摘要
水封止水元件的工作性能直接决定了闸门的止水效果,水封在大跨度和高压闸门的设计中占有重要地位。本文的主要工作围绕橡胶水封计算的客观性展开,努力寻找更优的算法以提高仿真的计算精度,力求更为客观地反映水封工作时的特征规律和评估封水效果。水封计算不能过分要求计算出的特征值是精确的,对于一个复杂的、受多种不可模拟因素困扰的系统,不可能得到一个精确的计算值。计算的客观性体现在对水封特征规律的把握程度,对封水效果评价的正确性和计算方法有无改进上。为提高水封仿真计算的精度,一方面希望通过完善水封计算理论得以实现,另一方面希望通过改进水封计算方法使计算精度提高。
本文首先对水封大变形的空间描述进行了探讨,研究了几何非线性大应变的度量方法、应力度量方法及应变张量、应力张量之间的严格关系,并通过变分原理建立有限元方程。详述了大变形计算的基本理论和非线性的处理方法,并通过仿真计算与模型试验的对比,提出针对不同工况和精度要求选择水封材料应变能函数的方法。
以往水封大变形计算的数学理论基础需要进一步完善是本文的一个观点。虽然采用Green应变张量度量应变是力学界的主流,但本文提出当变形体同时具有大应变和大转动时,采用Green应变张量度量应变计算上会出现虚假应变值,是不准确的,而采用陈至达的变形梯度和分解(F=St+R)的方法可避免这种偏差。以往我们对大变形体的仿真计算可能存在一些缺陷,笔者认为一方面原因是度量变形的方式失误,长久以来人们习惯采用Green应变张量度量应变,对于水封这类同时具有大应变和大转角的变形体,用Green应变张量度量应变不准确。
水封大变形往往伴随着大转动。基于“和分解”,本文论证了大变形的应变和转动是耦联关系,大变形并非是应变与刚体转动的叠加。当度量应变的方式改变,本构关系的描述也相应变化。本文分析和探讨了“和分解”形式对水封材料本构关系描述的影响(即对应变能函数显化为应力应变关系的影响),导出了“和分解”下水封材料的切线模量(包含：①变形张量不变量表示的应变能函数模型,“和分解”下的切线模量通式,公式4-13、公式4-14、公式4-15、公式4-16；②Mooney-Rivlin应变能函数模型“和分解”下的切线模量,公式4-17、公式4-18、公式4-19、公式4-20；③Ogden应变能函数模型“和分解”下的切线模量,公式4-21、公式4-22、公式4-23、公式4-24),从而建立了“和分解”下严格的材料切线刚度矩阵,修改了有限元计算中增量法在T.L.格式下由变分原理表达的平衡方程,编制了基于“和分解”的水封有限元计算用户材料子程序,消除了用Green应变张量度量应变带来的计算误差,得出了较完善的水封非线性有限元计算理论和方法,这是本文的一个亮点。
实践表明,仿真计算中由于无法完全真实的模拟实际工程中的所有因素和非线性计算的固有特性,造成无论如何计算出的结果仍与真实情况有偏差。本文采用响应面法构造了水封仿真逼近参数修正的数值模型,通过对材料参数的修正使仿真计算结果进一步逼近模型试验结果(工程真实的结果具有隐蔽性,尽管模型试验具有随机性,但人们认同模型试验结果能代替工程结果)。用含交叉项的二次函数响应面对水封仿真逼近的参数进行了反演,讨论了提高响应面精度的方法,用五次函数响应面对水封仿真逼近的参数进行了再次反演,在二次函数反演的基础上提高响应面精度,并通过试验验证了其有效性。
基于精确的测微技术,提出利用度量张量和Christoffel符号进行仿真修正的构想。
基于本文的研究,对长江三峡水利枢纽升船机下闸首工作门气压伸缩式止水水封进行了特征分析。三峡升船机闸门水封采用的是目前发现的封水性能最优的断面型式,具有典型性。
The work performance of water seal sealing up component directly decides the sealing up effectiveness of gates, thus water seal has an important position in large span and high pressure gate design.The article aims at the obiectivity of calculation of water seal, making effort to look for better arithmetic to enhance the accuracy of simulating calculation, striving to better reflect the characteristic rule while water seal is working and estimate the water sealing effect of water seal. It can not excessively require the accuracy for characteristic value of water seal calculation. Regarding a complex and fuzzy system which may be disturbed by many non-simulative factors, it is impossible to get an accurate calculation value. The obiectivity of calculation is mainly reflected in master degree of characteristic rule of water seal, correctness of water sealing effect evaluation of water seal, and whether the calculated method is improved. In order to improve the accuracy of the simulation calculation of water seal, on the one hand, we hope realize by to improve the calculation theory of water seal, on the other hand, we hope realize by improving calculation method.
