含物理缺陷薄壁钢构件的稳定性理论与应用
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摘要
本文采用局部—整体相结合的方法，建立了一套分析含裂纹薄壁钢构件的稳定性理论，并系统地研究了裂纹对受压薄壁钢构件的弹性屈曲行为和极限承载力的影响。其中整体受压柱按一维问题分析，裂纹所在的局部按三维问题分析。本文获得的一系列非常有用的理论结果，为推动含物理缺陷钢结构的安全性和耐久性评估奠定了必要的理论基础。
本文首先回顾和分析了近代薄壁结构非线性稳定性理论的发展历史和现状，阐明了本研究的理论意义和应用前景。然后，采用面场近似分析方法(CSSF)求得了含中心裂纹薄壁构件应力强度因子的解析表达式。再采用Rayleigh-Ritz能量变分法，分别按照平面裂纹模型和空间裂纹模型计算得到了含裂纹偏心受压柱的弹性挠度的级数解和最大挠度的通用解析解。最后，利用以上最大挠度解析解，推导了含裂纹受压柱平衡路径的控制方程，提出了一个带裂纹轴压柱弹性屈曲全过程的平衡路径模型，并进一步推导了利用双参数准则确定极限承载力的完备方程。本文还研究了利用位移引伸计测定薄板材料单轴损伤演化曲线的试验方法，提出了一种标定材料非线性塑性损伤参数的数值迭代拟合方法，并探讨了损伤力学在钢结构弹塑性稳定性分析中的应用问题。本文的主要工作和成果包括：
(1)首次提出了求解薄壁构件的应力强度因子的裂纹面场近似分析方法(CSSF)，并取得了常见薄壁构件无量纲应力强度因子的两个通用解析表达式。CSSF方法的要点是，先基于三维有限元计算分析的结果和无限大中心裂纹板的全场或近场应力解析公式，构建薄壁构件沿裂纹所在截面正应力的分布模型；然后利用构件的平衡条件确定无量纲应力强度因子。与现有的数值结果比较表明，这些解析解不仅形式简单，而且结果可靠。
(2)首次采用Rayleigh-Ritz能量变分法，分别按照平面裂纹模型和空间裂纹模型计算获得了含裂纹偏心受压柱的弹性挠度的级数解，特别是，取得了最大挠度的通用解析解。这对于解析研究受压构件弹性屈曲行为、确定极限承载力是非常重要的基础。与现有转动弹簧模型和等效截面刚度方法相比，该解的主要优点是可以考虑柱在轴向压力作用下裂纹的闭合效应。
(3)利用偏心柱最大挠度解析解，推导了含裂纹偏心柱平衡路径的控制方程，首次提出了一个带裂纹轴压柱弹性屈曲全过程的平衡路径模型。该模型首次揭示了裂纹对轴心受压柱稳定性的影响机理：当横向干扰位移大于一定程度时，裂纹才对轴压柱临界荷载有影响；当横向干扰位移小于一定程度时，裂纹只对轴压柱的屈曲后过程有作用，而对临界荷载无影响。从而指出了现有文献的一些错误结论。
(4)在建立含裂纹偏心柱的屈服荷载方程和断裂极限荷载方程后，进一步推导了利用屈服—断裂双参数准则确定结构极限承载力的完备方程，并研究了各种因素对由边缘屈服破坏向裂纹扩展破坏转变的临界长细比、裂纹相对长度和偏心度的影响规律。
(5)针对含边裂纹T形截面柱和带多个边裂纹矩形截面阶梯柱两种复杂情况，本研究求得了弹性挠度解，并建立了相应的屈曲平衡路径的控制方程和计算程序。
(6)系统地建立了一套利用位移引伸计测定薄板材料单轴损伤演化曲线的试验方法，首次提出了一种标定材料非线性塑性损伤参数的数值迭代拟合方法。文中就试样形状尺寸的确定、主损伤区弹塑性大应变的测控和卸载弹性模量的稳定性与精确测量等关键测试技术问题进行了深入细致的分析和实验研究，并从多角度对该试验方法的正确性进行了实验验证。针对LY12-CZ薄板材料的实验研究和分析表明，该损伤测试和数值拟合方法是切实可行的。
(7)本文还将幂强化材料模型和塑性损伤的非线性模型同时引入Shanley双模量理论，改进了弹塑性屈曲荷载的计算方法，推导了求解弹塑性屈曲荷载的迭代方程，并采用算例进行了分析讨论。
(8)系统分析了裂纹对薄壁截面柱弹性挠度和极限承载力的影响规律和程度，考查了平面裂纹模型和空间裂纹模型各自的特点和应用范围。文中还给出了许多数值计算结果的图表和相应的分析。
The effects of crack on the elastic deflection and the ultimate bearing capacity of thin-walled columns under both axially and eccentrically load were studied systematically by use of a local-global approach, where the local analysis for crack was according to one-dimensional model and the global analysis for column was according to three-dimensional model. And the stability theory and the method for determining ultimate bearing capacity of cracked steel-column were established. Thus a series of useful theoretical results were obtained, which are essential to evaluating the safety and durability of a damaged steel structure.
