基于等效应力的拱坝统一二次曲线体形优化研究
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摘要
由于我国对电能的需求越来越大,兴建水电工程无疑是缓和电能需求的有效方法。在众多的坝型中,拱坝以其独特的优势,正越来越受到设计工作人员的偏爱。拱坝承受的荷载通过拱梁作用传到两岸和坝底基岩,坝体主要依靠拱形推力结构来满足自身的强度要求和主要依靠两岸岩体来维持稳定,其最显著的优势有两个:一是相对其它坝型,拱坝所需建筑材料较少;二是拱坝的超载能力强。拱圈由复杂到简单的线型依次为:混合曲线→统一二次曲线→双曲线或椭圆→抛物线或三心圆→双心圆→单心圆。
目前,用于拱坝体形优化的应力计算方法主要有拱梁分载法和有限元法。有限单元法的计算功能远比结构力学方法强,运用有限元可以考虑大孔口、复杂基础、重力墩、不规则外形等多种因素的影响,可以进行仿真计算,且其计算精度高于结构力学法,由于计算软件的日趋完善,用有限元法计算已成为一种设计趋势。但是在用三维弹性有限元法计算拱坝应力时,近基础部位存在着显著的应力集中现象,往往拉应力大大超过混凝土的抗拉强度。而实际工程中,岩体内部存在着各种大小不等的裂隙,这些裂隙能够缓解应力集中的程度。为解决应力集中这一问题,我国一些学者提出了“有限元等效应力”法,为有限元计算拱坝时,消除应力集中的影响,提供了有效的可行方法,并确定了校核标准,载入了新的《混凝土拱坝设计规范》(SL282-2003)。
本文以有限元计算软件ANSYS8.1为平台,基于“有限元等效应力”原理,通过参数化编程,实现统一二次曲线拱坝体形的优化设计。首先,按照拱坝的几何方程采用布尔运算的方法来建立几何模型;其次采用合适的单元划分坝体及坝基,以形成有限单元模型。本论文采用SOLID95单元划分坝体,采用SOLID87单元划分坝基。它们都是二次等参单元,每个结点有3个自由度(X、Y和Z方向)能适应拱坝复杂的曲面。在计算结构应力场的同时要计算相应工况下的温度场,需要运用ANSYS的热—应力耦合分析,即在原有单元的基础上添加结点温度自由度,使每个结点存在四个自由度UX、UY、UZ和TEMP;然后,施加荷载并求解;最后进行优化分析。
最后本文在计算实例中,运用自编的APDL参数化统一二次曲线拱坝体型优化程序对其优化,结果表明:此程序能有效改善坝体的受力状态,优化出理想的拱坝体形。本文得出了在ANSYS8.1上有效实现等效应力的方法,此方法能缩短设计周期,减轻设计人员的劳动强度。
整篇论文回顾了有限单元法、优化等基础知识后,结合ANSYS软件具体功能,采用有效的方法实现统一二次曲线拱坝建模,在优化过程中,不会因改变参数取值,发生实体之间无法粘结的情况,也不会发生无法划分网格的情况,为基于等效应力的拱坝统一二次曲线体形优化打下坚实基础;在ANSYS优化过程中嵌入APDL自编程序,计算拱坝等效应力,计算实例的数据表明自编的APDL程序能有效缓解应力集中程度。整个自编程序运行通畅,结果合理。
实际拱坝体形设计时,还应考虑施工,本程序可粗略计算体形参数,实际体形还应考虑施工条件、施工质量、局部开孔等因素。本程序优化的坝形,可进一步用拱梁分载法校核。
The need to electric energy is bigger and bigger in our country. It is a effective method to building hydroelectric power station. In numerous types of dams, engineers are interested in arch dam especially, with its special advantage. The loads which are subject to arch dam are transferred to abutments and basic rock. The dam keeps its stable mainly depends on the reaction of abutments, not by its gravity. There are two advantages of arch dam, one is arch dam need less to concrete material, the other is the overload capacity of arch dam is larger. The sequence of arch dam's curve from good to bad is blending curve, quadratic curve, hyperbola or ellipse, parabola, three center circle, double center circle, single center circle.
