正交异性膜材大变形行为的有限质点法求解
|
摘要
建筑薄膜具有正交异性和拉伸非线性的力学特性,其本构关系的表征和大变形行为的描述都较为复杂,具有很强的几何、材料双重非线性特征。有限质点法是一种新颖的结构数值分析方法,它将传统分析力学方法中复杂的函数连续体模型用清晰的离散质点物理模型取代,通过质点的运动描述结构的行为。该文根据途径单元的基本概念直接在质点内力计算过程中引入不同的膜材本构,将有限质点法拓展应用于正交异性薄膜结构的几何与材料非线性大变形分析。为了准确表征膜材力学特性,根据复合材料本构理论分别建立了适用于有限质点法的正交异性膜材的线性与非线性拉伸本构模型,并通过若干算例探讨了该文方法和程序的适用性和正确性。
Due to the orthotropic and tensile nonlinear characteristics of thin structural membranes, the constitutive relation and large deformation behavior of these materials are complicated, as it always has strong geometry and material nonlinearity. The finite particle method(FPM) is a novel structural numerical method,which models the analyzed domain by a set of discretized particles instead of a mathematical continuous body in those traditional methods based on analytical mechanics. It describes structural behaviors by analyzing particles movement. With the concept of path unit, it is convenient to introduce various constitutive laws of membranes in the evaluation of internal forces. This paper explores the possibility of the proposed method being applied in the large deformation analysis of membrane structures exhibiting the geometric and material nonlinearity. According to the constitutive theory of composite materials, two material models(i.e. linear and nonlinear orthotropic models) are developed and implemented in the program. Numerical examples are presented to demonstrate the validity and applicability of this method.
Due to the orthotropic and tensile nonlinear characteristics of thin structural membranes, the constitutive relation and large deformation behavior of these materials are complicated, as it always has strong geometry and material nonlinearity. The finite particle method(FPM) is a novel structural numerical method,which models the analyzed domain by a set of discretized particles instead of a mathematical continuous body in those traditional methods based on analytical mechanics. It describes structural behaviors by analyzing particles movement. With the concept of path unit, it is convenient to introduce various constitutive laws of membranes in the evaluation of internal forces. This paper explores the possibility of the proposed method being applied in the large deformation analysis of membrane structures exhibiting the geometric and material nonlinearity. According to the constitutive theory of composite materials, two material models(i.e. linear and nonlinear orthotropic models) are developed and implemented in the program. Numerical examples are presented to demonstrate the validity and applicability of this method.
引文
[1]杨庆山,姜忆南.张拉索-膜结构分析与设计[M].北京:科学出版社,2004:45―70.Yang Qingshan,Jiang Yinan.Analysis and design of@@§?à§?€¨???€??à????è0èè°1èp7èp4p5è4è8è°7tensioned cable-membrane structure[M].Beijing:Science Press,2004:45―70.(in Chinese)
[2]Kao R,Perrone N.Large deflections of axisymmetric circular membranes[J].International Journal of Solids and Structures,1971,7(12):1601―1612.
[3]On?te E,Flores F G,Marcipar J.Membrane structures formed by low pressure inflatable tubes:New analysis method and recent construction[C]//On?te E,Kropelin B.Textile Composites and Inflatable Structures II.Netherlands:Springer,2008:163―194.
[4]Bletzinger K U,Linhard J,Wuchner R.Advanced numerical methods for the form finding and patterning of membrane structures[C]//Pimenta P D M,Wriggers P.New trends in thin structures:Formulaiton,Optimization and Coupled Problems.Vienna:Springer,2010:133―154.
[5]Zhang Y,Xu J,Zhang Q.Advances in mechanical properties of coated fabrics in civil engineering[J].Journal of Industrial Textiles,2018,48(1):255―271.
[6]Kato S,Yoshino T,Minami H.Formulation of constitutive equations for fabric membranes based on the concept of fabric lattice model[J].Engineering Structures,1999,21(8):691―708.
[7]Pargana J B,Lloyd-Smith D,Izzuddin B A.Advanced material model for coated fabrics used in tensioned fabric structures[J].Engineering Structures,2007,29(7):1323―1336.
[8]Reese S,Raible T,Wriggers P.Finite element modelling of orthotropic material behaviour in pneumatic membranes[J].International Journal of Solids and Structures,2001,38(52):9525―9544.
[9]Gon?alve F R,Campello E M B.Orthotropic material models for the nonlinear analysis of structural membranes[J].Journal of the Brazilian Society of Mechanical Sciences and Engineering,2014,36(4):887―899.
