【作者】 张国清；

【导师】 余建星；

【作者基本信息】 天津大学 ， 结构工程， 2004， 博士

【摘要】 本文尝试利用非线性理论中的分岔、突变和混沌理论对一类扁壳结构进行非线性分析。在静载荷和变温共同作用的情况下,对扁壳结构进行了突变分析,并对Koiter过屈曲一般理论应用初等突变理论进行了研究。对在扰动载荷,静预加载和变温共同作用下的一类扁壳结构在理论上进行了混沌研究,并对若干种不同情况的实际例题进行了数值分析并研究了这些结构单元的动力学性质,给出了周期运动和混沌运动的时程曲线,相平面轨迹和Poincare映射。现将这些工作简述如下: 1.在本文第二章中,针对板壳结构屈曲临界载荷与实验结果存在较大差异这一历史话题,利用非线性理论中的初等突变理论及分岔概念研究了弹性结构过屈曲形态的Koiter一般理论的非线性性质,建立了该理论所具有的非线性动力系统。用突变形态解释结构后屈曲状态的非线性跳跃现象。本文提出,正是由于初始缺陷的存在使得那些对初始缺陷敏感的壳体的非线性动力系统的平衡态发生了全局性的改变,即由拆叠突变变成了类尖点突变,从而导至了另外一种平衡态。2.在本文第三章中,研究了静载荷和变温作用下一类扁壳结构的后屈曲问题。在Donnel-Kàrmán非线性方程组的基础上推导了新的方程组,并对这个方程组进行了求解,求得了相应的应力函数和非线性动力系统。利用本文的结果可以直接对扁壳结构的超临界变形问题进行了定量计算,从而确定结构在后屈曲阶段的应力状态。在此基础上,本文对双曲扁壳,闭合圆柱壳进行了突变分析,同时考虑了侧压和初始缺陷的影响。双曲扁壳的结果可以推广到矩形板,开口圆柱壳和方底扁球壳等情况。3.在固体力学领域内对混沌问题的研究大都局限于屈曲梁,并且大都归结为典型的Duffing方程。对于板壳问题中是否存在混沌运动则极少有人曾涉及,本文第四章以一类扁壳结构为对象进行了混沌运动方面的研究。在第三章的基础上,我们建立了这些壳体的非线性动力系统,对双曲扁壳、矩形板、开口圆柱壳和圆底扁球壳进行了理论分析。在分析中考虑了静力预加载,变温、初始缺陷和扰动载荷,并给出了新的非线性动力方程。更多还原

【Abstract】 The bifurcation and the elementary catastrophe theory and chaos theory have been employed to investigate some shells for the purpose of nonlinear analysis in this paper. The catastrophe analysis of shallow shells subjected to static pressure load and varying temperature is studied. The chaotic motion of shallow shells subjected to transverse periodic load and static load, varying temperature and initial defect of shells is investigated by Milnikov method and numerical analysis. We can introduce the beneficial study in this paper as follows: 1. The catastrophe analysis of Koiter general theoty of postbuckling problem has been completed in chapter2. 2. The postbuckling problem of shallow shells is studied in chapter3. This investigation is based on Donnel-Kàrmán eguations and a new nonlinear eguation is established, and the stress function and nonlinear dynamic system are carried out. In addition, the catastrophe analysis of shallow shells has been completed in chapter3. 3. The nonlinear dynamic system of double-curve shallow shells, plate, cylindrical shell and shallow spherical shell subjected to transverse periodic load and varying temperature are established in chapter4. The critical chaotic motion of cylindrical shell is given by Melnikov function, and the numerical analysis is carried out in chapter5, which contain rectangular plate, cylindrical shell and shallow spherical shell. The time-displacement history diagram and phase –plane diagram, chaos-bifurcation diagram and Poincare map are employed to determine the motion is chaotic or not. Using these theoretical and numerical methods, the chaotic motion of the nonlinear dynamic systems are investigated in this paper.更多还原