具有分布材料特性的梁反应分析方法
|
摘要
同一梁单元内材料具有不同性质时,传统梁单元的单元位移插值函数不能合理地描述梁内部的位移变化,导致计算精度较低。给出了一种计算同一单元内具有分布材料特性的梁反应的有限元方法,有效解决了传统梁单元的局限性。同时,给出了同一单元内具有分布材料特性的梁单元的一致等效节点荷载和一致质量矩阵的建立方法。与传统梁单元相比,使用该方法进行静力分析和特征值分析均可获得较高的计算精度,并且使用一个单元即可给出精确的单元内力和位移分布。此研究为分析同一单元内具有分布材料特性的梁的静力与动力反应问题提供了简单的方法和有价值的理论基础。
Since the element interpolation functions of a traditional beam element cannot rationally describe the displacement filed in a beam with variable material properties, inaccuracies will arise. A method to compute responses of a beam with distributed material properties is presented, which effectively avoids the limitation of traditional beam elements. The consistent equivalent nodal load and consistent mass matrix are derived for the presented beam element. Compared with the traditional beam element, higher accuracy of the presented element in the static analysis and eigenproblems is observed and the accurate internal element force and displacement fields can be modeled by only one element. This study provides a simple method and a useful theoretical basis for static and dynamic analyses of the beam with distributed material properties.
Since the element interpolation functions of a traditional beam element cannot rationally describe the displacement filed in a beam with variable material properties, inaccuracies will arise. A method to compute responses of a beam with distributed material properties is presented, which effectively avoids the limitation of traditional beam elements. The consistent equivalent nodal load and consistent mass matrix are derived for the presented beam element. Compared with the traditional beam element, higher accuracy of the presented element in the static analysis and eigenproblems is observed and the accurate internal element force and displacement fields can be modeled by only one element. This study provides a simple method and a useful theoretical basis for static and dynamic analyses of the beam with distributed material properties.
引文
[1]Bathe K J.Finite element procedures[M].New Jersey:Prentice-Hall,1996.
[2]Belytschko T,Liu W K,Moran B.Nonlinear finite elements for continua and structures[M].New York:John Wiley and Sons,2000.
[3]王勖成.有限单元法[M].北京:清华大学出版社,2003.Wang Xucheng.Finite element method[M].Beijing:Tsinghua University Press,2003.(in Chinese)
[4]Taucer F F,Spacone E,Filippou F C.A fiber beam-column element for seismic response analysis of reinforced concrete structures[R].Earthquake Engineer-ing Research Center,University of California,Berkeley,Report No.UCB/EERC-91/17,1991.
[5]Spacone E,Filippou F C,Taucer F F.Fiber beam-column model for non-linear analysis of R/C frames:Part I.Formulation[J].Earthquake Engineering and Structural Dynamics,1996,25(7):711―725.
[6]Petrangeli M,Ciampi V.Equilibrium based iterative solu-tions for the non-linear beam problem[J].International Journal for Numerical Methods in Engineering,1997,40(3):423―437.
[7]Neuenhofer A,Filippou F C.Geometrically nonlinear flexibility-based frame finite element[J].Journal of Structural Engineering,1998,124(6):704―710.
[8]De Souza R M.Force-based finite element for large displacement inelastic analysis of frames[D].California:University of California,Berkeley,2000.
[9]陈滔.基于有限元柔度法的钢筋混凝土框架结构三维非弹性地震反应分析[D].重庆:重庆大学,2003.Chen Tao.3D inelastic seismic response analysis of rein-forced concrete frames based on finite element flexibility method[D].Chongqing:Chongqing University,2003.(in Chinese)
[10]Molins C,Roca P,Barbat A H.Flexibility-based linear dynamic analysis of complex structures with curved-3D beams[J].Earthquake Engineering and Structural Dynamics,1998,27(7):731―747.
[11]De Souza R M,Filippou F C,Pereira A M B,Aranha Jr G Y R.Force formulation of a non-prismatic Timoshenko beam finite element for dynamic analysis of frames[C].XXIV Iberian Latin-American Congress in Computa-tional Methods in Engineering.Brazil,2003.
[2]Belytschko T,Liu W K,Moran B.Nonlinear finite elements for continua and structures[M].New York:John Wiley and Sons,2000.
[3]王勖成.有限单元法[M].北京:清华大学出版社,2003.Wang Xucheng.Finite element method[M].Beijing:Tsinghua University Press,2003.(in Chinese)
[4]Taucer F F,Spacone E,Filippou F C.A fiber beam-column element for seismic response analysis of reinforced concrete structures[R].Earthquake Engineer-ing Research Center,University of California,Berkeley,Report No.UCB/EERC-91/17,1991.
[5]Spacone E,Filippou F C,Taucer F F.Fiber beam-column model for non-linear analysis of R/C frames:Part I.Formulation[J].Earthquake Engineering and Structural Dynamics,1996,25(7):711―725.
[6]Petrangeli M,Ciampi V.Equilibrium based iterative solu-tions for the non-linear beam problem[J].International Journal for Numerical Methods in Engineering,1997,40(3):423―437.
[7]Neuenhofer A,Filippou F C.Geometrically nonlinear flexibility-based frame finite element[J].Journal of Structural Engineering,1998,124(6):704―710.
[8]De Souza R M.Force-based finite element for large displacement inelastic analysis of frames[D].California:University of California,Berkeley,2000.
[9]陈滔.基于有限元柔度法的钢筋混凝土框架结构三维非弹性地震反应分析[D].重庆:重庆大学,2003.Chen Tao.3D inelastic seismic response analysis of rein-forced concrete frames based on finite element flexibility method[D].Chongqing:Chongqing University,2003.(in Chinese)
[10]Molins C,Roca P,Barbat A H.Flexibility-based linear dynamic analysis of complex structures with curved-3D beams[J].Earthquake Engineering and Structural Dynamics,1998,27(7):731―747.
[11]De Souza R M,Filippou F C,Pereira A M B,Aranha Jr G Y R.Force formulation of a non-prismatic Timoshenko beam finite element for dynamic analysis of frames[C].XXIV Iberian Latin-American Congress in Computa-tional Methods in Engineering.Brazil,2003.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心