This article firstly has discussed the space description of large deformation of water seal, analyzed and researched the measurement method of geometric nonlinearity large strain, the stress measurement method and a strict relationship between strain tensor and stress tensor, and established a finite element equation through variational principle. Has described in detail the basic theory and nonlinear handling method of calculation of large deformation, and proposed a method of selecting water seal material strain energy function according to various working conditions and accuracy requirements through the contrast of simulating calculation and model experiment.
The mathematical calculation theory of water seal before needs futher improvement, which is an opinion in this article. Although employ Green strain tensor to measure strain is a main trend in mechanics, this article proposes that employ Green strain tensor to measure strain will appear to a false strain value when deformation subject simultaneously has large strain and large twirl, which is not exact. While employ additive decomposition of deformation gradient from Cheng Zhida (F=St+R) to measure strain can avoid this deviation. The simulating calculation for large deformation subject was not accurate enough before, the writer thinks one of the reasons is the manner fault to measure deformation. People are used to employ Green strain tensor to measure strain for a long time, as for the deformation subject simultaneously having large strain and large twirl like water seal, however, strain measured by Green strain tensor is not enough accurate.
Large deformation of water seal often is accompanied with large twirl. Based on "Additive Decomposition", this article has demonstrated that large strain and large twirl of large deformation is a coupling relation, and not a superposition of strain and rigid rotation. If the measurement method is changed, the description of constitutive relationship is corresponding changed. This article has analyzed and discussed the affection of "Additive Decomposition" to constitutive relation presentation of water seal material (i.e. the affection to manifest to stress-strain relationship according strain-energy function), has educed tangent modulus (includes①strain energy function models which are represented by strain tensor invariant, tangent modulus formulas under "additive decomposition":formula4-13, formula4-14, formula4-15, formula4-16;②Mooney-Rivlin strain energy function model, tangent modulus formulas under "additive decomposition":formula4-17, formula4-18, formula4-19, formula4-20,③Ogden strain energy function model, tangent modulus formulas under "additive decomposition":formula4-21, formula4-22, formula4-23, formula4-24) of water seal material under "Additive Decomposition", thus has established strict material stiffness matrix of finite element calculation of water seal under "Additive Decomposition", amended balance equation expressed by variational principle under T.L. format of incremental method in finite element calculation, prepared the user material subroutine of finite element calculation of water seal based on "Additive Decomposition", eliminated the water seal calculation error caused by using Green strain tensor to measure strain. The presentation of the more perfect nonlinear finite element calculation theory and method is the highlight of this paper.
The practice shows that the simulating calculation cannot simulate all factors in an actual engineering completely in real and the inherent characteristics of nonlinear calculation, which results in a deviation between results figured out in any case and the actual situation. This article employs response surface method to constitute a numerical model of parameters modification of water seal simulation, the calculation result of simulation after modified to material parameters is further similar to the experiment result of model (the real result of engineering is elusive, although randomness exist in experiment, but people acknowledge the experiment result of model can replace engineering result). Has used response surface of quadratic function with a cross term to make an inversion to the material parameters, discussed the method to improve the accuracy of response surface; used response surface of five function to make an inversion again to the parameters, improved the accuracy of response surface based on the inversion of quadratic function, and verified its validity through experiments.
Propose the idea that makes use of metric tensor and Christoffel sign to process a simulation correction based on accurate measuring technique.
Based on the research of this article, has made a feature analysis for air pressure retractable sealing up water seal of working door of lock head under ship lift of the Three Gorges Dam. The water sealing performance of section type of gate water seal of ship lift of Three Gorges is optimal in all kinds of current water seals, the seal has typicalness.
引文
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