There are two method used in stress calculation of arch dam optimization. They are try load method and finite element method. The calculation function of finite element method is far stronger than try load method. We can consider the large orifice, complex foundation, gravity abutment, irregular contour, simulation and so on with finite element method. The accuracy of calculation is higher than try load method. With the development of software, finite element method is more and more popular. But when we use three-dimensional elastic finite element, stress concentration will be appear, and the value is often larger than the ensile strength of concrete. But in the actual programme, the inner part of rock exists much fracture, so that the stress concentration is alleviated. To resolve this problem, some scholars of our country put forward "equivalent finite element stress". The principle provides a effective method for software analysis,which is adopted in (SL282-2003) .
This paper is based on general finite element calculation software ANSYS8.1, to get a way to fond the best curve of arh dam on unified quadratic curve. First, build finite-element by geometric equation of arch dam with boolean operations of ANSYS; second, arch dam is divided by some certain element in order to build finite element model. In this paper, SOLID95 is adopted to arch dam; SOLID87 is adopted to foundation. They are a kind of quadratic isoparametric element, each node has 3 degree (X, Y and Z direction), which can adaptatde to complex body. But when we calculate structure stress field, we should also calculate stress of temperature field accordingly. In this case we will use "coupled hot and stress" of ANSYS8.1, that is to add a degree to each node as TEMP degree. So each node has four degree that is UX、UY、UZ and TEMP; At last, apply loads to element model, then solve the problem, optimize.
At the end of this paper, take Kuai Ze-he arch dam as an example, optimize the shape of the arch dam by the programme originally proposed by this paper. The result enunciation: this programme can alleviate stress concentration effectively and the outcome is economical. This method can shorten the design period, ease the labor strength of engineer.
The whole paper is reviewed the knowledge about finite element method and optimization, then we can build the arch dam successfully with the function of ANSYS software. In the process of APDL programme, although the parameters are changed,the optimization circulates smoothly,the entity can glue with each other,meshing correctly. In the ANSYS software APDL programme is embedded. The outcome of a case shows that the APDL programme used in circulating equivalent finite element stress is effective.
目前,用于拱坝体形优化的应力计算方法主要有拱梁分载法和有限元法。有限单元法的计算功能远比结构力学方法强,运用有限元可以考虑大孔口、复杂基础、重力墩、不规则外形等多种因素的影响,可以进行仿真计算,且其计算精度高于结构力学法,由于计算软件的日趋完善,用有限元法计算已成为一种设计趋势。但是在用三维弹性有限元法计算拱坝应力时,近基础部位存在着显著的应力集中现象,往往拉应力大大超过混凝土的抗拉强度。而实际工程中,岩体内部存在着各种大小不等的裂隙,这些裂隙能够缓解应力集中的程度。为解决应力集中这一问题,我国一些学者提出了“有限元等效应力”法,为有限元计算拱坝时,消除应力集中的影响,提供了有效的可行方法,并确定了校核标准,载入了新的《混凝土拱坝设计规范》(SL282-2003)。
本文以有限元计算软件ANSYS8.1为平台,基于“有限元等效应力”原理,通过参数化编程,实现统一二次曲线拱坝体形的优化设计。首先,按照拱坝的几何方程采用布尔运算的方法来建立几何模型;其次采用合适的单元划分坝体及坝基,以形成有限单元模型。本论文采用SOLID95单元划分坝体,采用SOLID87单元划分坝基。它们都是二次等参单元,每个结点有3个自由度(X、Y和Z方向)能适应拱坝复杂的曲面。在计算结构应力场的同时要计算相应工况下的温度场,需要运用ANSYS的热—应力耦合分析,即在原有单元的基础上添加结点温度自由度,使每个结点存在四个自由度UX、UY、UZ和TEMP;然后,施加荷载并求解;最后进行优化分析。
最后本文在计算实例中,运用自编的APDL参数化统一二次曲线拱坝体型优化程序对其优化,结果表明:此程序能有效改善坝体的受力状态,优化出理想的拱坝体形。本文得出了在ANSYS8.1上有效实现等效应力的方法,此方法能缩短设计周期,减轻设计人员的劳动强度。
整篇论文回顾了有限单元法、优化等基础知识后,结合ANSYS软件具体功能,采用有效的方法实现统一二次曲线拱坝建模,在优化过程中,不会因改变参数取值,发生实体之间无法粘结的情况,也不会发生无法划分网格的情况,为基于等效应力的拱坝统一二次曲线体形优化打下坚实基础;在ANSYS优化过程中嵌入APDL自编程序,计算拱坝等效应力,计算实例的数据表明自编的APDL程序能有效缓解应力集中程度。整个自编程序运行通畅,结果合理。
实际拱坝体形设计时,还应考虑施工,本程序可粗略计算体形参数,实际体形还应考虑施工条件、施工质量、局部开孔等因素。本程序优化的坝形,可进一步用拱梁分载法校核。
