多组载荷作用下含缺陷容器的下限安定分析
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摘要
大多数结构物都承受着多组随时间变化的载荷作用,正确评估它们的下限安定承载能力对于保证结构安全运行具有重要的意义。由于数值计算上的困难,前人只求得了一些平面问题和轴对称壳等简单情况的解,对工程实际中常见的含体积型缺陷压力容器的安定承载能力缺乏定量的计算。本文从下限安定定理出发,建立了考虑多组载荷作用的轴对称与三维结构的安定分析有限元计算格式,可以考虑材料屈服限随温度的升高而弱化的影响。并采用一系列方法克服了优化变量多、约束数目大所造成的数值困难,具体研究了二维、三维体积型缺陷对结构承载能力的影响。
本文采用温度参数法构造了安定分析所需的残余应力场,消去自平衡的约束条件。对多维应力空间中的非线性屈服条件采用线性化方案,将安定分析转化为线性规划问题,并讨论了具体应力状态下对线性化屈服面的选择办法,分析了计算误差的主要来源以及改进精度的措施。对于三维问题,利用调和函数应满足的唯一性定理,把结构内部的虚拟结点温度用边界结点温度来表示,大大降低了优化变量的数目,使工程中较大规模结构的安定分析得以实施。
具体研究了在内压作用下,内、外凹坑和气孔等缺陷对球壳安定、极限承载能力的影响,以及外凹坑对圆柱壳塑性承载能力的影响。所得部分结果与实验对比符合良好,验证了方法的可靠性。并与现行规范进行了比较,提出了相应的建议。从理论上得到了在单组载荷作用下结构安定载荷的规律性,探讨了安定分析工程评定方法的适用范围。进一步对含缺陷轴对称结构在恒定压力、脉动压力、脉动温度的共同作用进行了安定分析,得到了三维载荷空间的安定域。
本文系统研究了各种体积型缺陷对容器承载能力的影响,给出了一系列的计算图表、曲线,为完善压力容器的评定标准提供了较详细的数值结果和结论,对安定分析的理论应用于工程实际作出了有益的贡献。
Pressure vessels widely used in many fields of industry are usually subjected to multitypes of variable loads. It is very important to assess their shakedown carrying capacities for safety in operation. Because of large difficulties in numerical algorithm, shakedown analysis only for some simple problems has been solved up to now, which is still far away from engineering application. Especially, the investigations in the effects of 3-dimensional defects such as pits or gas holes on the limit carrying capacities of the pressure vessels are usually simplified to plane problems but not quantitative analysis. Due to the lower-bound shakedown analysis has important meaning for guarantee for the safety of structures, therefore in this thesis, plastic shakedown analysis in a finite element computational form is presented for axi-symmetric and 3-dimensional structures based on lower-bound shakedown theorem, and the effects of various kinds of 3-dimensional defects on the carrying capacities of spherical and cylindrical shells are investigated. The effects of multitypes of variable loads acting on the structures can be considered. The reduction of yield limit with the rising of material temperature is taken into account as well.In this thesis following steps are adopted to overcome the numerical difficulties. The pseudo-temperature field is put into a structure and the resulting thermo-elastic stress is considered as a residual-stress field. The nonlinear yield condition is piece wise linearized, so that shakedown analysis is transformed into a linear programming problem whose strategic variable is pseudo-temperature and object variable is loading multiplier.In axi-symmetric problems, two kinds of piece wise linearized schemes to the yield condition are presented, and the selection of the schemes based on the particular stress state is investigated, then the sources of computational errors are analyzed. In 3-dimensional problems, the pseudo temperature field is assumed as a harmonic function satisfying the uniqueness theorem. So the nodal temperature vector of the whole structure
can be expressed by the boundary nodal temperature. Therefore, the quantity of strategic variables can be significantly decreased. Then the quantity of constraints is decreased by removing the unnecessary constraints of linearized yield conditions for the particular stress state. Therefore, the optimization on a very large scale can be solved by using 486 PC and the shakedown analysis is applicable to the engineering structures.By the above computational form, the effects of internal, external pits and gas holes on carrying capacities of spherical shells, and the effects of external pits on carrying capacities of cylindrical shells under internal pressure are investigated. The computational schemes and programs are proved to be reliable by comparison between the computational results and the experimental ones. Then several suggestions on carrying capacities of pressure vessels are presented after comparing the numerical results with current codes and standards. The shakedown behaviors of structures under single loading case are obtained based on the shakedown theorems. Further, the shakedown domains in 3-dimensional loading space are obtained through investigating the axi-symmetric structures subjected to the combination of three kinds of loads, constant and pulsative internal pressure, and pulsative temperature fields.In a word, a series of computational graphs, tables and curves presenting the relationship between defects and the carrying capacities of structures are given in the thesis, which can make an important improvement on the safety assessment methods of pressure vessels.
