大变形动力固结问题系统方程及其变分原理
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摘要
基于动力荷载作用下地基土变形规律,提出了大变形动力固结及其数值建模问题.在构筑大变形动力固结问题系统方程表达形式的基础上,构建了基于瞬时最小势能分析的场耦合机理变分原理.引用广义变分原理的思想,证明了基于拉格朗日乘子所表达的大变形动力固结问题系统方程及其变分函数,使得孔隙水压力场变分成为无约束变分泛函.通过高阶拉格朗日乘子法的应用,消除了本构方程对有效应力场变分泛函的约束作用,使得动力固结有效应力场的变分泛函成为真实的三变量完全广义变分原理.
As for level of foundation strain under the action of dynamic load is not only to have forereached the small strain assumption of elastic mechanics but also to be notable consolidation characteristic of soil. Based on the research of deformation law of ground soil, in which result is under the action of dynamic load, the problem of Dynamic Consolidation of Large Deformation (DCLD) and its mathematical model must be shown. The systematic representative equation is presented as to the DCLD. Based on analysis of instantaneous minimum potential energy, the variational principle against coupling field mechanism about DCLD was established and its precision was strictly authenticated. Quoting the idea of generalized variational principle, the systematic problem of DCLD and its variational function based on method of Lagrangian multiplier operator was shown and certified, in which the variational principle had pore variational function of water pressure filed to be unrestricted. Application of high index Lagrangian multiplier operator into DCLD erased the restricted action of constitutive relationship from variational function of effective stress field, in which variational equation of effective stress field about DCLD was changed into real generalized variational principle of three type variable.
As for level of foundation strain under the action of dynamic load is not only to have forereached the small strain assumption of elastic mechanics but also to be notable consolidation characteristic of soil. Based on the research of deformation law of ground soil, in which result is under the action of dynamic load, the problem of Dynamic Consolidation of Large Deformation (DCLD) and its mathematical model must be shown. The systematic representative equation is presented as to the DCLD. Based on analysis of instantaneous minimum potential energy, the variational principle against coupling field mechanism about DCLD was established and its precision was strictly authenticated. Quoting the idea of generalized variational principle, the systematic problem of DCLD and its variational function based on method of Lagrangian multiplier operator was shown and certified, in which the variational principle had pore variational function of water pressure filed to be unrestricted. Application of high index Lagrangian multiplier operator into DCLD erased the restricted action of constitutive relationship from variational function of effective stress field, in which variational equation of effective stress field about DCLD was changed into real generalized variational principle of three type variable.
引文
[1]徐志英,周健.土坝地震孔隙水压力产生、扩散和消散的三维动力分析[J].地震工程与工程振动,1987,5(4):57—72
[2]孔令伟.流固耦合介质轴对称动力问题解法的改进[J].力学学报,1998,30(2):229—232
[3]罗晓辉,白世伟.应用样条有限元方法分析饱和土体的地震效应[J].岩石力学与工程学报,2003,22(1):90—95
[4]罗晓辉,李永乐,罗昕.大应变固结理论的分区变分原理及其广义变分原理[J].应用力学和数学,2005,26(7):867—874
[5]钱伟长.广义变分原理[M].北京:知识出版社,1985.
[6]钱伟长.高阶Lagrange乘子法和弹性力学中更为一般的广义变分原理[J].应用数学和力学,1983,4(2):137—150
[2]孔令伟.流固耦合介质轴对称动力问题解法的改进[J].力学学报,1998,30(2):229—232
[3]罗晓辉,白世伟.应用样条有限元方法分析饱和土体的地震效应[J].岩石力学与工程学报,2003,22(1):90—95
[4]罗晓辉,李永乐,罗昕.大应变固结理论的分区变分原理及其广义变分原理[J].应用力学和数学,2005,26(7):867—874
[5]钱伟长.广义变分原理[M].北京:知识出版社,1985.
[6]钱伟长.高阶Lagrange乘子法和弹性力学中更为一般的广义变分原理[J].应用数学和力学,1983,4(2):137—150
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