一种基于Gurtin变分原理的非时间步参数逐步积分法
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摘要
目的提供一种具有较高计算精度的结构动力分析逐步积分算法,更好地解决地震作用下结构的动力响应分析问题.方法利用由Gurtin变分原理给出的空间离散后只含单重卷积形式的泛函,在局部时间域上采用初位移、初速度和末速度、末加速度并加入一种非时间步参数的插值函数形式对时间域离散,进行变分运算给出逐步递推计算格式;采用参数α和θ控制算法的稳定性.结果确定了结构动力分析逐步积分算法在无条件稳定计算格式时所需要的非时间步参数α和θ值.结论此算法具有高于威尔逊θ法的计算精度.是一种具有较高计算精度的结构动力响应分析方法,可用于地震作用下结构的动力响应分析.
Based on Gurtin variational principle,a kind of unconditionally stable step-by-step integration method is presented.The method is given by first adopting a single convolution integral functional after spatial discretization operation,and then adopting interpolation function consisting of initial displacement,initial velocity,later instant velocity,and later instant acceleration with a non-time-step parameter α in them to approximate the nodal displacements within local time domain.In Wilson θ method,parameter is used to obtain optimum stability and accuracy.In this method,two parameters θ and α can be varied to obtain optimum stability and accuracy.Two optimal values of θ and α are determined based on the stability analysis of the new algorithm.Accuracy analysis and numerical examples show that the algorithm here possesses satisfying accuracy and it is also an effective method for analyzing dynamic response in practical engineering.Finally the algorithm is used to offer the horizontal shear forces of a six-storey building under the action of earthquake.
Based on Gurtin variational principle,a kind of unconditionally stable step-by-step integration method is presented.The method is given by first adopting a single convolution integral functional after spatial discretization operation,and then adopting interpolation function consisting of initial displacement,initial velocity,later instant velocity,and later instant acceleration with a non-time-step parameter α in them to approximate the nodal displacements within local time domain.In Wilson θ method,parameter is used to obtain optimum stability and accuracy.In this method,two parameters θ and α can be varied to obtain optimum stability and accuracy.Two optimal values of θ and α are determined based on the stability analysis of the new algorithm.Accuracy analysis and numerical examples show that the algorithm here possesses satisfying accuracy and it is also an effective method for analyzing dynamic response in practical engineering.Finally the algorithm is used to offer the horizontal shear forces of a six-storey building under the action of earthquake.
引文
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[9]罗恩,朱慧坚.有限变形弹性动力学的非传统Gurtin型变分原理[J].固体力学学报,2003,24(1):1-7.
[10]Yang X,Cheng C.Gurtin variational principle and fi-nite element simulation for dynamical problems offluid-saturated porous media[J].ACTA MechanicaSolida Sinica,2003,16(1):24-32.
[11]He J H.A generalized variational principle in micro-morphic thermoelasticity[J].Mechanics ResearchCommunications,2005,32(1):93-98.
[2]Peng J S,Lewist R W,Zhang J Y.A semi-analyticalapproach for solving forced vibration problems basedon a convolution-type variational principle[J].Com-puters&Structures,1996,59(1):167-177.
[3]刘铁林,吕和祥,赵金城.基于位移型Gurtin变分原理计算动力响应的逐步积分法[J].计算力学学报,1999,16(2):151-156.
[4]刘铁林,吕和祥,赵金城.基于Gurtin变分原理的非时间步参数逐步积分法[J].工程力学,2000,17(3):43-48.
[5]刘铁林,刘钧玉.基于最小转换能原理的一种逐步积分法[J].工程力学,2005,22(2):38-42.
[6]Nappa L.Variational principles in micromorphic ther-moelasticity[J].Mechanics Research Communica-tions,2001,28(4):405-412.
[7]王连广,张海霞,吴利权.钢骨高强混凝土框架结构非线性地震反应分析[J].沈阳建筑大学学报:自然科学版,2004,19(4):247-249.
[8]毕继红,楚劲.基于卷积型的时空样条元[J].工程力学,2002,19(1):94-96.
[9]罗恩,朱慧坚.有限变形弹性动力学的非传统Gurtin型变分原理[J].固体力学学报,2003,24(1):1-7.
[10]Yang X,Cheng C.Gurtin variational principle and fi-nite element simulation for dynamical problems offluid-saturated porous media[J].ACTA MechanicaSolida Sinica,2003,16(1):24-32.
[11]He J H.A generalized variational principle in micro-morphic thermoelasticity[J].Mechanics ResearchCommunications,2005,32(1):93-98.
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