贮液结构地震反应数值分析及应用方法研究
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摘要
贮液结构是一种极为重要的结构,与人民群众日常生产和生活息息相关。随着贮液不同,贮液结构广泛应用于生命线工程和能源与化工领域,如水塔、水箱、储油罐、储酸罐、消化池、降温池、冷凝器等,其结构形式也多种多样,包括半地下式、立式、卧式、支承式等。
由于存在液固耦合作用,这种结构动力反应极为复杂,尤其是强地震动作用下,引起的震害现象千差万别。历次震害表明,高烈度区大量贮液结构受到破坏,如浮放支座移位、支承结构移位、基底开裂、结构壁断裂等等,这些地震灾害直接导致贮液结构损坏,其原有功能丧失,生产和生活被迫中断,造成极大的经济损失。
此外,贮液结构内部的贮液有时也是极大危险源,贮液结构受到破坏后,容易引起贮液泄露,进而引发火灾、爆炸、环境污染等次生灾害。2011年3月11日日本东海岸发生9.0级地震,地震和随后的海啸造成福岛核电站中的贮液结构系统受损,致使降温系统失去功能,引发了重大核泄漏事故。
从上世纪三十年代开始,大批学者针对贮液结构地震反应进行了相关研究,其中包括建立理论分析模型、液固耦合作用效应、简化方法工程应用、地震反应规律分析、抗震设计方法和数值分析技术等等。但是从工程应用角度,贮液结构地震反应仍然有很多课题需要去研究,包括有限元建模方法、非线性算法、地震反应规律分析、工程抗震分析应用方法、优化设计等等。
本文基于此背景,针对贮液结构地震反应及相关数值分析方法进行了研究,主要工作和取得的成果如下：
1.总结了贮液结构解析解难点是求解给定边界条件和初始条件下的Laplace方程,弹性壁解析解和Housner简化计算均是建立在脉冲压力和对流压力理论假设基础上的；Haroun-Housner模型和有限元数值模型分别是建立在Housner刚性壁理论和速度势理论基础上的,本文对四种方法进行了对比,说明了有限元数值模型的可靠性。
2.基于数值迭代理论,进行了贮液结构非线性数值迭代计算方法的研究。利用经典的N-R数值迭代理论,提出改进N-R算法,考虑切线刚度和法线刚度共同协作的方式,增加单步迭代步长,提高非线性数值迭代求解效率；基于改进N-R算法,提出超N-R算法,建立数值迭代和材料本构之间的关联性,进一步提高非线性数值迭代求解效率,并通过大量试算给出对于钢材,比例系数77较为稳定的取值范围在1.46左右；并针对贮液结构非线性数值分析方法,提出采用外挂开发模式和生死单元技术相结合的方法进行数值模拟,通过举例,验证该方法的可行性和有效性。这两种算法极大地提高了贮液结构非线性数值反应分析的计算效率。
3.基于APDL语言,进行了有限元建模数值二次开发研究。提出外挂模式的有限元二次开发方法,成功实现了在ANSYS平台上进行用户自定义子程序编制和调用；基于该方法,有效地简化了利用ANSYS进行复杂贮液结构地震反应建模、计算、数据处理等工作,便于工程技术人员应用。本文的有限元二次开发工作包括：提出针对大型复杂的有限元模型,进行三维梯度网格优化划分方法,以提高网格划分质量；提出编制针对有限元结构信息存储、读取、批处理等程序,利用波前法技术,实现通过刚度矩阵修改等多种方法进行数据存储量和计算量的压缩,以提高有限元分析的高效性和实用性。
4.基于模态影响线控制网格划分技术、ATOS转换程序的开发、圣维南原理子模型技术等多方面说明了贮液结构有限元分析模型的有效性；基于此,对贮液结构基本地震反应规律进行了研究,获取了贮液结构液固耦合体系特性,以及地震动输入、壁厚、贮液量、径高比等因素对贮液结构地震反应的影响；并研究了贮液结构弹性变形对液动压力、结构有效应力、基底弯矩、基底剪力等的影响,为贮液结构抗震分析和设计提供了理论依据。
5.基于有限元数值分析和插值理论,对常规立式贮液结构“象足”效应问题进行了研究,通过编制了样条插值分析和拟合程序,提出对“象足”效应易发位置进行快速确定的函数形式,并通过大量计算,给出了拟合函数中各系数取值参照表。利用该方法,实现了快速确定“象足”效应位置,据此,可以一定程度上针对“象足”效应进行高效的抗震设计应用。
6.基于ESO形状拓扑理论,进行了贮液结构轮廓形状优化设计方法的研究,介绍了基于Mises应力、刚度约束、频率控制的ESO优化算法；提出将单元非连续性分类方式引入到ESO理论中,可以有效地解决在贮液结构轮廓拓扑计算过程中,为提高效率而增加删除率BDR,时引起的结构刚度矩阵奇异、拓扑过程不连续问题,提高了贮液结构拓扑分析的稳定性。
7.基于智能优化算法,进行了贮液结构参数优化设计方法的研究,对穷举法、ACO算法、PSO算法和DE算法进行了介绍和分析；提出将ACO方法和子结构方法进行互相嵌入使用,通过该方法可以有效减小贮液结构参数优化计算的计算量；提出了PSO-DE联合优化方法对,利用飞行、变异、交叉理论,扩大了全局搜索范围,避免了优化计算过早陷入局优,提高了优化算法效率,并加速了迭代收敛的速度。
本文的研究工作为贮液结构地震反应研究提供了有效的数值分析方法,为贮液结构地震反应研究结果在工程中的应用提供了极大地便利性,为贮液结构工程抗震设计提供了重要的应用方法,为贮液结构防灾减灾工作提供了重要的理论和应用基础。
LCS (Liquid container structure) is a kind of very important structure which is closely linked with people's daily life. For different liquid, LCSs, such as water tower, water tank, storage tank, acid tank, digestion pool, cooling tank, and condenser, are widely used in lifeline engineering, energy and chemical industry fields. The structural forms of LCS are varied, including half-underground type, horizontal type, vertical type and supporting type, etc.
