建筑结构连续性倒塌数值模拟方法研究
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摘要
为了进行建筑结构连续性倒塌全过程的力学模拟,针对建筑结构倒塌数值模拟梁壳单元几何、材料、接触三重非线性且连续介质向非连续介质转化的动力计算问题,系统地研究了非线性动力计算相关的力学原理,提出了能够考虑多重非线性用于连续介质与非连续介质共同作用的质点元方法,建立了一个具有大位移大转动计算能力的梁元模型,研究了具有大位移大转动能力的平板壳元模型和用于初应力施加的动力松弛方法,主要研究内容如下：
(1)建筑结构连续性倒塌问题的现状研究。依据建筑结构连续性倒塌现有文献资料,从理论研究现状、规范研究现状、数值模拟现状以及软件应用现状等方面进行了对比分析,总结了建筑结构连续倒塌的研究重点,并针对非线性动力计算问题,分析了材料、几何和接触非线性的研究现状。
(2)结构多重非线性计算的力学原理研究。针对建筑结构倒塌材料、几何和接触三重非线性的力学特点,系统研究和对比了隐式有限元、显式有限元、离散元、显式有限元与离散元耦合等方法的力学实现原理和过程,进而针对建筑结构连续倒塌的力学模拟,分析了各种方法的优缺点和适用性。
(3)用于建筑结构倒塌数值模拟的质点元方法研究。提出了用于建筑结构倒塌模拟的质点元方法,该方法以质点运动学为基础,建模过程与通用有限元一致,通过定义广义连接模型、构造连接模型转化法则和建立接触碰撞算法,将显式有限元与离散元统一于相同的计算框架之下,具有效率优先、精度可调的特点,能够用于建筑结构倒塌等强非线性的动力计算。
(4)具有大位移大转动计算能力的梁元模型研究。为了数值模拟建筑结构倒塌过程中的梁柱构件,建立了一个具有大位移大转动非线性动力计算能力的显式梁元。该梁元基于更新拉格朗日列式,考虑了转动的不可交换性,选用共旋方法分离单元刚体位移和变形位移,采用欧拉梁假设进行变形位移插值,通过应力更新算法来考虑材料的本构关系,最后开发了显式梁元程序并进行了数值检验,算例表明该梁元力学性能良好,具有一定的工程应用价值。
(5)具有大位移大转动计算能力的壳元模型研究。为了数值模拟在结构倒塌过程中的墙板构件,研究了具有大位移大转动计算能力的显式平板壳元,该壳元基于中厚板理论,采用膜元与板元叠加的方式实现,涉及壳元的单元定位方法、质量矩阵的生成方法、稳定时间步长以及单元破坏准则等内容,开发了显式壳元计算程序,并进行了数值检验,算例数值结果表明该显式平板壳元具有较好的计算精度和适用性。
(6)动力松弛方法研究。参照隐式有限元刚度阻尼的生成方法,并考虑显式有限元的计算原理,研究了显式有限元通过材料本构实现刚度阻尼的方法；进而针对三维梁元研究了刚度阻尼系数对稳定时间步长的影响规律,确定了折减系数与阻尼系数和单元特征长度的函数对应关系。数值计算表明,刚度阻尼严重降低稳定时间步长,对于结构显式动力分析不建议采用刚度阻尼,而是采用质量阻尼的方式进行施加。
In order to simulate the nonlinear dynamic process of progressive collapse of building structure,considering the coupled nonlinearity of geometrical,material and contact from continuum to non-continuum,a particle element method(PEM) was proposed to simulate the nonlinear dynamics process of building structure collapse after the principles of nonlinear dynamical mechanics were studied systematically. Then the beam and shell element with the large displacement and large rotation capability were researched.Finally, the dynamic relaxation method was studied to apply the initial stress.The detailed research contents are as follows:
(1)Research on the present state of the progressive collapse of building structure.Firstly,the present state of structure progressive collapse was analyzed from theory research,code research, numerical simulation and the software application respectively.Then considering material,geometrically and contact nonlinearity, the present state of nonlinear dynamics analysis was studied.
