【作者】 李云翔；

【导师】 刘振海；

【作者基本信息】 中南大学 ， 应用数学， 2011， 博士

【摘要】 本文主要研究一类双曲型H-半变分不等式及其在粘弹性接触力学中的应用。第二章主要研究如下H-半变分不等式：这是一类双曲型H-半变分不等式,通过将它嵌入到一类二阶发展包含问题中,再利用多值算子的满射性结果证明了该H-半变分不等式的解的存在性。第三章研究了粘弹性压电体与基座间的动力学摩擦接触问题。其接触条件由通常的法向阻尼响应条件与摩擦定律来描述,接触条件是非单调的、有可能是多值的且具有Clarke次微分形式,因而导出的数学模型由关于位移的双曲型H-半变分不等式与关于电势的与时间有关的椭圆方程所组成。我们给出了该接触问题的解的存在性结果。第四章研究了变形体与基座间的静力学摩擦接触问题。我们假定变形体是粘弹性的,且具有长效记忆特性。接触面的接触条件由法向柔度条件来描述。法向应力与法向位移间具有Clarke次微分形式的非单调关系,而接触摩擦假定切向剪应力是切向位移的非单调多值函数。同时我们也考虑了材料的损伤。材料的损伤会降低物体的承载能力,从而使机械系统的功能与安全性受到很大影响。我们导出了该问题的变分公式,它由一个抛物方程与一个H-半变分不等式所构成。我们陈述并证明了其存在性与唯一性结果。更多还原

【Abstract】 The dissertation investigates a type of hyperbolic hemivariational inequality and its applications to viscoelastic contact mechanics.In chapter two, we investigate the following hemivariational inequality: This is a type of hyperbolic hemivariational inequality. We prove the existence result by embedding the problem into a class of second-order evolution inclusion and by applying a surjectivity result for multivalued operators.In chapter three, we investigate the dynamic frictional contact problem between a viscoelastic-piezoelectric body and a foundation. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. We state the existence result on the contact problem.In chapter four, we investigate the quasistatic process of frictional contact between a deformable body and a foundation. The body is assumed to be viscoelastic with long memory. The contact is modelled with a general normal compliance condition. The dependence of the the normal stress on the normal displacement is assumed to have nonmonotone character of the subdifferential form. We model the frictional contact assuming that the tangential shear on the contact surface is given as a nonmonotone and possibly multivalued function of the tangential displacement. We also consider the damage of the material. The effect due to the damage leads to decrease the carrying capacity of the body. The effective functioning and safety of a mechanical system may be deteriorated by this decrease as the material undergoes damaged. We derive the variational formulation of the problem, which is in the form of a system coupling a parabolic equation and a hemivariational inequality. We state and prove our main existence and uniqueness result.更多还原