矫直过程的弹塑性B样条有限条分析

发布时间：2018-09-08 09:30

【摘要】：中厚钢板是重要的钢材品种之一,多用于高压容器、大型舰船、大直径输油气管线、大桥桥架、高层建筑等对钢材性能要求高的重要地方,是国防、交通运输、建筑设施等国家安全、国民经济建设中不可或缺的重要基础材料。随着社会现代化生产、制造的需要以及控轧控冷技术的广泛使用,在品种规格趋于多样化的同时,对具有较好平直度、极小内应力的要求也越来越高。因此,为了减小内应力、改善内应力分布、确保中厚板产品满足平直度标准的高精度要求,矫直是中厚板生产过程中一道必不可少的重要工序。本文针对板材的平行辊式矫直过程,旨在提供一个兼具矫直理论解析计算快捷性和有限元数值计算完备性的数值计算方法。根据板材的几何特性及其在矫直过程中的弹塑性变形特点,建立了基于有限条法的板材平行辊式数值计算体系。根据薄板大挠度屈曲理论和最小势能原理,建立了基于翘曲几何参数的反解计算模型,研究了通过表征翘曲程度的少数几个宏观几何尺寸即可求解出残余应变分布形式的方法。通过实测的翘曲几何参数和预设挠曲函数,对引起边部翘曲、中部翘曲等典型的翘曲缺陷的残余应变(应力)进行求解,并与实测值进行了对比。建立了满足条单元简支端和自由端边界条件的B样条位移函数,在位移函数的基础上,建立了应力应变矩阵、条单元刚度矩阵和结线等效载荷列阵。分析了结点数和条单元数对计算规模和计算精度的影响。分析了B样条有限条单元刚度矩阵和总刚度矩阵的计算特点。分析了条单元结线结点数和条单元数目对总刚度矩阵稀疏程度的影响。重点推导了Ziegler随动强化平面应力问题弹塑性应力应变关系矩阵。利用B样条函数的特点,推导了真实位移与广义位移之间的关系矩阵以及在处理位移边界条件时的计算方法。针对弹塑性本构关系,推导了基于Zeigler随动强化准则的应力应变更新隐式算法,给出了应力增量和应变增量的计算公式。在待矫直板形缺陷计算、B样条有限条法计算体系以及相关的数值计算方法的基础之上,建立了连续矫直过程的弹塑性B样条有限条法分析模型,并对计算结果进行分析和工业数据验证。
[Abstract]:Medium and thick steel plate is one of the most important steel products. It is widely used in high pressure vessels, large ships, large diameter oil and gas pipelines, bridge bridges, high-rise buildings and other important places that require high steel performance. They are national defense, transportation and transportation. Construction facilities and other national security, national economic construction in the indispensable important basic materials. With the development of modern production, manufacture and wide use of controlled rolling and cooling control technology, the requirements of better flatness and minimal internal stress are becoming higher and higher while the variety specifications tend to be diversified. Therefore, in order to reduce the internal stress, improve the distribution of internal stress and ensure that the plate products meet the high precision requirements of flatness standard, straightening is an essential and important process in the production process of medium and thick plate. Aiming at the parallel roller straightening process of plate, this paper aims to provide a numerical calculation method with both the analytical calculation speed of straightening theory and the completeness of finite element numerical calculation. According to the geometric characteristics of sheet metal and its elastoplastic deformation in the straightening process, a numerical calculation system of plate parallel roller based on finite strip method is established. Based on the theory of large deflection buckling of thin plates and the principle of minimum potential energy, the inverse solution calculation model based on warpage geometric parameters is established. The method of calculating residual strain distribution by a few macroscopic geometric dimensions of warpage degree is studied. The residual strain (stress) of typical warping defects, such as edge warping and middle warpage, is solved by the measured geometric parameters and the preset deflection function, and the results are compared with the measured values. The B-spline displacement function satisfying the boundary conditions of simple support and free end of strip element is established. Based on the displacement function, the stress-strain matrix, stiffness matrix and equivalent load matrix are established. The influence of the number of knots and the number of bar cells on the calculation scale and accuracy is analyzed. The calculation characteristics of B spline finite strip element stiffness matrix and total stiffness matrix are analyzed. The effects of the number of nodes and the number of bar elements on the sparse degree of the total stiffness matrix are analyzed. The elastic-plastic stress-strain relation matrix of plane stress problem of Ziegler follow-up strengthening is derived emphatically. Based on the characteristic of B-spline function, the relation matrix between real displacement and generalized displacement is derived, and the calculation method of the displacement boundary condition is given. According to the elastoplastic constitutive relation, an implicit algorithm of stress-strain updating based on Zeigler's following strengthening criterion is derived, and the formulas of stress increment and strain increment are given. An elastic-plastic B-spline finite strip model for continuous straightening process is established on the basis of the calculation system of B-spline finite strip method and the related numerical method. The calculation results are analyzed and the industrial data are verified.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TG306

【相似文献】