(2)Research on the principles of nonlinear dynamical mechanics. Considering the coupled nonlinearity of geometrical, material and contact of building progressive collapse, the nonlinear dynamical mechanics principles of the implicit finite element method, the explicit finite element method and the discrete element method were studied. Then the advantages and disadvantages of those methods to simulate the process of building progressive collapse were compared.
(3)Research on the particle element method(PEM) which was proposed to simulate the nonlinear dynamics process of building structure collapse from continuum to non-continuum. Based on the theory of particle dynamics, this method unifies the explicit finite element method and discrete element method to the same computation framework by defining the generalized link modal, constructing the conversion law of the link modal and creating the contact collision algorithm. The particle element method,which has the computation accuracy of finite element method during the continuum phase and the computation capability of discrete element method during the non-continuum phase, could be used for strong nonlinear dynamics simulation of building structure collapse.
(4)Research on the explicit geometrical beam element.In order to achieve the nonlinear dynamic analysis of the beams and columns during structure collapse, the realization procedure of a nonlinear dynamic beam with explicit algorithms was researched.Based on the updated Lagrange formulation,the finite rotation method was adopted to consider the rotation non-swappable, which was used to determine the element coordinate. Combining with the Co-Rotational method, the exact element internal force was calculated after the deformation and rigid displacement was separated. A nonlinear dynamic procedure of beam element with explicit algorithms, which could be used for the structure dynamic analysis, was presented. The numerical result shows that the beam element has very good performance.
(5)Research on the explicit geometrical shell element. In order to achieve the nonlinear dynamic analysis of the walls and plates during structure collapse, the realization procedure of a nonlinear dynamic shell with explicit algorithms was researched. The shell, which is combined by the membrane and plate element, is based on the mindlin theory. The detailed realization techniques such as the local element coordinate, element formulations, the mass matrix calculation and the element broken criterion were studied. Finally, a nonlinear dynamic procedure of shell element with explicit algorithms was presented. The numerical result shows that the shell element has very good performance.
(6)Research on the dynamic relaxation method. Considering the implementation method of implicit finite element stiffness damp, a stress stiffness damp was realized in the explicit finite element framework by the stress updated procedure. The influence rule of stiffness damp to the stability time step was studied through a three dimensional beam dynamic analysis. The numerical result shows that the stiffness damp coefficient will reduce the stability time step length greatly. Therefore, the application of the stiffness damp coefficient is not suggested in the explicit dynamic analysis, while the mass damp coefficient is recommended when the damp should be considered.
(1)建筑结构连续性倒塌问题的现状研究。依据建筑结构连续性倒塌现有文献资料,从理论研究现状、规范研究现状、数值模拟现状以及软件应用现状等方面进行了对比分析,总结了建筑结构连续倒塌的研究重点,并针对非线性动力计算问题,分析了材料、几何和接触非线性的研究现状。
(2)结构多重非线性计算的力学原理研究。针对建筑结构倒塌材料、几何和接触三重非线性的力学特点,系统研究和对比了隐式有限元、显式有限元、离散元、显式有限元与离散元耦合等方法的力学实现原理和过程,进而针对建筑结构连续倒塌的力学模拟,分析了各种方法的优缺点和适用性。
(3)用于建筑结构倒塌数值模拟的质点元方法研究。提出了用于建筑结构倒塌模拟的质点元方法,该方法以质点运动学为基础,建模过程与通用有限元一致,通过定义广义连接模型、构造连接模型转化法则和建立接触碰撞算法,将显式有限元与离散元统一于相同的计算框架之下,具有效率优先、精度可调的特点,能够用于建筑结构倒塌等强非线性的动力计算。
(4)具有大位移大转动计算能力的梁元模型研究。为了数值模拟建筑结构倒塌过程中的梁柱构件,建立了一个具有大位移大转动非线性动力计算能力的显式梁元。该梁元基于更新拉格朗日列式,考虑了转动的不可交换性,选用共旋方法分离单元刚体位移和变形位移,采用欧拉梁假设进行变形位移插值,通过应力更新算法来考虑材料的本构关系,最后开发了显式梁元程序并进行了数值检验,算例表明该梁元力学性能良好,具有一定的工程应用价值。
(5)具有大位移大转动计算能力的壳元模型研究。为了数值模拟在结构倒塌过程中的墙板构件,研究了具有大位移大转动计算能力的显式平板壳元,该壳元基于中厚板理论,采用膜元与板元叠加的方式实现,涉及壳元的单元定位方法、质量矩阵的生成方法、稳定时间步长以及单元破坏准则等内容,开发了显式壳元计算程序,并进行了数值检验,算例数值结果表明该显式平板壳元具有较好的计算精度和适用性。
(6)动力松弛方法研究。参照隐式有限元刚度阻尼的生成方法,并考虑显式有限元的计算原理,研究了显式有限元通过材料本构实现刚度阻尼的方法；进而针对三维梁元研究了刚度阻尼系数对稳定时间步长的影响规律,确定了折减系数与阻尼系数和单元特征长度的函数对应关系。数值计算表明,刚度阻尼严重降低稳定时间步长,对于结构显式动力分析不建议采用刚度阻尼,而是采用质量阻尼的方式进行施加。
