【作者】 陈逵；

【导师】 沈蒲生；

【作者基本信息】 湖南大学 ， 结构工程， 2005， 硕士

【摘要】 结构分析是工程结构设计的关键环节,无论是精确的数学解析方法还是传统有限单元法,都存在缺陷。前者求解的弹性力学问题很有限;后者通用性较好,但场函数难于构造,计算量大,而且材料非线性分析塑性阶段,往往难以得到稳定的结果。为此,本文从桁架结构出发,基于位移等效原则和有限元基本思想,构造了一种新的单元模型——等效平面桁架单元(矩形单元和三角形单元),在满足工程精度下,寻求到一种更简单实用的近似计算方法来解决复杂的二维问题。同时,将本单元应用于钢筋混凝土一般构件和转换结构的线性有限元分析及钢筋混凝土的非线性分析中。大量算例证实本文方法的正确可行,可供工程应用结构分析参考。 1.针对平面应力问题,构造了等效矩形平面桁架单元,将较复杂的二维问题一维化。在结点荷载作用下等效矩形桁架结构模型内只有二力杆单元,单元受力、变形简单清晰,易于计算、观察和判断,并能满足工程精度要求。 2.对于边界不规则的结构情况构造了对边界形状适应性较好的三角形单元,推导了单元截面的计算公式。 3.编制了平面应力问题等效平面桁架单元有限元法分析计算机程序。用所编制的计算机程序对悬臂梁、简支梁等一般构件进行计算分析,并将其计算结果与一般有限元法计算结果进行比较,发现二者基本吻合。 4.将构造的等效平面桁架单元用于结构的静力线性分析中。分析了一个十一层托柱形梁式转换结构和一个十层的框架剪力墙结构。计算出采用本文单元时转换梁及剪力墙的应力、挠度、结构位移、结构层间位移角。并将结果与四结点有限元计算结果比较,发现两者基本吻合。 5.将本文提出的单元用于钢筋混凝土的非线性分析中。提出了等效平面桁架单元模型的破坏准则及其裂缝模式。该模型中,钢筋混凝土结构被离散为等效混凝土单元和钢筋单元,混凝土单元采用等效铰结平面桁架单元,钢筋单元采用一维杆单元,直接利用混凝土的单向应力应变关系对结构进行弹塑性分析。因此,简化了分析方法,提高了非线性分析的效率,解决了传统弹塑性单元难以处理裂缝的问题。运用本文方法,借助通用有限元分析软件ANSYS7.0,对钢筋混凝土简支梁材料非线性分析,并将计算结果与实验数据进行比较,发现二者差别很小。更多还原

【Abstract】 Structural analysis plays a key role in the engineering design. Both analytic method in mathematics and traditional finite element method (FEM) have defects. The former can only resolve limited elasticity problems, while the latter can be used in much available situations. But it is more difficult to build displacement interpolating function and process huge data in FEM, the analysis results are always unstable in plasticity phase of material nonlinear. Aiming at plane stress problem, based on the fundamental of equivalent displacement in two structures with the same load and restrictions and the thought of FEM, a kind of novelelement------equivalent plane truss element(rectangle element and triangleelement) is constructed in this paper. The approximate calculation method realizes a simple and utilitarian solution to complicated two-dimension problems under tantamount precision. Further, this kind of element is applied in linear and nonlinear analysis of reinforced concrete(RC) structure and the equivalent plane truss element model of RC structure is proposed in the paper. Abundant examples prove that the method is applicable which can be referenced by in engineering.Firstly, focusing on plane stress problems, a kind of equivalent rectangle plane truss element is constructed in this paper, which converts complex two-dimension problems to one dimension problems. There are only axial force link elements in the new model under nodal loads, thus the internal force and deformation of elements becomes simple and explicit to be calculated and judged easily. Furthermore, it can meet the requirements of engineering precision.Secondly, in order to mesh various geometries and transitions, a kind of equivalent triangle plane truss element is constructed also.Thirdly, the equivalent plane truss element analysis program of plane stress problem is worked out, by which cantilever beam, simple beam and vertical structure are analyzed. The calculation results and other results of traditional FEM are consistent.Forthly, the transfer structure in High-Rise building and the frame-shell wall structure are analysised with the new elements in this paper. The linear analysis to a example of 12 floors with transfer beams and 10 frame-shell wall floors are worked. The results of stress and displacement have less differents with the results of 4-node shell elements. An wreck rules of equivalent plain truss element model更多还原