基于比例边界有限元法的结构-地基动力相互作用时域算法的改进
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摘要
本文基于比例边界有限元法(Scaled Boundary Finite Element Method)的缩减基函数解法,对结构-无限地基动力相互作用的时域算法进行了改进。通过选择适当的基函数数目,缩减结构-地基接触面上的自由度,以减小卷积积分所带来的计算工作量,推导了缩减自由度后运动方程的表达式。通过重力坝和拱坝加速度频响曲线的算例,对比了不同程度缩减的基函数和全部基函数对计算精度和效率的影响。结果表明,基函数的缩减可使计算效率明显提高,但精度损失不大。当采用60%的基函数时,计算效率提高5倍,而峰值频响曲线的精度损失却不超过4%。因此,该算法比较适合于大型结构-地基动力相互作用问题的时域分析。
Based on the reduced set of base function in scaled boundary element method(SBFEM) an improved time domain numerical approach for the dynamic structure-foundation interaction analysis was proposed.With reasonable choice of the number of base functions,the degrees of freedom on the structure-foundation interface were reduced and the associated computation for the calculation of convolution integral was greatly reduced.The results of this proposed approach applied to calculation of a gravity dam and an arch dam were given.The acceleration frequency response functions were calculated and the influences affected by different reduced set of base functions as well as full set were compared.It was found that a higher degree of reduced set of base functions resulted in significant increase of computational efficiency but a little loss bit of accuracy.When the reduced set was decreased by 60% the efficiency may elevated for five times,while the loss of accuracy of peak value of response will less than 4%.It may conclude that the proposed approach is suitable for large-scale structure-foundation interaction analysis.
Based on the reduced set of base function in scaled boundary element method(SBFEM) an improved time domain numerical approach for the dynamic structure-foundation interaction analysis was proposed.With reasonable choice of the number of base functions,the degrees of freedom on the structure-foundation interface were reduced and the associated computation for the calculation of convolution integral was greatly reduced.The results of this proposed approach applied to calculation of a gravity dam and an arch dam were given.The acceleration frequency response functions were calculated and the influences affected by different reduced set of base functions as well as full set were compared.It was found that a higher degree of reduced set of base functions resulted in significant increase of computational efficiency but a little loss bit of accuracy.When the reduced set was decreased by 60% the efficiency may elevated for five times,while the loss of accuracy of peak value of response will less than 4%.It may conclude that the proposed approach is suitable for large-scale structure-foundation interaction analysis.
引文
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[3]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):717-719.
[4]Song C M,Wolf J P.The scaled boundary finitc-element method———alias consistent infinitesimal finite-element cellmethod———for elastodynamics[J].Computer Methods in Applied Mechanics Engineering,1997,147(3):329-355.
[5]Yan J Y,Jin F,Zhang C H.A coupling procedure of FE and SBFE for soil-structure interaction in time domain[J].International Journal for Numerical Methods in Engineering,2004,59:1453-1471.
[6]杜建国,林皋.地基刚度和不均匀性对混凝土大坝地震响应的影响[J].岩土工程学报,2005,27(7):819-823.
[7]Doherty J P,Deeks A J.Application of the scaled boundary finite-element method to offshore foundation systems[A].Proceeding of the 12th International Offshore and Polar Enginecring Conference[C].Kitakyushu,2002.
[8]Song C M,Wolf J P.Semi-analytical representation of stress singularities as occurring in cracks in multi-materials with thescaled boundary finite-element method[J].Computers and Structures,2002,80(2):183-197.
[9]Deeks A J,Cheng L.Potential flow around obstacles using the scaled boundary finite-element method[J].InternationalJournal for Numerical Methods in Fluids,2003,41(7):721-741.
[10]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.
[11]Song C M.Weighted block-orthogonal base functions for static analysis of unbounded domains[A].Proceedings of the 6thWorld Congress on Computational Mechanics[C].Beijing,China,2004.615-620.
[12]Song C M.Dynamic analysis of unbounded domains by a reduced set of base functions[J].Computer Methods in AppliedMechanics and Engineering,2006,195(33-36):4075-4094.
[13]Wolf J P,Song C M.Finite-Element Modelling of Unbounded Media[M].New York:Wiley,1996.
[14]杜建国,林皋,钟红.基于锥体理论的三维拱坝无限地基SBFEM模型[J].水电能源科学,2006,24(1):25-29.
[2]刘云贺,张伯艳,陈厚群.拱坝地震输入模型中黏弹性边界与黏性边界的比较[J].水利学报,2006,37(6):758-763.
[3]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):717-719.
[4]Song C M,Wolf J P.The scaled boundary finitc-element method———alias consistent infinitesimal finite-element cellmethod———for elastodynamics[J].Computer Methods in Applied Mechanics Engineering,1997,147(3):329-355.
[5]Yan J Y,Jin F,Zhang C H.A coupling procedure of FE and SBFE for soil-structure interaction in time domain[J].International Journal for Numerical Methods in Engineering,2004,59:1453-1471.
[6]杜建国,林皋.地基刚度和不均匀性对混凝土大坝地震响应的影响[J].岩土工程学报,2005,27(7):819-823.
[7]Doherty J P,Deeks A J.Application of the scaled boundary finite-element method to offshore foundation systems[A].Proceeding of the 12th International Offshore and Polar Enginecring Conference[C].Kitakyushu,2002.
[8]Song C M,Wolf J P.Semi-analytical representation of stress singularities as occurring in cracks in multi-materials with thescaled boundary finite-element method[J].Computers and Structures,2002,80(2):183-197.
[9]Deeks A J,Cheng L.Potential flow around obstacles using the scaled boundary finite-element method[J].InternationalJournal for Numerical Methods in Fluids,2003,41(7):721-741.
[10]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.
[11]Song C M.Weighted block-orthogonal base functions for static analysis of unbounded domains[A].Proceedings of the 6thWorld Congress on Computational Mechanics[C].Beijing,China,2004.615-620.
[12]Song C M.Dynamic analysis of unbounded domains by a reduced set of base functions[J].Computer Methods in AppliedMechanics and Engineering,2006,195(33-36):4075-4094.
[13]Wolf J P,Song C M.Finite-Element Modelling of Unbounded Media[M].New York:Wiley,1996.
[14]杜建国,林皋,钟红.基于锥体理论的三维拱坝无限地基SBFEM模型[J].水电能源科学,2006,24(1):25-29.
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