In order to simulate the nonlinear dynamic process of progressive collapse of building structure,considering the coupled nonlinearity of geometrical,material and contact from continuum to non-continuum,a particle element method(PEM) was proposed to simulate the nonlinear dynamics process of building structure collapse after the principles of nonlinear dynamical mechanics were studied systematically. Then the beam and shell element with the large displacement and large rotation capability were researched.Finally, the dynamic relaxation method was studied to apply the initial stress.The detailed research contents are as follows:
(1)Research on the present state of the progressive collapse of building structure.Firstly,the present state of structure progressive collapse was analyzed from theory research,code research, numerical simulation and the software application respectively.Then considering material,geometrically and contact nonlinearity, the present state of nonlinear dynamics analysis was studied.
(2)Research on the principles of nonlinear dynamical mechanics. Considering the coupled nonlinearity of geometrical, material and contact of building progressive collapse, the nonlinear dynamical mechanics principles of the implicit finite element method, the explicit finite element method and the discrete element method were studied. Then the advantages and disadvantages of those methods to simulate the process of building progressive collapse were compared.
(3)Research on the particle element method(PEM) which was proposed to simulate the nonlinear dynamics process of building structure collapse from continuum to non-continuum. Based on the theory of particle dynamics, this method unifies the explicit finite element method and discrete element method to the same computation framework by defining the generalized link modal, constructing the conversion law of the link modal and creating the contact collision algorithm. The particle element method,which has the computation accuracy of finite element method during the continuum phase and the computation capability of discrete element method during the non-continuum phase, could be used for strong nonlinear dynamics simulation of building structure collapse.
(4)Research on the explicit geometrical beam element.In order to achieve the nonlinear dynamic analysis of the beams and columns during structure collapse, the realization procedure of a nonlinear dynamic beam with explicit algorithms was researched.Based on the updated Lagrange formulation,the finite rotation method was adopted to consider the rotation non-swappable, which was used to determine the element coordinate. Combining with the Co-Rotational method, the exact element internal force was calculated after the deformation and rigid displacement was separated. A nonlinear dynamic procedure of beam element with explicit algorithms, which could be used for the structure dynamic analysis, was presented. The numerical result shows that the beam element has very good performance.
(5)Research on the explicit geometrical shell element. In order to achieve the nonlinear dynamic analysis of the walls and plates during structure collapse, the realization procedure of a nonlinear dynamic shell with explicit algorithms was researched. The shell, which is combined by the membrane and plate element, is based on the mindlin theory. The detailed realization techniques such as the local element coordinate, element formulations, the mass matrix calculation and the element broken criterion were studied. Finally, a nonlinear dynamic procedure of shell element with explicit algorithms was presented. The numerical result shows that the shell element has very good performance.
(6)Research on the dynamic relaxation method. Considering the implementation method of implicit finite element stiffness damp, a stress stiffness damp was realized in the explicit finite element framework by the stress updated procedure. The influence rule of stiffness damp to the stability time step was studied through a three dimensional beam dynamic analysis. The numerical result shows that the stiffness damp coefficient will reduce the stability time step length greatly. Therefore, the application of the stiffness damp coefficient is not suggested in the explicit dynamic analysis, while the mass damp coefficient is recommended when the damp should be considered.
引文
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