Hemivariational Inequalities: Applications in Mechanics and Engineering
Hemivariational Inequalities: Applications in Mechanics and Engineering
复制标题
DOI：
--
复制
发表时间：
1993-10
期刊：
影响因子：
--
通讯作者：
P. Panagiotopoulos
中科院分区：
文献类型：
--
作者：
P. Panagiotopoulos
本文的目的是制定，数学研究和数值处理的静态和动态问题，在机械和工程科学涉及非凸和非光滑的能量函数，或非单调和多值应力应变法。这样的问题导致一种新的类型的变分形式，半变分不等式，这也导致多值微分或积分方程。提出了用于处理现实工程问题的创新数值方法。文本涉及变分理论的工程问题，涉及非单调多值关系，其机械基础，其数学研究（存在性和某些近似结果）和相应的特征值和最优控制问题。所有的数值应用都为尚未解决或部分解决的工程问题提供了创新性的答案，如裂缝中的粘结接触，分层问题，复合材料中的非线性应力应变规律，复合梁中的剪力连接件，钢结构中的半刚性连接，机器人中的粘结抓取，等书关闭考虑hemivarianation不平等的分形型几何和神经网络方法的数值处理hemivarianation不平等。
The aim of this text is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanical and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treatment of realistic engineering problems. The text deals with the variational theory of engineering problems involving nonmonotone multivalue relations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, such as the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with a consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.