Firstly, the development in nonlinear theories of stability for thin-walled structures was reviewed and a systematic exposition of the theoretical significance and application prospect of this study was made. Secondly, in order to take account of the effects of the cracks in structures, the expression of the stress intensity factor (SIF) of center cracked thin-walled members was achieved by means of the crack-section stress field (CSSF) method. Then, the elastic deflection of an eccentric thin-walled column with a model-I crack were calculated by mean of Rayleigh-Ritz energy method, where the plane crack model and spatial crack model where employed respectively. Furthermore, the control equations of the equilibrium path of the elastic buckling were derived for cracked columns subjected to both axial and eccentric compressive load. And an analytical model of the equilibrium path of both before and post buckling was suggested for the cracked column under axial load, where the crack closure and fracture condition are considered. Finally, the two-criteria approach to analyze the failure of thin-walled columns has been suggested and the analytical equations for determinate the ultimate bearing capacity were given. In addition, a simple test method for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for determining the material damage constants of the non-linear equations of Lemaiter-Chaboche's damage model. Based on above damage test results, the application of the theory of elastic-plastic damage in stability analysis of the steel structures was discussed preliminarily. The main works and achievements of this dissertation are as follows:
(1) The crack-section stress field (CSSF) method for determining the stress intensity factor (SIF) of center cracked thin-walled bars was proposed and a universal expression of the dimensionless stress intensity factors for thin-walled and center-cracked members with unequal-thickness sections was acquired by use of the equilibrium condition of semi cracked member. The key to CSSF method is to establish a normal stress distribution model on the cracked cross section according to the numerical results of the finite element analysis and expression of the local or global stress field of an infinite center cracked plate. In comparison with the existing finite SIF results of thin-walled members, the simple formula given in this paper are simple and reliable to evaluate the residual bearing capacity or working life of engineering cracked thin-walled structures.
(2) A method for determining the elastic deflection of the eccentric thin-walled column with model-I crack has been developed according to the plane crack model and spatial crack model respectively and a trigonometric series solution of the elastic deflection equation was obtained by mean of Rayleigh-Ritz energy method, where the change in elastic energy caused by introducing the crack was considered. Especially, A universal analytical-solution of the maximum deflection for cracked columns with various cross-sections was developed, that is useful to examine analytically the elastic buckling behavior and to estimate the ultimate bearing capacity. By comparison with the current rotational spring model and the equivalent stiffness method, the main advantage of the present solution is that the effect of axial compression on crack closure is considered.
(3) The governing equation for whole process of an eccentric compressive column with model I crack was established, based on above analytical expression of the maximum deflection and an analytical model of the equilibrium path of both before and post buckling was suggested for the a cracked axial column, where the crack closure and fracture condition are considered. The equilibrium path model shows that when an excessive lateral interfering deflection appears the cracks will have the critical load decreased, while when the lateral interfering deflection is small the cracks will have no effects on critical load but post-buckling process. Thus the unreasonable conclusions in some references that cracks have certainly effects on critical load were corrected.
(4) After the equations of ultimate yielding and fracture load were established for cracked eccentric column, the perfect equations for determining the stability factors were derived according to the two-failure criteria, i.e., yielding and fracture criteria. And effects of some factors on the critical transition crack-length, slenderness and eccentricity from yielding failure to fracture failure were investigated respectively.
(5) For the two complex cases of a T-section column with a single-side crack and a multi-step compressive rectangular column with arbitrary number of cracks, thel expressions of the elastic deflections were obtained. And hence the governing equation for the buckling equilibrium path and the computational programs were established.
(6) A simple test technique by use of clip gage for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for fitting the non-linear damage equation of Lemaiter-Chaboche's model. Some special techniques for measuring damage parameters of materials, such as the specimen size requirements, gauge length, the stability of the repeated-unloading elastic modulus and measuring and controlling of large strain, were proposed and discussed. The results tested from the thin-slabs of LY12-CZ aluminum alloys showed that the test method suggested for determining the uniaxial ductile damage curves of thin-slabs is feasible and effective.
(7) The calculation method for determining the elastic-plastic buckling load was improved by introducing the material model of exponential strengthening and nonlinear plastic damage model into Shanley's theory. The interactive equation for finding the elastic-plastic stability coefficients was derived and an example of its application was gived and analyzed.