For liquid-structure interaction, the seismic response of LCS is very complex. Especially under the strong earthquake action, the damage patterns are varied. Previous earthquakes have demonstrated that, in the high intensity zones, a number of LCSs were damaged such as floating support moving, support structure moving, foundation cracking, and wall fracturing, etc. Great economic loss would be caused by the directly damages of LCSs, and the production and life would be forced to be interrupted.
In addition, the liquid of LCS sometimes is a kind of dangerous source. When the LCS is damaged during earthquake, the terrible secondary disasters such as fire, explosion and environment pollution could be caused by liquid leakage. On March11,2011, the M9.0East Coast Earthquake occurred in Japan, the LCS of Fukushima Nuclear Power Station was damaged by the earthquake and subsequent tsunami. For this reason, the cooling system was failure to be controlled which caused nuclear leakages.
The related research on the seismic response for the LCS could be traced back to1930's, which consists of establishment of theoretical analysis model, liquid-structure coupling effect, simplification method for engineering application, seismic response analysis, method of seismic design and numerical analysis technique, and so on. However, in the view of engineering application, there are many subjects should be discussed deeply such as FE (finite element) analytical method, nonlinear algorithm, seismic response analysis, application method of seismic design for engineering and optimization design, etc.
Based on the mentioned above, study on the seismic response analysis and application method for the LCS are mainly carried out in the thesis. The main work and achievements are listed as follows:
1. It is concluded that the difficulty of analytical solution of LCS is to solve the Laplace equation with given boundary conditions and initial conditions. And the analytical solution about elastic wall theory and Housner simplified method are both established on base of the theory of impulse pressure and convenes pressure. To numerical solution about LCS, the Haroun-Housner analysis model is based upon the rigid wall theory and FE model upon velocity potential theory. In this thesis, an example is used to make comparison among the four methods, and the result shows that FE numerical model is reliable.