[10]喻莹.基于有限质点法的空间钢结构连续倒塌破坏研究[D].杭州:浙江大学,2010.Yu Ying.Progressive collapse of space steel structures based on the finite particle method[D].Hangzhou:Zhejiang University,2010.(in Chinese)
[11]Yu Y,Luo Y Z.Motion analysis of deployable structures based on the rod hinge element by the finite particle method[J].Proceedings of The Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering,2009,223(7):156―171.
[12]俞锋,尹雄,罗尧治,等.考虑接触点摩擦的索滑移行为分析[J].工程力学,2017,34(8):42―50.Yu Feng,Yin Xiong,Luo Yaozhi,et al.Cable sliding analysis considering frictional effect[J].Engineering Mechanics,2017,34(8):42―50.(in Chinese)
[13]张鹏飞,罗尧治,杨超.薄壳屈曲问题的有限质点法求解[J].工程力学,2017,34(2):12―20.Zhang Pengfei,Luo Yaozhi,Yang Chao.Buckling analysis of thin shell using the finite particle method[J].Engineering Mechanics,2017,34(2):12―20.(in Chinese)
[14]喻莹,谭长波,金林,等.基于有限质点法的单层球面网壳强震作用下连续倒塌破坏研究[J].工程力学,2016,33(5):134―141.Yu Ying,Tan Changbo,Jin Lin,et al.Research on seismic progressive collapse of single-layer reticulated dome using the finite particle method[J].Engineering Mechanics,2016,33(5):134―141.(in Chinese)
[15]罗尧治,杨超.求解平面固体几何大变形问题的有限质点法[J].工程力学,2013,30(4):260―268.Luo Yaozhi,Yang Chao.The finite particle method for solving geometric large deformation of planar solids[J].Engineering Mechanics,2013,30(4):260―268.(in Chinese)
[16]Yang C,Shen Y,Luo Y.An efficient numerical shape analysis for light weight membrane structures[J].Journal of Zhejiang University Science A,2014,15(4):255―271.
[17]郑延丰,罗尧治.基于有限质点法的多尺度精细化分析[J].工程力学,2016,33(9):21―29.Zheng Yanfeng,Luo Yaozhi.Multi-scale fine analysis based on the finite particle method[J].Engineering Mechanics,2016,33(9):21―29.(in Chinese)
[18]Belytschko T,Liu W K,Moran B.Nonlinear Finite Elements for Continua and Structures[M].New York:John Wiley&Son,2000:544―549.
[19]Rezaiee-Pajand M,Kadkhodayan M,Alamatian J.A new method of fictitious viscous damping determination for the dynamic relaxation method[J].Computers&Structures,2011,89(9/10):783―794.
[20]Oakley D R,Knight Jr N F.Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I.Formulation[J].Computer Method in Applied Mechanics and Engineering,1995,126(1/2):67―89.
[21]Tsiatas G,Katsikadelis J.Large deflection analysis of elastic space membranes[J].International Journal For Numerical Methods in Engineering,2006,65(2):264―294.
[22]易洪雷,丁辛,陈守辉.PES/PVC膜材料拉伸性能的各向异性及破坏准则[J].复合材料学报,2005,22(6):98―102.Yi Honglei,Ding Xin,Chen shouhui.Orthotropic behavior and strength criterion of PES/PVC membrane materials under tensile loading[J].Acta Materiae Compositae Sinica,2005,22(6):98―102.(in Chinese)
[23]Ambroziak A,Klosowski P.Mechanical testing of technical woven fabrics[J].Journal of Reinforced Plastics and Composites,2013,32(10):726―739.
[24]Bonet J,Wood R D,Mahaney J.Finite element analysis of air supported membrane structures[J].Computer Methods in Applied Mechanics and Engineering,2000,190(10):579―595.
[2]Kao R,Perrone N.Large deflections of axisymmetric circular membranes[J].International Journal of Solids and Structures,1971,7(12):1601―1612.
[3]On?te E,Flores F G,Marcipar J.Membrane structures formed by low pressure inflatable tubes:New analysis method and recent construction[C]//On?te E,Kropelin B.Textile Composites and Inflatable Structures II.Netherlands:Springer,2008:163―194.
[4]Bletzinger K U,Linhard J,Wuchner R.Advanced numerical methods for the form finding and patterning of membrane structures[C]//Pimenta P D M,Wriggers P.New trends in thin structures:Formulaiton,Optimization and Coupled Problems.Vienna:Springer,2010:133―154.
[5]Zhang Y,Xu J,Zhang Q.Advances in mechanical properties of coated fabrics in civil engineering[J].Journal of Industrial Textiles,2018,48(1):255―271.