本文采用温度参数法构造了安定分析所需的残余应力场,消去自平衡的约束条件。对多维应力空间中的非线性屈服条件采用线性化方案,将安定分析转化为线性规划问题,并讨论了具体应力状态下对线性化屈服面的选择办法,分析了计算误差的主要来源以及改进精度的措施。对于三维问题,利用调和函数应满足的唯一性定理,把结构内部的虚拟结点温度用边界结点温度来表示,大大降低了优化变量的数目,使工程中较大规模结构的安定分析得以实施。
具体研究了在内压作用下,内、外凹坑和气孔等缺陷对球壳安定、极限承载能力的影响,以及外凹坑对圆柱壳塑性承载能力的影响。所得部分结果与实验对比符合良好,验证了方法的可靠性。并与现行规范进行了比较,提出了相应的建议。从理论上得到了在单组载荷作用下结构安定载荷的规律性,探讨了安定分析工程评定方法的适用范围。进一步对含缺陷轴对称结构在恒定压力、脉动压力、脉动温度的共同作用进行了安定分析,得到了三维载荷空间的安定域。
本文系统研究了各种体积型缺陷对容器承载能力的影响,给出了一系列的计算图表、曲线,为完善压力容器的评定标准提供了较详细的数值结果和结论,对安定分析的理论应用于工程实际作出了有益的贡献。
Pressure vessels widely used in many fields of industry are usually subjected to multitypes of variable loads. It is very important to assess their shakedown carrying capacities for safety in operation. Because of large difficulties in numerical algorithm, shakedown analysis only for some simple problems has been solved up to now, which is still far away from engineering application. Especially, the investigations in the effects of 3-dimensional defects such as pits or gas holes on the limit carrying capacities of the pressure vessels are usually simplified to plane problems but not quantitative analysis. Due to the lower-bound shakedown analysis has important meaning for guarantee for the safety of structures, therefore in this thesis, plastic shakedown analysis in a finite element computational form is presented for axi-symmetric and 3-dimensional structures based on lower-bound shakedown theorem, and the effects of various kinds of 3-dimensional defects on the carrying capacities of spherical and cylindrical shells are investigated. The effects of multitypes of variable loads acting on the structures can be considered. The reduction of yield limit with the rising of material temperature is taken into account as well.In this thesis following steps are adopted to overcome the numerical difficulties. The pseudo-temperature field is put into a structure and the resulting thermo-elastic stress is considered as a residual-stress field. The nonlinear yield condition is piece wise linearized, so that shakedown analysis is transformed into a linear programming problem whose strategic variable is pseudo-temperature and object variable is loading multiplier.In axi-symmetric problems, two kinds of piece wise linearized schemes to the yield condition are presented, and the selection of the schemes based on the particular stress state is investigated, then the sources of computational errors are analyzed. In 3-dimensional problems, the pseudo temperature field is assumed as a harmonic function satisfying the uniqueness theorem. So the nodal temperature vector of the whole structure
can be expressed by the boundary nodal temperature. Therefore, the quantity of strategic variables can be significantly decreased. Then the quantity of constraints is decreased by removing the unnecessary constraints of linearized yield conditions for the particular stress state. Therefore, the optimization on a very large scale can be solved by using 486 PC and the shakedown analysis is applicable to the engineering structures.By the above computational form, the effects of internal, external pits and gas holes on carrying capacities of spherical shells, and the effects of external pits on carrying capacities of cylindrical shells under internal pressure are investigated. The computational schemes and programs are proved to be reliable by comparison between the computational results and the experimental ones. Then several suggestions on carrying capacities of pressure vessels are presented after comparing the numerical results with current codes and standards. The shakedown behaviors of structures under single loading case are obtained based on the shakedown theorems. Further, the shakedown domains in 3-dimensional loading space are obtained through investigating the axi-symmetric structures subjected to the combination of three kinds of loads, constant and pulsative internal pressure, and pulsative temperature fields.In a word, a series of computational graphs, tables and curves presenting the relationship between defects and the carrying capacities of structures are given in the thesis, which can make an important improvement on the safety assessment methods of pressure vessels.
引文
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