2. Based on classical N-R nonlinear iteration principle algorithm, the advanced N-R algorithm is proposed to solve nonlinear numerical calculation about LCS. In this algorithm, both tangent stiffness and normal stiffness are considered that increases the single iteration step length and improved the calculation efficiency. Based on the advanced N-R algorithm, the super N-R algorithm is proposed by establishing the relation between numerical iteration theory and the constitutive relation of material. The super N-R algorithm works more efficient than the advanced N-R method. By a large number trial calculations, the stable proportional coefficient value η of steel is suggested to be around1.46. Plug-in mode and technique of birth-death element are combined to verify the effectiveness of the both improved nonlinear iteration algorithms in the simulation process of LCS by examples. The results provide the proof that the two algorithms improve calculation efficiency of nonlinear numerical seismic response analysis of LCS greatly.
3. By using APDL language, the second developing method of establishing FE model is studied which make user subroutines programed and called successfully in ANSYS environment. Based on this method, it is simplified effectively to build FE model, calculate and analyze data for the complex structure form of LCS, which provides convenience for engineers to make seismic analysis about LCS. The main work about second development in this thesis includes several contents as follows:to provide gradient meshing technique for3D complex FE model which could improve the meshing quality; to provide the subroutines about save, read and batch process; to provide the method of stiffness matrix modification based on the technique of wave front. With these methods, the quantity of storage and calculation are decreased, and the efficiency and practicality of FE model are improved.
4. Based on the technique of influence line by modal analysis to control meshing quality, ATOS subroutines realizing transformation of FE model from ANSYS to other general finite element software and sub-model approach of the Saint-Venant principle, the effectiveness of FE model during seismic analysis about LCS is improved. Hereby, the FE model of LCS is built and the seismic response is studied such as the influence of factors of basic frequency, earthquake load input, thickness, liquid storage and diameter-height ratio. Besides, the influence on the hydrodynamic pressure, the effective stress, base moment and base shear from elastic deforms of LCS are analyzed. These studies provide the basis for seismic analysis and design of LCS.
5. Based on the analysis about seismic response of vertical LCS and interpolation theory, earthquake damage such as elephant-foot buckling is studied. According to the elephant-foot buckling damage, a new function form is proposed to help obtain the location of elephant-foot damage quickly by programming subroutines of spline interpolation and numerical fitting. Based on a lot of calculations, the value table of coefficients in the function is suggested. With this method, it shows that the fast determination of elephant-foot location has been realized, which could provide the base for more efficient seismic design to apply.
6. Based on the shape topology theory, ESO (Evolutionary Strucure Optimization), the method of topological design about the outline of LCS during seismic design is studied. ESO methods such as based Misses stress, stiffness constraint and frequency control are introduced. The method, introducing non-continuous classification of elements into ESO topology theory, is developed. This method could solve the problem increasing the delete rate, BDRi which causes the irreversibility of stiffness matrix or elements discontinuity during the process of topology calculation. And in this method the stability of topology analysis on outline of LCS is improved.
7. Based on the intelligent algorithms, parameter optimization design method of LCS is studied. The intelligent algorithms such as exhaustive algorithm, ACO algorithm, PSO algorithm and DE algorithm are introduced. The method of combination ACO algorithm with substructure technique is provided to decrease the computational cost about the parameter optimization calculation of LCS. And the PSO-DE algorithm is proposed to optimization calculation. Considered flight, mutation and cross in this method, the global searching scope could be expanded to avoid the optimization trapps in local optimum and the speed of convergence increased, and the optimization efficiency could be improved much.
