基于板壳有限元理论的薄壁箱梁剪力滞效应
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摘要
为了分析计算薄壁箱梁剪力滞效应,直接从壳体结构特点出发,由8节点曲边四边形膜单元和基于Reinssner中厚板理论的弯曲单元推导考虑剪切闭锁效应的薄壁箱梁空间壳单元刚度矩阵及相应的刚度方程,并在MATLAB上编制相应的计算程序。通过数值算例,将理论计算值与ANSYS有限元结果,模型试验的实测值进行比较,三者吻合良好,验证了理论公式推导的正确性与可靠性。本文采用8节点的等参单元和二次型位移场形函数,不仅适用于计算直线箱梁,也适用于曲线箱梁,因而更具有普遍性。最后,从平衡微分方程的角度解释剪力滞产生的真正原因,不仅仅是由于剪应力沿横向分布不均匀,其本质更在于剪应力沿横向不均匀变化。
In order to compute shear lag effect of thin-walled box girder, this paper started from the characteristic of shell structure. The spatial shell element stiffness matrix and corresponding stiffness equation of thin-walled box girder considering shear locking effect were deduced by 8-nodes curve-edge-quadrangle membrane element and bending element based on Reinssner's moderately-thick plate theory. The corresponding computational procedure was programmed on MATAB. Then, a numerical analysis example was presented and the theoretical value was compared with the finite element results of ANSYS and measured value of model test. The good agreement of the results verified the correctness and reliability of the deducing theoretical formulas. In this paper, 8-nodes isoparametric element and quadric form displacement field sigmoid function are used, it is not only applied to straight box girder but also curved box girder. Therefore, this method is more universal. Finally, from the perspective of balance differential equations, the reason of shear lag is accounted for, which is not merely non-uniformed distribution of shear stress along transverse direction,but more of its non-uniformed variation.
In order to compute shear lag effect of thin-walled box girder, this paper started from the characteristic of shell structure. The spatial shell element stiffness matrix and corresponding stiffness equation of thin-walled box girder considering shear locking effect were deduced by 8-nodes curve-edge-quadrangle membrane element and bending element based on Reinssner's moderately-thick plate theory. The corresponding computational procedure was programmed on MATAB. Then, a numerical analysis example was presented and the theoretical value was compared with the finite element results of ANSYS and measured value of model test. The good agreement of the results verified the correctness and reliability of the deducing theoretical formulas. In this paper, 8-nodes isoparametric element and quadric form displacement field sigmoid function are used, it is not only applied to straight box girder but also curved box girder. Therefore, this method is more universal. Finally, from the perspective of balance differential equations, the reason of shear lag is accounted for, which is not merely non-uniformed distribution of shear stress along transverse direction,but more of its non-uniformed variation.
引文
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[4]赵志峰,蔺鹏臻,方炜彬.比拟杆法分析研究单箱三室箱梁剪力滞效应[J].铁道科学与工程学报,2016,13(4):697-704.ZHAO Zhifeng,LIN Pengzhen,FANG Weibin.The bar simulation method for shear lag effect of three-cell box girder[J].Journal of Railway Science and Engineering,2016,13(4):697-704.
[5]蔺鹏臻,孙理想,杨子江,等.单箱双室简支箱梁的剪力滞效应研究[J].铁道工程学报,2014,31(1):59-63.LIN Pengzhen,SUN Lixiang,YANG Zijiang,et al.research on shear lag effect of twin-cell box girder[J].Journal of Railway Engineering Society,2014,31(1):59-63.
[6]ZHOU Wangbao,JIANG Lizhong,LIU Zhijie,et al.Closed-form solution for shear lag effects of steelconcrete composite box beams considering shear deformation and slip[J].Journal of Central South University,2012,(10):2976-2982.
[7]ZHOU Wangbao,JIANG Lizhong,LIU Zhijie,et al.Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag[J].Journal of Central South University,2012(9):2650-2655.
[8]罗旗帜.薄壁箱型梁剪力滞计算的梁段有限元法[J].湖南大学学报,1991,18(2):33-39.LUO Qizhi.Calculation of the shear lag in thin-walled box girders by the finite segment method[J].Journal of Hunan University,1991,18(2):33-39.
[9]罗旗帜,刘光栋,杜嘉斌.薄壁曲线箱梁剪力滞效的梁段有限元法[J].湖南大学学报,2006,33(5):21-25.LUO Qizhi,LIU Guangdong,DU Jiabin.Finite segment method for shear lag effect of thin-walled curved box girder[J].Journal of Hunan University,2006,33(5):21-25.
[10]吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪力滞计算的梁段有限元法[J].中国铁道科学,2003,24(4):64-68.WU Youming,LUO Qizhi,YUE Zhufeng.Finite element method for calculating the shear lag in box girders[J].China Railway Science,2003,24(4):64-68.
[11]吴幼明,岳珠峰,吕震宙.薄壁曲线箱梁剪力滞计算的有限段方法[J].物理学报,2009,58(6):4002-4010.WU Youming,YUE Zhufeng,LüZhenzhou.Finite segment method for calculating the shear lag in thin walled curved box girders[J].Acta Physica Sinica,2009,58(6):4002-4010.
[12]何云勇.一种分析曲线箱梁剪力滞效应的传递矩阵法[J].重庆交通大学学报,2010,29(5):670-673.HE Yunyong.Transfer analyzing matrix method for analyzing shear lag effect of curved box girder[J].Journal of Chongqing Jiaotong University,2010,29(5):670-673.
