统一分析梁和有限节线法的若干应用
发布时间：2018-08-22 18:45
【摘要】：针对杆状类工程结构构件和结构体系,本文提出了一种新的梁模型——统一分析梁与一种新的数值分析方法——有限节线法。利用统一分析梁和有限节线法不仅可以解决任意杆状类结构构件或结构体系的力学分析问题,而且当问题的性质与传统梁理论的前提条件一致时,会得出同样精度的解答。算例计算结果也证明了统一分析梁的合理性与有限节线法的正确性。论文的主要工作如下:1论述了梁的发展历史以及本文的研究意义;2引入了统一分析梁和有限节线法的概念,并根据最小势能原理,推导出了在静力作用下的常微分方程组及其相应的边界条件;3论述了统一分析梁和有限节线法在固体力学中实体构件中的应用,分别与传统梁理论中的Euler梁、Timoshenko梁和自由扭转作用时的Saint Venant梁进行了比较,并给出了非圆非对称厚壁截面的统一分析梁算例;4论述了统一分析梁和有限节线法在约束扭转时薄壁杆件中的应用,分别与Vlasov梁和Umansky梁进行了比较,并给出了半开半闭截面薄壁杆件的统一分析梁算例;5指出了统一分析梁在解决更广泛工程问题时需要克服的问题。
[Abstract]:In this paper, a new beam model-unified analysis beam and a new numerical analysis method-finite nodal line method are proposed for rod-like engineering structural members and structural systems. The unified analytical beam and finite nodal line method can not only solve the mechanical analysis problem of any rod-like structural member or structural system, but also obtain the same precision solution when the properties of the problem are consistent with the premise of the traditional beam theory. The calculation results also prove the rationality of the unified analysis and the correctness of the finite nodal method. The main work of this paper is as follows: 1. The history of beam development and the significance of this paper are discussed. 2 the concept of unified analysis beam and finite nodal line method is introduced, and according to the principle of minimum potential energy, The ordinary differential equations under static force and their corresponding boundary conditions are derived. The application of unified analysis beam and finite nodal line method to solid members in solid mechanics is discussed. The results are compared with that of Euler beam and Saint Venant beam under free torsion respectively in traditional beam theory. An example of unified analysis of non-circular asymmetric thick wall section is given. 4. The application of unified analysis beam and finite node line method in torsional restrained thin-walled member is discussed, which is compared with Vlasov beam and Umansky beam, respectively. The unified analysis of thin-walled members with semi-open and semi-closed section is given. 5. The problems to be overcome in solving more extensive engineering problems are pointed out.
【学位授予单位】：河南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU323
本文编号：2197980
[Abstract]:In this paper, a new beam model-unified analysis beam and a new numerical analysis method-finite nodal line method are proposed for rod-like engineering structural members and structural systems. The unified analytical beam and finite nodal line method can not only solve the mechanical analysis problem of any rod-like structural member or structural system, but also obtain the same precision solution when the properties of the problem are consistent with the premise of the traditional beam theory. The calculation results also prove the rationality of the unified analysis and the correctness of the finite nodal method. The main work of this paper is as follows: 1. The history of beam development and the significance of this paper are discussed. 2 the concept of unified analysis beam and finite nodal line method is introduced, and according to the principle of minimum potential energy, The ordinary differential equations under static force and their corresponding boundary conditions are derived. The application of unified analysis beam and finite nodal line method to solid members in solid mechanics is discussed. The results are compared with that of Euler beam and Saint Venant beam under free torsion respectively in traditional beam theory. An example of unified analysis of non-circular asymmetric thick wall section is given. 4. The application of unified analysis beam and finite node line method in torsional restrained thin-walled member is discussed, which is compared with Vlasov beam and Umansky beam, respectively. The unified analysis of thin-walled members with semi-open and semi-closed section is given. 5. The problems to be overcome in solving more extensive engineering problems are pointed out.
【学位授予单位】：河南理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU323
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