In this thesis, effective numerical analysis method and implementation technology are provided to study on seismic response of LCS. Based on it, by using the analysis results, great convenience is brought to the engineering application Besides, some efficient application methods is proposed to seismic design of LCS, the important theories and application base are provide for the work of disaster prevention and mitigation engineering of LCS.
由于存在液固耦合作用,这种结构动力反应极为复杂,尤其是强地震动作用下,引起的震害现象千差万别。历次震害表明,高烈度区大量贮液结构受到破坏,如浮放支座移位、支承结构移位、基底开裂、结构壁断裂等等,这些地震灾害直接导致贮液结构损坏,其原有功能丧失,生产和生活被迫中断,造成极大的经济损失。
此外,贮液结构内部的贮液有时也是极大危险源,贮液结构受到破坏后,容易引起贮液泄露,进而引发火灾、爆炸、环境污染等次生灾害。2011年3月11日日本东海岸发生9.0级地震,地震和随后的海啸造成福岛核电站中的贮液结构系统受损,致使降温系统失去功能,引发了重大核泄漏事故。
从上世纪三十年代开始,大批学者针对贮液结构地震反应进行了相关研究,其中包括建立理论分析模型、液固耦合作用效应、简化方法工程应用、地震反应规律分析、抗震设计方法和数值分析技术等等。但是从工程应用角度,贮液结构地震反应仍然有很多课题需要去研究,包括有限元建模方法、非线性算法、地震反应规律分析、工程抗震分析应用方法、优化设计等等。
本文基于此背景,针对贮液结构地震反应及相关数值分析方法进行了研究,主要工作和取得的成果如下：
1.总结了贮液结构解析解难点是求解给定边界条件和初始条件下的Laplace方程,弹性壁解析解和Housner简化计算均是建立在脉冲压力和对流压力理论假设基础上的；Haroun-Housner模型和有限元数值模型分别是建立在Housner刚性壁理论和速度势理论基础上的,本文对四种方法进行了对比,说明了有限元数值模型的可靠性。
2.基于数值迭代理论,进行了贮液结构非线性数值迭代计算方法的研究。利用经典的N-R数值迭代理论,提出改进N-R算法,考虑切线刚度和法线刚度共同协作的方式,增加单步迭代步长,提高非线性数值迭代求解效率；基于改进N-R算法,提出超N-R算法,建立数值迭代和材料本构之间的关联性,进一步提高非线性数值迭代求解效率,并通过大量试算给出对于钢材,比例系数77较为稳定的取值范围在1.46左右；并针对贮液结构非线性数值分析方法,提出采用外挂开发模式和生死单元技术相结合的方法进行数值模拟,通过举例,验证该方法的可行性和有效性。这两种算法极大地提高了贮液结构非线性数值反应分析的计算效率。
3.基于APDL语言,进行了有限元建模数值二次开发研究。提出外挂模式的有限元二次开发方法,成功实现了在ANSYS平台上进行用户自定义子程序编制和调用；基于该方法,有效地简化了利用ANSYS进行复杂贮液结构地震反应建模、计算、数据处理等工作,便于工程技术人员应用。本文的有限元二次开发工作包括：提出针对大型复杂的有限元模型,进行三维梯度网格优化划分方法,以提高网格划分质量；提出编制针对有限元结构信息存储、读取、批处理等程序,利用波前法技术,实现通过刚度矩阵修改等多种方法进行数据存储量和计算量的压缩,以提高有限元分析的高效性和实用性。
4.基于模态影响线控制网格划分技术、ATOS转换程序的开发、圣维南原理子模型技术等多方面说明了贮液结构有限元分析模型的有效性；基于此,对贮液结构基本地震反应规律进行了研究,获取了贮液结构液固耦合体系特性,以及地震动输入、壁厚、贮液量、径高比等因素对贮液结构地震反应的影响；并研究了贮液结构弹性变形对液动压力、结构有效应力、基底弯矩、基底剪力等的影响,为贮液结构抗震分析和设计提供了理论依据。
5.基于有限元数值分析和插值理论,对常规立式贮液结构“象足”效应问题进行了研究,通过编制了样条插值分析和拟合程序,提出对“象足”效应易发位置进行快速确定的函数形式,并通过大量计算,给出了拟合函数中各系数取值参照表。利用该方法,实现了快速确定“象足”效应位置,据此,可以一定程度上针对“象足”效应进行高效的抗震设计应用。
6.基于ESO形状拓扑理论,进行了贮液结构轮廓形状优化设计方法的研究,介绍了基于Mises应力、刚度约束、频率控制的ESO优化算法；提出将单元非连续性分类方式引入到ESO理论中,可以有效地解决在贮液结构轮廓拓扑计算过程中,为提高效率而增加删除率BDR,时引起的结构刚度矩阵奇异、拓扑过程不连续问题,提高了贮液结构拓扑分析的稳定性。
7.基于智能优化算法,进行了贮液结构参数优化设计方法的研究,对穷举法、ACO算法、PSO算法和DE算法进行了介绍和分析；提出将ACO方法和子结构方法进行互相嵌入使用,通过该方法可以有效减小贮液结构参数优化计算的计算量；提出了PSO-DE联合优化方法对,利用飞行、变异、交叉理论,扩大了全局搜索范围,避免了优化计算过早陷入局优,提高了优化算法效率,并加速了迭代收敛的速度。
本文的研究工作为贮液结构地震反应研究提供了有效的数值分析方法,为贮液结构地震反应研究结果在工程中的应用提供了极大地便利性,为贮液结构工程抗震设计提供了重要的应用方法,为贮液结构防灾减灾工作提供了重要的理论和应用基础。
