【作者】 向红；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 固体力学， 2007， 博士

【摘要】 本论文以杆、板和蜂窝结构为研究对象,综合考虑了材料粘弹性、损伤、几何非线性、初始挠度等因素,系统地研究了杆、板和蜂窝材料结构的蠕变屈曲与后屈曲行为。其研究成果不仅具有重要的理论价值,也具有非常重要的工程应用意义。本论文的主要研究工作如下;基于粘弹性理论、压杆稳定理论,针对压杆的工程实际情况,研究了具初始挠度、两端弹性支承、偏心加载压杆的弹性屈曲与蠕变延迟失稳行为,分析了弹性约束系数的实验确定方法。提出了一种分析蠕变屈曲的半解析方法,该方法可得出每一时间步中压杆的挠度与截面应力,且精度可以控制。利用本文提出的半解析方法,分析了夹层模型的精度及影响因素,为夹层模型的工程应用提供了理论依据。采用Karchanov损伤理论,考虑拉压应力对损伤的不同贡献,分析了损伤对粘弹性压杆蠕变屈曲的影响。分别采用线粘弹性和非线性稳态Norton蠕变本构关系,对比研究了在小挠度和考虑几何非线性的两种情况下,具初始缺陷压杆的蠕变屈曲失效时间,分析了初始挠度,载荷与材料参数对压杆蠕变屈曲失效时间的影响,得到了压杆小挠度理论的适应条件。基于损伤力学和Von Karman非线性板理论,建立了在横向和轴向载荷共同作用下考虑蠕变损伤效应的矩形板的非线性控制平衡方程,考虑了拉压应力对损伤演化的不同贡献,采用数值积分方法计算了横截面上的合力和力偶,然后应用迭代法对题进行求解。算例中,讨论了损伤效应、几何非线性、横向载荷、轴向载荷、等效应力等因素对板蠕变后屈曲过程的影响。基于代数不变量和不可逆热力学理论,建立了正交各向异性材料的损伤本构关系及损伤演化方程,研究了具损伤各向异性矩形板的后屈曲问题。基于压弯耦合梁柱稳定理论,分析了在面内双向荷载作用下不规则蜂窝材料的弹性屈曲行为,得到了不规则形状和不等壁厚蜂窝材料的两种屈曲模式的转换条件,以及两种屈曲模式下临界条件的解析表达式。分析了壁厚、倾斜壁与水平方向夹角、孔壁长度等因素对两种临界屈曲载荷的影响,并采用ANSYS商业软件对理论分析结果进行了验证。采用Norton蠕变理论和自由能守恒原理,分析了一般蜂窝结构在面内单向和双向载荷作用下的蠕变屈曲问题,得到了蠕变屈曲失效时间的通用解析表达式,分析了载荷、壁厚、倾斜壁与水平方向夹角、孔壁长度等因素对蜂窝材料结构蠕变屈曲失效时间的影响,得到了双向加载蜂窝材料结构以第一种模式屈曲的条件。本文的研究成果有助于从理论上深入了解杆、板及蜂窝与泡沫材料结构在蠕变条件下的力学本质特征,可为粘弹性杆、板与蜂窝材料结构的安全寿命评估与极限载荷设计等提供理论基础和依据。更多还原

【Abstract】 In this dissertation, the synthetical influences of viscoelasticity, geometric nonlinearity and initial deflection on the creep buckling and post-buckling of columns, plates and honeycombs are investigated systematically. The results are of great importance not only in the corresponding academic theories but also in the practical engineering. The main contents and results of this dissertation include as follows:Based on the linear stability theory, the creep buckling of the viscoelastic columns with initial deflection, torsional elastic restraint and eccentricity load is analyzed. Consequently, the instantaneous critical load, the creep buckling life and the torsional elastic restraint coefficient are determined. Additionally, a semi-analytical method for creep buckling of columns is presented to analyze the creep buckling of a compressed column with initial imperfection, of which the accuracy can be controlled easily. By the present semi-analytical method, the deflection of column and the stresses of section in every time step can be obtained. And the results are comparable to that of sandwich model. By employing Kachanov’s damage theory, in which the tension and compression have different contribution to the damage rate of the material, the influence of damage on creep buckling of viscoelastic column is analyzed.According to the linear viscoelastic theory and Norton’s power law creep constitutive equation respectively, the failure life for creep-buckling of column with initial deflection is determined. And the results corresponding to the geometrical linearity and nonlinearity are compared with each other. The influences of initial deflection, compressive load and material parameter on the failure time for creep-buckling of column are investigated in detail. And the range of application of geometrical linear theory for the creep-buckling of column is discussed.On the basis of Kachanov’s continuum damage theory and Von Karman’s nonlinear theory of plates, the nonlinear equilibrium equations of plate subjected to in-plane and lateral loads are established including creep damage effect. In the Kachanov’s damage evolution equation, tension and compression are assumed to have different contribution to the damage rate. With the stresses, forces and moments of the section of the plate calculated from numerical integral, the nonlinear equilibrium equations are solved by iterative method. The influences of several parameters, such as geometric nonlinearity, in-plane and lateral load, damage, as well as equivalent stress etc., on the creep post-buckling process are discussed. An orthotropic constitutive relationship and damage evolution equations of orthotropic material are derived by employing the algebra invariant theory and irreversible thermodynamics theory. The post-buckling of plate with orthotropic material is researched bade on the above damage constitutive and evolution equations.Employing the compression-bending coupling stability theory of beam-column, the elastic buckling behavior of general honeycombs subject to in-plane biaxial loading are analyzed, the critical loading expressions of two different buckling-morphologies are derived under different loading cases. The influences of the cell-edge thickness, cell angle, cell length and material properties of honeycombs on critical load are discussed. The analytical solution shows a good agreement with the numerical results obtained from the ANSYS commercial finite element program.Based on Norton’s power law creep theory and the principle of free energy conservation, the creep-buckling behavior of general honeycombs subjected to in-plane uniaxial and biaxial loading are investigated respectively. The relation of the stresses and the failure time for creep-buckling is derived. The effects of the loads, cell-edge thickness, cell angle, cell length and initial imperfection of honeycombs on the response curves of the critical loading and failure time for creep-buckling are discussed.The research results in this dissertation will be helpful to understanding the behaviors of creep-buckling of columns, plates, honeycombs. The results provide the theoretical basis for safe life assessment and design of limit load for viscoelastic columns, plates and honeycombs.更多还原