[13]张元海,李乔.考虑剪滞变形时箱形梁广义力矩的数值分析[J].工程力学,2010,27(4):30-36.ZHANG Yuanhai,LI Qiao.Numerical analysis of generalized moment in box girder considering shear lag deformation[J].Engineering Mechanics,2010,27(4):30-36.
[14]张元海,王来林,李乔.箱形梁剪滞效应分析的一维有限元法及其应用[J].土木工程学报,2010,43(8):44-50.ZHANG Yuanhai,WANG Lailin,LI Qiao.One dimensional finite element method and its application for the analysis of shear lag effect in box girders[J].China Civil Engineering Journal,2010,43(8):44-50.
[15]卢海林.预应力混凝土曲线箱梁剪力滞效应理论分析与试验研究[D].天津:天津大学,2005:30-31.LU Hailin.Theoretical analysis and experimental study on hear-lag effect of prestress concrete curved box beam[D].Tianjin:Tianjin University,2005:30-31.
[2]孙璐,王文雷,吴国琦,等.客运专线箱梁端部裂纹成因分析及施工控制[J].铁道工程学报,2007(10):46-51.SUN Lu,WANG Wenlei,WU Guoqi,et al.Analyses of the causes for crack on the end side of box girder for railway passenger dedicated line and its construction control[J].Journal of Railway Engineering Society,2007(10):46-51.
[3]张元海,李琳,林丽霞,等.以附加挠度作为广义位移时薄壁箱梁剪力滞效应的梁段有限元分析[J].土木工程学报,2013,46(10):100-107.ZHANG Yuanhai,LI Lin,LIN Lixia,et al.Beamsegment finite element analysis on shear lag effect of thin-walled box girder adopting additional deflection as generalized displacement[J].China Civil Engineering Journal,2013,46(10):100-107.
[4]赵志峰,蔺鹏臻,方炜彬.比拟杆法分析研究单箱三室箱梁剪力滞效应[J].铁道科学与工程学报,2016,13(4):697-704.ZHAO Zhifeng,LIN Pengzhen,FANG Weibin.The bar simulation method for shear lag effect of three-cell box girder[J].Journal of Railway Science and Engineering,2016,13(4):697-704.
[5]蔺鹏臻,孙理想,杨子江,等.单箱双室简支箱梁的剪力滞效应研究[J].铁道工程学报,2014,31(1):59-63.LIN Pengzhen,SUN Lixiang,YANG Zijiang,et al.research on shear lag effect of twin-cell box girder[J].Journal of Railway Engineering Society,2014,31(1):59-63.
[6]ZHOU Wangbao,JIANG Lizhong,LIU Zhijie,et al.Closed-form solution for shear lag effects of steelconcrete composite box beams considering shear deformation and slip[J].Journal of Central South University,2012,(10):2976-2982.
[7]ZHOU Wangbao,JIANG Lizhong,LIU Zhijie,et al.Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag[J].Journal of Central South University,2012(9):2650-2655.
[8]罗旗帜.薄壁箱型梁剪力滞计算的梁段有限元法[J].湖南大学学报,1991,18(2):33-39.LUO Qizhi.Calculation of the shear lag in thin-walled box girders by the finite segment method[J].Journal of Hunan University,1991,18(2):33-39.
[9]罗旗帜,刘光栋,杜嘉斌.薄壁曲线箱梁剪力滞效的梁段有限元法[J].湖南大学学报,2006,33(5):21-25.LUO Qizhi,LIU Guangdong,DU Jiabin.Finite segment method for shear lag effect of thin-walled curved box girder[J].Journal of Hunan University,2006,33(5):21-25.
[10]吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪力滞计算的梁段有限元法[J].中国铁道科学,2003,24(4):64-68.WU Youming,LUO Qizhi,YUE Zhufeng.Finite element method for calculating the shear lag in box girders[J].China Railway Science,2003,24(4):64-68.
[11]吴幼明,岳珠峰,吕震宙.薄壁曲线箱梁剪力滞计算的有限段方法[J].物理学报,2009,58(6):4002-4010.WU Youming,YUE Zhufeng,LüZhenzhou.Finite segment method for calculating the shear lag in thin walled curved box girders[J].Acta Physica Sinica,2009,58(6):4002-4010.
[12]何云勇.一种分析曲线箱梁剪力滞效应的传递矩阵法[J].重庆交通大学学报,2010,29(5):670-673.HE Yunyong.Transfer analyzing matrix method for analyzing shear lag effect of curved box girder[J].Journal of Chongqing Jiaotong University,2010,29(5):670-673.
[13]张元海,李乔.考虑剪滞变形时箱形梁广义力矩的数值分析[J].工程力学,2010,27(4):30-36.ZHANG Yuanhai,LI Qiao.Numerical analysis of generalized moment in box girder considering shear lag deformation[J].Engineering Mechanics,2010,27(4):30-36.
[14]张元海,王来林,李乔.箱形梁剪滞效应分析的一维有限元法及其应用[J].土木工程学报,2010,43(8):44-50.ZHANG Yuanhai,WANG Lailin,LI Qiao.One dimensional finite element method and its application for the analysis of shear lag effect in box girders[J].China Civil Engineering Journal,2010,43(8):44-50.
[15]卢海林.预应力混凝土曲线箱梁剪力滞效应理论分析与试验研究[D].天津:天津大学,2005:30-31.LU Hailin.Theoretical analysis and experimental study on hear-lag effect of prestress concrete curved box beam[D].Tianjin:Tianjin University,2005:30-31.
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