LCS (Liquid container structure) is a kind of very important structure which is closely linked with people's daily life. For different liquid, LCSs, such as water tower, water tank, storage tank, acid tank, digestion pool, cooling tank, and condenser, are widely used in lifeline engineering, energy and chemical industry fields. The structural forms of LCS are varied, including half-underground type, horizontal type, vertical type and supporting type, etc.
For liquid-structure interaction, the seismic response of LCS is very complex. Especially under the strong earthquake action, the damage patterns are varied. Previous earthquakes have demonstrated that, in the high intensity zones, a number of LCSs were damaged such as floating support moving, support structure moving, foundation cracking, and wall fracturing, etc. Great economic loss would be caused by the directly damages of LCSs, and the production and life would be forced to be interrupted.
In addition, the liquid of LCS sometimes is a kind of dangerous source. When the LCS is damaged during earthquake, the terrible secondary disasters such as fire, explosion and environment pollution could be caused by liquid leakage. On March11,2011, the M9.0East Coast Earthquake occurred in Japan, the LCS of Fukushima Nuclear Power Station was damaged by the earthquake and subsequent tsunami. For this reason, the cooling system was failure to be controlled which caused nuclear leakages.
The related research on the seismic response for the LCS could be traced back to1930's, which consists of establishment of theoretical analysis model, liquid-structure coupling effect, simplification method for engineering application, seismic response analysis, method of seismic design and numerical analysis technique, and so on. However, in the view of engineering application, there are many subjects should be discussed deeply such as FE (finite element) analytical method, nonlinear algorithm, seismic response analysis, application method of seismic design for engineering and optimization design, etc.
Based on the mentioned above, study on the seismic response analysis and application method for the LCS are mainly carried out in the thesis. The main work and achievements are listed as follows:
1. It is concluded that the difficulty of analytical solution of LCS is to solve the Laplace equation with given boundary conditions and initial conditions. And the analytical solution about elastic wall theory and Housner simplified method are both established on base of the theory of impulse pressure and convenes pressure. To numerical solution about LCS, the Haroun-Housner analysis model is based upon the rigid wall theory and FE model upon velocity potential theory. In this thesis, an example is used to make comparison among the four methods, and the result shows that FE numerical model is reliable.
