平面Cosserat理论有限单元法的建立及混凝土抗折强度尺寸效应研究

发布时间：2018-01-31 14:28

本文关键词： Cosserat理论有限元混凝土尺寸效应　出处：《北京交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：尽管经典连续统理论在工程实践中取得了巨大的成就,但在描述材料在宏细观等不同尺度下的力学性能有着明显的局限性,无法解释不同结构尺度下所表现出来的尺寸效应。Cosserat连续统理论是有别于传统连续统理论的微极连续介质力学,它将物体视为连续分布并有一定尺寸的微极颗粒组成,在物理方程中引入了材料内禀尺度,由此建立了宏观尺度和微细观尺度的联系。因此Cosserat连续统理论在分析微米尺度或有颗粒材料组成的宏观尺度下的力学性能时,表现出很高的求解精度和良好的模拟效果。本文主要研究内容和成果如下:(1)推导了平面问题的一般Cosserat理论的平衡方程、几何方程和物理方程,构造了线位移和转角各自独立的四边形八节点的Cosserat有限元模型,采用FORTRAN语言,编制并调通了有限元程序CFEM。对纯弯悬臂梁进行了数值模拟分析,其数值解与基于经典弹性理论解析解和通用有限元软件ANSYS数值解进行了对比,验证了 Cosserat有限元模型及程序的正确性。(2)在一般Cosserat理论基础上,当忽略了微极颗粒的微观转角,其转角位移不再独立而等于宏观转角位移时,该理论则退化为约束转动Cosserat理论。本文推导了约束转动Cosserat理论的基本方程,并以应力分量作为基本未知函数,对矩形梁纯弯构件进行了求解并给出了解析解。(3)用有限元程序CFEM对悬臂梁纯弯构件进行了数值模拟分析,研究了不同内禀尺寸参数和宏观尺寸对构件力学性能的影响。研究表明,偶应力沿横截面为常量,且随着内禀尺寸的增大,偶应力逐渐增大,竖向位移、转角及跨中截面正应力则逐渐减小。当内禀尺寸一定时,随着构件宏观尺寸的增大,跨中截面下边缘处的正应力σx逐渐增大。(4)通过程序CFEM对混凝土抗折构件进行了数值模拟,研究了混凝土不同强度等级的内禀尺寸参数的取值,并确定了其合理取值范围。(5)通过数值模拟,研究了混凝土抗折强度的尺寸效应,研究表明,混凝土构件的最小宏观尺寸与内禀长度的比值越小,尺寸效应越明显;比值越大,尺寸效应越弱。混凝土强度越高,尺寸效应越明显。
[Abstract]:Although the classical continuum theory has made great achievements in engineering practice, it has obvious limitations in describing the mechanical properties of materials at different scales such as macroscopes and meso-scopes. Cosserat continuum theory is different from traditional continuum theory in micropolar continuum mechanics. It treats the object as a continuous distribution with a certain size of micropolar particles, and introduces the intrinsic scale of material into the physical equation. Therefore, the Cosserat continuum theory is used to analyze the mechanical properties of micron scale or macroscopically composed of granular materials. The main contents and results of this paper are as follows: 1) the equilibrium equations of the general Cosserat theory for plane problems are derived. Geometric equation and physical equation, the Cosserat finite element model of quadrilateral and eight-node which is independent of linear displacement and rotation angle is constructed. FORTRAN language is used. The finite element program CFEM.The numerical simulation of pure curved cantilever beam is carried out. The numerical solution is compared with the analytical solution based on classical elastic theory and the general finite element software ANSYS. The correctness of Cosserat finite element model and program is verified. Based on the general Cosserat theory, the micro rotation angle of micropolar particles is neglected. When the angular displacement is no longer independent but equal to the macroscopic angular displacement, the theory is reduced to the constrained rotational Cosserat theory. In this paper, the basic equations of the constrained rotational Cosserat theory are derived. Taking the stress component as the basic unknown function, the pure bending member of rectangular beam is solved and the analytical solution is given. (3) the numerical simulation of the pure bending member of cantilever beam is carried out by using the finite element program CFEM. The effects of different intrinsic dimension parameters and macroscopic dimensions on the mechanical properties of the members are studied. The results show that the coupling stress along the cross section is constant and the coupling stress increases gradually and the vertical displacement increases with the increase of intrinsic size. The normal stress of rotation angle and mid-span section decrease gradually. When the intrinsic dimension is fixed, with the increase of macroscopic size of the member. The normal stress (蟽 x) at the edge of the middle section is gradually increased. (4) numerical simulation of concrete flexural members is carried out by program CFEM, and the intrinsic dimension parameters of different strength grades of concrete are studied. Through numerical simulation, the size effect of concrete flexural strength is studied. The study shows that the ratio of minimum macro size to intrinsic length of concrete member is smaller. The size effect is more obvious; The bigger the ratio is, the weaker the size effect is, and the higher the strength of concrete is, the more obvious the size effect is.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU528

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