The need to electric energy is bigger and bigger in our country. It is a effective method to building hydroelectric power station. In numerous types of dams, engineers are interested in arch dam especially, with its special advantage. The loads which are subject to arch dam are transferred to abutments and basic rock. The dam keeps its stable mainly depends on the reaction of abutments, not by its gravity. There are two advantages of arch dam, one is arch dam need less to concrete material, the other is the overload capacity of arch dam is larger. The sequence of arch dam's curve from good to bad is blending curve, quadratic curve, hyperbola or ellipse, parabola, three center circle, double center circle, single center circle.
There are two method used in stress calculation of arch dam optimization. They are try load method and finite element method. The calculation function of finite element method is far stronger than try load method. We can consider the large orifice, complex foundation, gravity abutment, irregular contour, simulation and so on with finite element method. The accuracy of calculation is higher than try load method. With the development of software, finite element method is more and more popular. But when we use three-dimensional elastic finite element, stress concentration will be appear, and the value is often larger than the ensile strength of concrete. But in the actual programme, the inner part of rock exists much fracture, so that the stress concentration is alleviated. To resolve this problem, some scholars of our country put forward "equivalent finite element stress". The principle provides a effective method for software analysis,which is adopted in
This paper is based on general finite element calculation software ANSYS8.1, to get a way to fond the best curve of arh dam on unified quadratic curve. First, build finite-element by geometric equation of arch dam with boolean operations of ANSYS; second, arch dam is divided by some certain element in order to build finite element model. In this paper, SOLID95 is adopted to arch dam; SOLID87 is adopted to foundation. They are a kind of quadratic isoparametric element, each node has 3 degree (X, Y and Z direction), which can adaptatde to complex body. But when we calculate structure stress field, we should also calculate stress of temperature field accordingly. In this case we will use "coupled hot and stress" of ANSYS8.1, that is to add a degree to each node as TEMP degree. So each node has four degree that is UX、UY、UZ and TEMP; At last, apply loads to element model, then solve the problem, optimize.
At the end of this paper, take Kuai Ze-he arch dam as an example, optimize the shape of the arch dam by the programme originally proposed by this paper. The result enunciation: this programme can alleviate stress concentration effectively and the outcome is economical. This method can shorten the design period, ease the labor strength of engineer.
The whole paper is reviewed the knowledge about finite element method and optimization, then we can build the arch dam successfully with the function of ANSYS software. In the process of APDL programme, although the parameters are changed,the optimization circulates smoothly,the entity can glue with each other,meshing correctly. In the ANSYS software APDL programme is embedded. The outcome of a case shows that the APDL programme used in circulating equivalent finite element stress is effective.
引文
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[3]张惠英等编译.世界大坝发展史[M].北京:五洲传播出版社,2001.
[4]汝乃华,姜忠胜.大坝事故与安全.拱坝[M].中国水利水电出版社,1999
[5]朱伯芳.中国拱坝建设的成就[J].水力发电,1999,45(10):38-40.
[6]吴佩佩,闫金良.国内拱坝的建设及发展[J].西北水电,2006,(4):4-7.
[7]陈知渊.拱坝及其优化方法的发展现状与展望[J].水利与建筑工程学报,2006,4(4):91-97
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