[6]Kato S,Yoshino T,Minami H.Formulation of constitutive equations for fabric membranes based on the concept of fabric lattice model[J].Engineering Structures,1999,21(8):691―708.
[7]Pargana J B,Lloyd-Smith D,Izzuddin B A.Advanced material model for coated fabrics used in tensioned fabric structures[J].Engineering Structures,2007,29(7):1323―1336.
[8]Reese S,Raible T,Wriggers P.Finite element modelling of orthotropic material behaviour in pneumatic membranes[J].International Journal of Solids and Structures,2001,38(52):9525―9544.
[9]Gon?alve F R,Campello E M B.Orthotropic material models for the nonlinear analysis of structural membranes[J].Journal of the Brazilian Society of Mechanical Sciences and Engineering,2014,36(4):887―899.
[10]喻莹.基于有限质点法的空间钢结构连续倒塌破坏研究[D].杭州:浙江大学,2010.Yu Ying.Progressive collapse of space steel structures based on the finite particle method[D].Hangzhou:Zhejiang University,2010.(in Chinese)
[11]Yu Y,Luo Y Z.Motion analysis of deployable structures based on the rod hinge element by the finite particle method[J].Proceedings of The Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering,2009,223(7):156―171.
[12]俞锋,尹雄,罗尧治,等.考虑接触点摩擦的索滑移行为分析[J].工程力学,2017,34(8):42―50.Yu Feng,Yin Xiong,Luo Yaozhi,et al.Cable sliding analysis considering frictional effect[J].Engineering Mechanics,2017,34(8):42―50.(in Chinese)
[13]张鹏飞,罗尧治,杨超.薄壳屈曲问题的有限质点法求解[J].工程力学,2017,34(2):12―20.Zhang Pengfei,Luo Yaozhi,Yang Chao.Buckling analysis of thin shell using the finite particle method[J].Engineering Mechanics,2017,34(2):12―20.(in Chinese)
[14]喻莹,谭长波,金林,等.基于有限质点法的单层球面网壳强震作用下连续倒塌破坏研究[J].工程力学,2016,33(5):134―141.Yu Ying,Tan Changbo,Jin Lin,et al.Research on seismic progressive collapse of single-layer reticulated dome using the finite particle method[J].Engineering Mechanics,2016,33(5):134―141.(in Chinese)
[15]罗尧治,杨超.求解平面固体几何大变形问题的有限质点法[J].工程力学,2013,30(4):260―268.Luo Yaozhi,Yang Chao.The finite particle method for solving geometric large deformation of planar solids[J].Engineering Mechanics,2013,30(4):260―268.(in Chinese)
[16]Yang C,Shen Y,Luo Y.An efficient numerical shape analysis for light weight membrane structures[J].Journal of Zhejiang University Science A,2014,15(4):255―271.
[17]郑延丰,罗尧治.基于有限质点法的多尺度精细化分析[J].工程力学,2016,33(9):21―29.Zheng Yanfeng,Luo Yaozhi.Multi-scale fine analysis based on the finite particle method[J].Engineering Mechanics,2016,33(9):21―29.(in Chinese)
[18]Belytschko T,Liu W K,Moran B.Nonlinear Finite Elements for Continua and Structures[M].New York:John Wiley&Son,2000:544―549.
[19]Rezaiee-Pajand M,Kadkhodayan M,Alamatian J.A new method of fictitious viscous damping determination for the dynamic relaxation method[J].Computers&Structures,2011,89(9/10):783―794.
[20]Oakley D R,Knight Jr N F.Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I.Formulation[J].Computer Method in Applied Mechanics and Engineering,1995,126(1/2):67―89.
[21]Tsiatas G,Katsikadelis J.Large deflection analysis of elastic space membranes[J].International Journal For Numerical Methods in Engineering,2006,65(2):264―294.
[22]易洪雷,丁辛,陈守辉.PES/PVC膜材料拉伸性能的各向异性及破坏准则[J].复合材料学报,2005,22(6):98―102.Yi Honglei,Ding Xin,Chen shouhui.Orthotropic behavior and strength criterion of PES/PVC membrane materials under tensile loading[J].Acta Materiae Compositae Sinica,2005,22(6):98―102.(in Chinese)
[23]Ambroziak A,Klosowski P.Mechanical testing of technical woven fabrics[J].Journal of Reinforced Plastics and Composites,2013,32(10):726―739.
[24]Bonet J,Wood R D,Mahaney J.Finite element analysis of air supported membrane structures[J].Computer Methods in Applied Mechanics and Engineering,2000,190(10):579―595.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |