考虑损伤效应的粘弹性复合材料板的非线性静、动力学分析

【作者】 李平恩；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 固体力学， 2003， 硕士

【摘要】 综合考虑损伤、粘弹性和几何非线性效应，对复合材料结构的非线性静、动力学行为进行分析，将更接近复合材料及其结构的实际状况，更深入地揭示其力学性能的本质特征。目前，这方面的研究成果还相当少。主要原因在于：粘弹性复合材料损伤本构关系的建立一般是很困难的；而且由于损伤变量的引入，控制方程数目相应增加且更加复杂；控制方程一般是积分—偏微分形式，由于损伤与应力和应变相互耦合，Galerkin方法不再适用，因此控制方程的求解相当困难。 本文对考虑损伤效应的复合材料粘弹性板进行了非线性静、动力学方面的研究，分析了损伤、粘弹性效应对结构非线性动力响应以及后屈曲行为的影响，同时，对求解该类问题的一般分析和求解方法进行了探讨。本文的主要研究内容和取得的主要研究成果为：采用KBM平均法分析了具微分型本构关系的粘弹性椭圆板的非线性动力响应问题，结果表明，粘弹性性质体现为阻尼作用；针对具积分型本构关系，且材料松弛模量为Prony级数形式的粘弹性结构的非线性动力学问题，结合Newmark方法和Newton-Cotes数值积分公式，提出了一种适于求解该类问题的有效数值方法，揭示了粘弹性结构所具有的丰富的非线性动力学行为；基于Schapery三维损伤本构关系，引入沈为基于试验的损伤演化规律和Kachanov损伤演化方程，建立了横向基体开裂的纤维单一方向铺设粘弹性板的损伤模型；对于积分-偏微分形式的控制方程组，综合应用差分法、Newmark方法、Newton-Cotes数值积分方法进行求解，获得了求解复杂非线性问题的有效方法；对受横向周期载荷作用下的纤维单一方向铺设粘弹性板，研究了损伤对其非线性动力响应行为的影响；对考虑损伤效应的具有初始挠度的纤维单一方向铺设粘弹性板的压屈问题，分析了损伤对其后屈曲行为的影响。研究表明，基体横向开裂导致结构刚度下降，挠度增加，但不会造成结构的整体失效。更多还原

【Abstract】 By considering the influence of damage, viscoelasticity and geometric nonlinearity synthetically, the actual state of composite material and structure can be described accurately and the essential character of the mechanics property can be revealed fully. In the present, the research achievement of this field is much few. The main reasons are as follows: (l)the establishment of the constitutive equations for the viscoelastic composite with damage is much difficulty. (2)the governing equations will increase and are complicated when damage variable is introduced. (3)generally, the governing equations are integral- partial differential equations, further more, because damage variable is coupling with stress and strain, Galerkin method is no longer suitable, it is quite difficult to solve the equations.In this paper, the nonlinear static and dynamic behavior of the composite viscoelastic plate with growing damage is investigated. The effects of damage and viscoelasticity on the nonlinear dynamic response and postbuckling character of the composite plate are analysed. At the same time, a general method for analysing and solving this type problem are studied. The main researching contents and results are as follows: The nonlinear dynamic response of viscoelastic elliptical plate with differential constitutive relation is investigated by applying KBM method, and the results show that viscoelasticity exhibits damping property in dynamic system. For the nonlinear dynamic problems of the viscoelastic structure, in which the constitutive relation is integral form and relaxed modulus are Prony series form, based on the Newmark method and Newton-Cotes numerical integration method, a new numerical approach is established, and by using this approach the abundant dynamic behaviors of viscoelastic structure are obtained. Based on Schapery three-dimensional viscoelastic constitutive with growing damage, through introducing Shenwei and Kachanov damage evolution equation, a damage model with matrix transverse cracks for the viscoelastic unidirectional laminated composite is established. By synthetically applying finite difference method, Newmark method and Newton-Cotes numerical integration formula, the integral- partial differential governing equations are solved. For the viscoelastic unidirectional laminatedcomposite under transverse periodic loading, the effects of damage on the nonlinear dynamic responses are investigated. For the viscoeiastic fibre reinforced unidirectional composite structure with initial deflection under compression load in plane, the effects of damage on the postbuckling behaviors are analysed. The research results indicate that transverse crack will cause a decrease of the structure’s rigidity and an increase of the deflection, but not lead to the whole structure’s failure.更多还原