力学系的学术报告 8月5日(报告人：Dr Liping Liu）
发布时间: 2010-07-21 02:51:00
SEMINAR SERIES
北京大学工学院 ![]()
力学与空天技术系
力学与空天技术系 湍流与复杂系统国家重点实验室
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题目：New extremal inclusions and their applications to two-phase composites
Dr Liping Liu
Department of Mechanical Engineering, University of Houston
Email: liuliping（at）uh.edu
Abstract: In this talk, I present a class of special inclusions that have the same property with respect to second order linear partial differential equations as holds for ellipsoids. That is, in the simplest case and in physical terms, constant magnetization of the inclusion implies constant magnetic field on the inclusion. The special inclusions are found as solutions of a simple variational inequality. This variational inequality allows us to prescribe the connectivity and periodicity properties of the inclusions. For example we find periodic arrays of inclusions in two and three dimensions for which constant magnetization of the inclusions implies constant magnetic field on the inclusions. The volume fraction of the inclusions can be any number between zero and one. We find such inclusions with any finite number of components and components that are multiply connected. These special inclusions enjoy many useful properties with respect to homogenization and energy minimization. For example, we use them to give new results on a) the effective properties of two-phase composites and b) optimal bounds and optimal structures for two-phase composites.
Brief CV:
Dr. Liping Liu received his Bachelor degree in Mechanics and Engineering Science of Peking University in 2000, received his Master degree and Ph.D. degree from University of Minnesota in 2003 and 2006, respectively. After that he worked at California Institute of Technology from 2006 to 2008 as a Postdoctoral Scholar. Now he works in University of Houston as Assistant Professor since 2008. His research focuses on Mechanics and Materials, such as Solid Mechanics, Elasticity and Fracture Mechanics, Applied Mathematics and Multiscale-Multiphysics Modelings. He got the best dissertation award of University of Minnesota. He has many publications in peer-reviewed journals including J. Mech. Phys.Solids, Archive for Rational Mechanics and Analysis, J. Appl. Phys, Mathematics and Mechanics of Solids, and Proc. Roy. Soc. A.
主持人：段慧玲 特聘研究员
时 间：8月5日（周四）上午10:00~11:30
地 点：力学楼434会议室
欢迎广大师生光临！