【作者】 彭凡；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 固体力学， 2005， 博士

【摘要】 本学位论文较为系统地研究了粘弹性层合板壳结构的非线性静、动力稳定性力学行为,主要研究工作如下。 基于Timoshenko-Mindlin剪切变形理论和小挠度假设,导出粘弹性层合板和层合圆柱壳的压曲方程,并利用Laplace变换,得到相空间的临界荷载,由Laplace逆变换的初、终值定理,获得层合板和层合圆柱壳的瞬时临界荷载与持久临界荷载,由此证明了持久临界荷载的粘弹性解法与准弹性解法的一致性。通过对瞬时临界荷载与持久临界荷载的分析,以硼纤维环氧树脂基复合材料为例,揭示了粘弹性层合板和层合圆柱壳在蠕变荷载下的延迟失稳机制。对完善层合板建立了扰动模型,给出了持久临界荷载含义的一种新的力学解释,且通过定义临界荷载与临界时间,对粘弹性结构延迟失稳的力学含义进行了分析与讨论。 设材料服从Boltzmann积分型本构关系,其松弛模量由Prony-Dirichlet级数描述,分别基于小挠度和几何非线性理论,从参数振动的角度研究了线粘弹性板壳的动力稳定性。根据谐波平衡法与增量谐波平衡法,建立了分析粘弹性板壳动力不稳定区域的一般性方法。结合材料的动态粘弹性力学性质,综合分析了粘弹性结构的线性与非线性动力稳定性特征;讨论了材料的粘性参数、结构的振动频率对主要动力不稳定区域的缩小以及下移的影响。提出了谐波平衡法与增量谐波平衡法应用的简化途径以简化求解过程,且验证了这一简化途径的有效性。基于Kirchhoff薄板理论与浅壳理论,应用简化途径,分析了粘弹性层合板和层合圆柱壳的动力稳定性。 基于Timoshenko—Mindlin剪切变形理论和Donnel-Karman几何非线性理论,用准弹性法研究了轴向受压粘弹性正交层合圆柱曲板的蠕变“跳跃”屈曲,针对两种各向异性程度差别较大的硼纤维/环氧树脂和玻璃纤维/环氧树脂复合材料,分析了横向剪切变形效应对粘弹性层合圆柱曲板蠕变屈曲行为的影响。进一步利用Schapery的耦合基体开裂损伤的粘弹性本构关系,研究了具基体开裂损伤的粘弹性正交铺设层合圆柱曲板的蠕变“跳跃”屈曲,分析了基体开裂损伤对两种材料层合圆柱曲板蠕变屈曲行为的影响。 研究了对称角铺设粘弹性层合圆柱壳在均匀轴向压力作用下的非线性蠕变分叉屈曲问题。基于薄壳理论和Donnel-Karman几何非线性理论,利用Schapery的耦合基体开裂损伤的粘弹性本构关系,并假设分叉屈曲时,材料呈现瞬时弹性性质,建立了考虑轴对称初始几何缺陷和耦合基体开裂损伤的粘弹性层合圆柱壳的前屈曲.变形以及蠕变分叉屈曲的控制方程;构造了相应的数值分析方法,利用差更多还原

【Abstract】 The mechanical behavior of nonlinear static and dynamic stability for viscoelastic composite laminated plates and cylindrical shells is systematically investigated in the dissertation. The main research contents and results are given as follow.Based on Timoshenko-Mindlin shear deformation theory and small deflection hypothesis, the creep buckling for viscoelastic laminated plates and cylindrical shells are analyzed. Laplace Transformation is employed to the governing equation to derive the critic loads in the phase space, and extremum theorems of Laplace Inversion Transformation is then used to acquire the instantaneous critic loads and durable critic loads. It is verified that the results of two types of critic loads, obtained by viscoelastic approach and quasi-elastic approach respectively, are identical. By the investigation of instantaneous critic loads and durable critic loads, the mechanism of creep buckling of boron fiber/epoxy matrix laminated plates and boron fiber/epoxy matrix cylindrical shells exhibiting viscoelastic behavior is revealed. In the case of perfect laminated plates and shells, a disturbance model is constructed to exploit the new mechanics signification for durable critic loads, and to explain the phenomena of delay loss of stability according to the time-dependent evolution of deflection.In the analysis of dynamic stability of viscoelastic plates and shells within the geometrically linear and nonlinear theory, the Boltzmann hereditary constitutive relationship is used to model the viscoelastic behavior and relaxation modulus is characterized with Prony-Dirichlet series. A general approach to determine the boundaries of unstable regions is presented by employing harmonic balance method and incremental harmonic method corresponding to linear and nonlinear dynamic stability. The general features of dynamic stability, including the shrink and downward shift of dynamic unstable region, are examined for plate and shell structures by taking into account of material viscoelastic property. To simplify the analysis procedure, a approximate approach for the application of both harmonic balance method and incremental harmonic method is proposed, and the validity of this method is examined. Based on the thin plat and shallow shell theory respectively, the linear dynamic stability of vicoelastic laminated plates and cylindrical shells is analyzed by using this approximate approach.The quasi-elastic approach is employed to investigate the behavior ofsnap-through creep buckling of viscoelastic cross-ply cylindrical panels, with the nonliear governing equations obtained within both Timenshenko-Mindlin shear deformation theory and Donnel-Karman geometrically nonlinear relationship. Effects of transverse shear deformation on the critic time of snap-through creep buckling is examined with respect to both boron fiber /epoxy matrix laminated cylindrical panels and glass fiber/epoxy matrix laminated cylindrical panels, which exhibit obvious difference on anisotropic property. By using Schapery’s viscoelastic constitutive equations coupling matrix cracking damage, the analysis of snap-through creep buckling for viscoelastic cross-ply cylindrical panels containing transverse matrix cracking is performed, also the effects of damage on the behavior of time-dependent delay loss of stability is examined corresponding to two types of materials mentioned above.The creep bifurcation buckling of viscoelastic symmetric angle-ply cylindrical shells subjected to axial compression is analyzed. Based on thin shallow shell theory and Donnel-Karman geometrically nonlinear relationship as well as Schapery’s viscoelastic constitutive equations coupling matrix cracking damage, the governing equations for pre-buckling creep deformation and bifurcation buckling are obtained according to the assumption of instantaneous elasticity occurred during the bifurcation. Combining the discretization of space variable by finite difference with Taylor’s numerical integration of convolution integral, the pre-buckling creep deformation is analyzed. By taking the separate expression of unknown functions with respect to axial and circumferential space variables, and employing the technique of finite difference, A semi-analytic solution strategy is performed to solve the governing equations of bifurcation buckling with incremental forms. Critic time of bifurcation buckling is determined by the change of sign of characteristic determinant. The effect on the behavior of bifurcation creep buckling, exerted by boundary conditions > matrix cracking evolution and the magnitude of axisymmetric imperfection as well as the ration of radius to thickness, is examined.更多还原