(8) For some sections of columns, the influence of crack on the elastic deflection and ultimate bearing capacity of thin-walled columns was studied. And the differences between plane crack model and spatial crack model and their application limitation were discussed. A number of curves and tables of numerical results were given and analyzed in this dissertation.
本文首先回顾和分析了近代薄壁结构非线性稳定性理论的发展历史和现状，阐明了本研究的理论意义和应用前景。然后，采用面场近似分析方法(CSSF)求得了含中心裂纹薄壁构件应力强度因子的解析表达式。再采用Rayleigh-Ritz能量变分法，分别按照平面裂纹模型和空间裂纹模型计算得到了含裂纹偏心受压柱的弹性挠度的级数解和最大挠度的通用解析解。最后，利用以上最大挠度解析解，推导了含裂纹受压柱平衡路径的控制方程，提出了一个带裂纹轴压柱弹性屈曲全过程的平衡路径模型，并进一步推导了利用双参数准则确定极限承载力的完备方程。本文还研究了利用位移引伸计测定薄板材料单轴损伤演化曲线的试验方法，提出了一种标定材料非线性塑性损伤参数的数值迭代拟合方法，并探讨了损伤力学在钢结构弹塑性稳定性分析中的应用问题。本文的主要工作和成果包括：
(1)首次提出了求解薄壁构件的应力强度因子的裂纹面场近似分析方法(CSSF)，并取得了常见薄壁构件无量纲应力强度因子的两个通用解析表达式。CSSF方法的要点是，先基于三维有限元计算分析的结果和无限大中心裂纹板的全场或近场应力解析公式，构建薄壁构件沿裂纹所在截面正应力的分布模型；然后利用构件的平衡条件确定无量纲应力强度因子。与现有的数值结果比较表明，这些解析解不仅形式简单，而且结果可靠。
(2)首次采用Rayleigh-Ritz能量变分法，分别按照平面裂纹模型和空间裂纹模型计算获得了含裂纹偏心受压柱的弹性挠度的级数解，特别是，取得了最大挠度的通用解析解。这对于解析研究受压构件弹性屈曲行为、确定极限承载力是非常重要的基础。与现有转动弹簧模型和等效截面刚度方法相比，该解的主要优点是可以考虑柱在轴向压力作用下裂纹的闭合效应。
(3)利用偏心柱最大挠度解析解，推导了含裂纹偏心柱平衡路径的控制方程，首次提出了一个带裂纹轴压柱弹性屈曲全过程的平衡路径模型。该模型首次揭示了裂纹对轴心受压柱稳定性的影响机理：当横向干扰位移大于一定程度时，裂纹才对轴压柱临界荷载有影响；当横向干扰位移小于一定程度时，裂纹只对轴压柱的屈曲后过程有作用，而对临界荷载无影响。从而指出了现有文献的一些错误结论。
(4)在建立含裂纹偏心柱的屈服荷载方程和断裂极限荷载方程后，进一步推导了利用屈服—断裂双参数准则确定结构极限承载力的完备方程，并研究了各种因素对由边缘屈服破坏向裂纹扩展破坏转变的临界长细比、裂纹相对长度和偏心度的影响规律。
(5)针对含边裂纹T形截面柱和带多个边裂纹矩形截面阶梯柱两种复杂情况，本研究求得了弹性挠度解，并建立了相应的屈曲平衡路径的控制方程和计算程序。
(6)系统地建立了一套利用位移引伸计测定薄板材料单轴损伤演化曲线的试验方法，首次提出了一种标定材料非线性塑性损伤参数的数值迭代拟合方法。文中就试样形状尺寸的确定、主损伤区弹塑性大应变的测控和卸载弹性模量的稳定性与精确测量等关键测试技术问题进行了深入细致的分析和实验研究，并从多角度对该试验方法的正确性进行了实验验证。针对LY12-CZ薄板材料的实验研究和分析表明，该损伤测试和数值拟合方法是切实可行的。
(7)本文还将幂强化材料模型和塑性损伤的非线性模型同时引入Shanley双模量理论，改进了弹塑性屈曲荷载的计算方法，推导了求解弹塑性屈曲荷载的迭代方程，并采用算例进行了分析讨论。
(8)系统分析了裂纹对薄壁截面柱弹性挠度和极限承载力的影响规律和程度，考查了平面裂纹模型和空间裂纹模型各自的特点和应用范围。文中还给出了许多数值计算结果的图表和相应的分析。
The effects of crack on the elastic deflection and the ultimate bearing capacity of thin-walled columns under both axially and eccentrically load were studied systematically by use of a local-global approach, where the local analysis for crack was according to one-dimensional model and the global analysis for column was according to three-dimensional model. And the stability theory and the method for determining ultimate bearing capacity of cracked steel-column were established. Thus a series of useful theoretical results were obtained, which are essential to evaluating the safety and durability of a damaged steel structure.
