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分析结构非线性问题的杂交可变基Galerkin方法

赵琪 叶天麒

赵琪, 叶天麒. 分析结构非线性问题的杂交可变基Galerkin方法[J]. 应用数学和力学, 1995, 16(7): 625-631.
引用本文: 赵琪, 叶天麒. 分析结构非线性问题的杂交可变基Galerkin方法[J]. 应用数学和力学, 1995, 16(7): 625-631.
Zhao Qi, Ye Tianqi. Hybrid Changeable Basis Galerkin Technique for Nonlinear Analysis of Structures[J]. Applied Mathematics and Mechanics, 1995, 16(7): 625-631.
Citation: Zhao Qi, Ye Tianqi. Hybrid Changeable Basis Galerkin Technique for Nonlinear Analysis of Structures[J]. Applied Mathematics and Mechanics, 1995, 16(7): 625-631.

分析结构非线性问题的杂交可变基Galerkin方法

Hybrid Changeable Basis Galerkin Technique for Nonlinear Analysis of Structures

  • 摘要: 基于渐近摄动理论和Galer-kin方法,本文提出分析结构非线性问题的杂交可变基Galer-kin方法。本文方法首次引入可变基函数的概念,可大幅度降低计算量,而且在有限元法等数值方法中易于推广应用,在解决非线性问题领域有广泛应用前景。最后本文分析圆板大挠度问题和扁球壳大挠度问题,以验证本文方法的有效性。
  • [1] A.K.Noor Hybrid analytical teehni UUe for nonlinear analysis of structures,AIAA J.,23(1985).938-946.
    [2] J.F.Geer,A hybrid perturbation-Galerhin method for differential equations containing parameters,Appl.Mech.Rev.,42.11(2)(1989)
    [3] A.K.Noor,Recent advances in reduction problems for nonlinear problems,Computers and Structures.13(1981).31-44.
    [4] A.K.Noor,C.M.Andersen and J.M,Peters,Reduced basis technique for collapse analysis of shell.AIAA J.,19(1981).393-397.
    [5] A.K.Noor and J.M.Peters,Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique,Comp.Meth.Appl.Mach.Eng.,29(1981)271-295.
    [6] A.K.Noor and J.M.Peters,MultiPle-parameter reduced basis technique for bifurcation and post-buckling analysis of composite plates,Int.J.Num.Meth.Eng.,19(1983).1783-1803.
    [7] A.K.Noor and J.M.Peters.Resents adv,mces in reduction methods for instability analysis of structures,Computers and Structure.10(1983),.67-80.
    [8] A.K.Noor and J.M.Peters,Reduced basis technidue for nonlinear analysis of structures,.AIAA J.,18(1980),455-462.
    [9] A.K.Noor and C.D.Balch.hybrid perturbation Bubnov-Galerkin technique for nonlinear thermal analysis,AIAA J.,22(1984).287-294.
    [10] A.K.Noor.C.D.Balch and M.A.Shibut.Reduction methods for nonlinear steady state thermal analysis,Int.J.Num.Meth.Eng.,20(1984),1323-1348.
    [11] J.F.Geer and C.M.Anderson,.A hybrid perturbation Galerkin technique with applications to slender body theory.SIAM J.Appl.Meth.,49(1989).344-356.
    [12] J.F.Geer and C.M.Anderson,,A hybrid perturbation Galerkin method which combines mutiple expansions.NASA Langley Research Center ICASE Report.89(8)(1989).
    [13] 石钟慈,样条有限元,计算数学,1(1979),50-72.
    [14] 钱伟长等.《奇异摄动理论及其在力学中的应用》,科学出版社,北京(1981).
    [15] 赵琪,叶天麒,杂交可变基Galerkin方法在圆板大挠度问题中的应用,航空学报,A版(已收录).
    [16] Zhao Qi and Ye Tianqi,The large deflection of spherical caps under centrally distributed pressures,7th Brazilian Symposium on Piping and Pressure Vessels.
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出版历程
  • 收稿日期:  1994-06-30
  • 刊出日期:  1995-07-15

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