基于区段混合能的位移有限元法研究及其应用

发布时间：2018-01-12 02:25

本文关键词：基于区段混合能的位移有限元法研究及其应用　出处：《河北工程大学》2017年硕士论文　论文类型：学位论文

【摘要】：现行的双、多重抗侧力结构体系研究中,通常对框架只考虑其剪切变形,对剪力墙(或支撑、筒体)仅考虑其弯曲变形的影响,各层楼板将两者连接起来,它仅传递水平力并且使得受弯和受剪两部分变形协调。而实际工程中广泛采用的框架一剪力墙结构体系、框架一核芯筒结构体系等多种双重抗侧力体系中的剪力墙结构、筒体结构与普通实腹式构件不同,通常采用空腹式、格构式,在水平荷载作用下发生侧向变形,其自身的剪切变形所占总的变形的比例是很大的,对于某些钢桁架、支撑框架,甚至剪切变形的比例大于弯曲变形。如此看来,对这样的结构体系,传统结构理论的简化会造成一定的误差。本文同时考虑弯曲变形和剪切变形,将双、多重抗侧力结构体系的所有子结构等效为弯剪型结构,在刚性楼板假定下,分别采用了楼板、连梁及框架对抗侧力结构的作用沿结构高度连续化和非连续化的简化模型,对双、多重抗侧力结构体系协同分析进行了深入的研究。首先从建筑结构的总势能出发,写出其拉格朗日函数,导入哈密顿函数,引入区段混合能,利用精细积分法求解区段混合能矩阵,然后由混合能矩阵推导出结构的单元刚度矩阵和等效节点荷载列阵,由位移有限元集成整体刚度矩阵,最后引入边界条件,转为位移法用一维有限元法求解,通过计算步骤编制MATLAB程序,得到多重抗侧力结构体系的侧移和内力。本文结合了4个多重抗侧力结构协同分析的实例对结构的侧移和内力沿高度变化情况进行了分析,并与相关文献方法得到结果进行了对比分析,结果表明本论文算法适用性较强,计算简单,精度高,不仅适用于多重抗侧力结构体系的协同分析,而且还对于变截面的多重抗侧力结构体系的协同分析同样适用,可方便应用于多重抗侧力结构高层建筑的计算。
[Abstract]:In the current research of double and multiple resisting lateral force structure system, the shear deformation of frame is usually considered only, and the influence of bending deformation on shear wall (or bracing, tube body) is only considered, and each floor connects the two. It only transfers horizontal force and makes both bending and shear deformation coordinate. However, the frame-shear wall structure system is widely used in practical engineering. The shear wall structure in the frame-core-tube structure system and other dual lateral force resistant systems is different from the common full-web structure, usually using the empty stomach and lattice structure, under the action of horizontal load, lateral deformation occurs. The ratio of shear deformation to total deformation is very large for some steel trusses, braced frames, and even shear deformation is larger than bending deformation. The simplification of traditional structural theory will lead to certain errors. In this paper, the bending deformation and shear deformation are considered at the same time, and all substructures of double and multiple resisting lateral force structures are equivalent to flexural shear structures under the assumption of rigid floor. The simplified models of high continuity and discontinuity of the action of floor slab, connecting beam and frame against lateral force structure along the structure are adopted, respectively. Based on the total potential energy of the building structure, the Lagrangian function is written out, the Hamiltonian function is introduced, and the section mixing energy is introduced. Then the element stiffness matrix and equivalent node load matrix of the structure are derived from the mixed energy matrix, and the integral stiffness matrix is integrated by the displacement finite element method. Finally, the boundary condition is introduced, and the displacement method is used to solve the problem by one-dimensional finite element method. The MATLAB program is compiled through the calculation steps. The lateral displacement and internal force of the multi-counteracting lateral force structure system are obtained. In this paper, the lateral displacement and internal force along the height of the structure are analyzed with four examples of cooperative analysis of the multi-anti-lateral force structure. The results are compared with the results obtained from the related literature. The results show that the algorithm is applicable, simple and accurate, and it is not only suitable for the collaborative analysis of multi-anti-lateral force structure system. It is also applicable to the cooperative analysis of multi-lateral force resistant structures with variable cross-sections, and can be applied to the calculation of high-rise buildings with multi-lateral force resistance structures.
【学位授予单位】：河北工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU311

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