2. Based on classical N-R nonlinear iteration principle algorithm, the advanced N-R algorithm is proposed to solve nonlinear numerical calculation about LCS. In this algorithm, both tangent stiffness and normal stiffness are considered that increases the single iteration step length and improved the calculation efficiency. Based on the advanced N-R algorithm, the super N-R algorithm is proposed by establishing the relation between numerical iteration theory and the constitutive relation of material. The super N-R algorithm works more efficient than the advanced N-R method. By a large number trial calculations, the stable proportional coefficient value η of steel is suggested to be around1.46. Plug-in mode and technique of birth-death element are combined to verify the effectiveness of the both improved nonlinear iteration algorithms in the simulation process of LCS by examples. The results provide the proof that the two algorithms improve calculation efficiency of nonlinear numerical seismic response analysis of LCS greatly.
3. By using APDL language, the second developing method of establishing FE model is studied which make user subroutines programed and called successfully in ANSYS environment. Based on this method, it is simplified effectively to build FE model, calculate and analyze data for the complex structure form of LCS, which provides convenience for engineers to make seismic analysis about LCS. The main work about second development in this thesis includes several contents as follows:to provide gradient meshing technique for3D complex FE model which could improve the meshing quality; to provide the subroutines about save, read and batch process; to provide the method of stiffness matrix modification based on the technique of wave front. With these methods, the quantity of storage and calculation are decreased, and the efficiency and practicality of FE model are improved.
4. Based on the technique of influence line by modal analysis to control meshing quality, ATOS subroutines realizing transformation of FE model from ANSYS to other general finite element software and sub-model approach of the Saint-Venant principle, the effectiveness of FE model during seismic analysis about LCS is improved. Hereby, the FE model of LCS is built and the seismic response is studied such as the influence of factors of basic frequency, earthquake load input, thickness, liquid storage and diameter-height ratio. Besides, the influence on the hydrodynamic pressure, the effective stress, base moment and base shear from elastic deforms of LCS are analyzed. These studies provide the basis for seismic analysis and design of LCS.
5. Based on the analysis about seismic response of vertical LCS and interpolation theory, earthquake damage such as elephant-foot buckling is studied. According to the elephant-foot buckling damage, a new function form is proposed to help obtain the location of elephant-foot damage quickly by programming subroutines of spline interpolation and numerical fitting. Based on a lot of calculations, the value table of coefficients in the function is suggested. With this method, it shows that the fast determination of elephant-foot location has been realized, which could provide the base for more efficient seismic design to apply.
6. Based on the shape topology theory, ESO (Evolutionary Strucure Optimization), the method of topological design about the outline of LCS during seismic design is studied. ESO methods such as based Misses stress, stiffness constraint and frequency control are introduced. The method, introducing non-continuous classification of elements into ESO topology theory, is developed. This method could solve the problem increasing the delete rate, BDRi which causes the irreversibility of stiffness matrix or elements discontinuity during the process of topology calculation. And in this method the stability of topology analysis on outline of LCS is improved.
7. Based on the intelligent algorithms, parameter optimization design method of LCS is studied. The intelligent algorithms such as exhaustive algorithm, ACO algorithm, PSO algorithm and DE algorithm are introduced. The method of combination ACO algorithm with substructure technique is provided to decrease the computational cost about the parameter optimization calculation of LCS. And the PSO-DE algorithm is proposed to optimization calculation. Considered flight, mutation and cross in this method, the global searching scope could be expanded to avoid the optimization trapps in local optimum and the speed of convergence increased, and the optimization efficiency could be improved much.
In this thesis, effective numerical analysis method and implementation technology are provided to study on seismic response of LCS. Based on it, by using the analysis results, great convenience is brought to the engineering application Besides, some efficient application methods is proposed to seismic design of LCS, the important theories and application base are provide for the work of disaster prevention and mitigation engineering of LCS.
引文
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