface expansion into account and an association flow rule is incorporated into the material nonlinearity consideration,and the constitutive equations based on isotropic plastic accumulative damage are considered in the process.The accuracy and efficiency of the proposed analytical configuration are verified by numerical examples,and the method may provide a foundation for the advanced analysis of space steel frames considering damage.
According to the increment virtual displacement principle based on the updated Lagrange configuration and 3D space thin-walled member theory,the solutions of equilibrium equations under stretch-bending,compression-bending,pure bending and torsion,are taken as the interpolation functions,and the geometrical nonlinear stiffness matrix of space thin-walled beam-column elements considering cross-section warping effect is derived. The Von Mises yield criterion in combination with the Zeigler mixed hardening assumption which takes the Bauschinger effect and yield surface expansion into account and an association flow rule is incorporated into the material nonlinearity consideration,and the constitutive equations based on isotropic plastic accumulative damage are considered in the process.The accuracy and efficiency of the proposed analytical configuration are verified by numerical examples,and the method may provide a foundation for the advanced analysis of space steel frames considering damage.
引文
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[2]CHEN W F,KINM S E.LRFD steel design using ad-vanced analysis[M].London,UK:CRC Press Inc.,1997:46-82.
[3]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社.1997:1-31.
[4]LEMAITRE J.A course on damage mechanics[M].Berlin,Germany:Springer-Verlag,1992:1-76.
[5]宋振森,顾强,苏明周.考虑混合强化和弹塑性损伤的有限元模型[J].西安交通大学学报,2000,34(11):95-98.SONG Zhensen,GU Qiang,SU Mingzhou.Large de-flection finite element method model based on damagetheory and mixed hardening[J].Journal of Xi′an Jiao-tong University,2000,34(11):95-98.
[6]CHEN W F,HAN D J.Plasticity for structural engi-neers[M].New York,USA:Springer-Verlag,1988:26-88.
[7]YANG Y B,KUO S R.Theory and analysis of non-linear frame structure[M].Singapore:Prentice Hall,1994:30-39.
[8]LIEW J Y R,CHEN Hong,SHANMUGAM N E,etal.Improved nonlinear plastic hinge analysis of spaceframe structures[J].Engineering Structures,2000,22(10):1324-1338.
[9]宋振森.刚性钢框架梁柱连接在地震作用下的累积损伤破坏机理及抗震设计对策[D].西安:西安建筑科技大学土木工程学院,2001.
[10]YANG Y B,MCGUIRE W.Joint rotation and geo-metric nonlinear analysis[J].ASCE Journal of Struc-tural Engineering,1986,112(4):879-905.
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