Firstly, the development in nonlinear theories of stability for thin-walled structures was reviewed and a systematic exposition of the theoretical significance and application prospect of this study was made. Secondly, in order to take account of the effects of the cracks in structures, the expression of the stress intensity factor (SIF) of center cracked thin-walled members was achieved by means of the crack-section stress field (CSSF) method. Then, the elastic deflection of an eccentric thin-walled column with a model-I crack were calculated by mean of Rayleigh-Ritz energy method, where the plane crack model and spatial crack model where employed respectively. Furthermore, the control equations of the equilibrium path of the elastic buckling were derived for cracked columns subjected to both axial and eccentric compressive load. And an analytical model of the equilibrium path of both before and post buckling was suggested for the cracked column under axial load, where the crack closure and fracture condition are considered. Finally, the two-criteria approach to analyze the failure of thin-walled columns has been suggested and the analytical equations for determinate the ultimate bearing capacity were given. In addition, a simple test method for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for determining the material damage constants of the non-linear equations of Lemaiter-Chaboche's damage model. Based on above damage test results, the application of the theory of elastic-plastic damage in stability analysis of the steel structures was discussed preliminarily. The main works and achievements of this dissertation are as follows:
(1) The crack-section stress field (CSSF) method for determining the stress intensity factor (SIF) of center cracked thin-walled bars was proposed and a universal expression of the dimensionless stress intensity factors for thin-walled and center-cracked members with unequal-thickness sections was acquired by use of the equilibrium condition of semi cracked member. The key to CSSF method is to establish a normal stress distribution model on the cracked cross section according to the numerical results of the finite element analysis and expression of the local or global stress field of an infinite center cracked plate. In comparison with the existing finite SIF results of thin-walled members, the simple formula given in this paper are simple and reliable to evaluate the residual bearing capacity or working life of engineering cracked thin-walled structures.
(2) A method for determining the elastic deflection of the eccentric thin-walled column with model-I crack has been developed according to the plane crack model and spatial crack model respectively and a trigonometric series solution of the elastic deflection equation was obtained by mean of Rayleigh-Ritz energy method, where the change in elastic energy caused by introducing the crack was considered. Especially, A universal analytical-solution of the maximum deflection for cracked columns with various cross-sections was developed, that is useful to examine analytically the elastic buckling behavior and to estimate the ultimate bearing capacity. By comparison with the current rotational spring model and the equivalent stiffness method, the main advantage of the present solution is that the effect of axial compression on crack closure is considered.
(3) The governing equation for whole process of an eccentric compressive column with model I crack was established, based on above analytical expression of the maximum deflection and an analytical model of the equilibrium path of both before and post buckling was suggested for the a cracked axial column, where the crack closure and fracture condition are considered. The equilibrium path model shows that when an excessive lateral interfering deflection appears the cracks will have the critical load decreased, while when the lateral interfering deflection is small the cracks will have no effects on critical load but post-buckling process. Thus the unreasonable conclusions in some references that cracks have certainly effects on critical load were corrected.
(4) After the equations of ultimate yielding and fracture load were established for cracked eccentric column, the perfect equations for determining the stability factors were derived according to the two-failure criteria, i.e., yielding and fracture criteria. And effects of some factors on the critical transition crack-length, slenderness and eccentricity from yielding failure to fracture failure were investigated respectively.
(5) For the two complex cases of a T-section column with a single-side crack and a multi-step compressive rectangular column with arbitrary number of cracks, thel expressions of the elastic deflections were obtained. And hence the governing equation for the buckling equilibrium path and the computational programs were established.
(6) A simple test technique by use of clip gage for determining the uniaxial ductile damage curves of thin-slab was studied systematically and a numerical iterative-fit method was suggested for fitting the non-linear damage equation of Lemaiter-Chaboche's model. Some special techniques for measuring damage parameters of materials, such as the specimen size requirements, gauge length, the stability of the repeated-unloading elastic modulus and measuring and controlling of large strain, were proposed and discussed. The results tested from the thin-slabs of LY12-CZ aluminum alloys showed that the test method suggested for determining the uniaxial ductile damage curves of thin-slabs is feasible and effective.
(7) The calculation method for determining the elastic-plastic buckling load was improved by introducing the material model of exponential strengthening and nonlinear plastic damage model into Shanley's theory. The interactive equation for finding the elastic-plastic stability coefficients was derived and an example of its application was gived and analyzed.
(8) For some sections of columns, the influence of crack on the elastic deflection and ultimate bearing capacity of thin-walled columns was studied. And the differences between plane crack model and spatial crack model and their application limitation were discussed. A number of curves and tables of numerical results were given and analyzed in this dissertation.
引文
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