报告主题：高阶与表面弹性力学理论及其在小尺度领域的应用

报告时间：5月12日（本周四）下午2点

报告地点：18新利体育 北校区工科楼1108（机器人与微系统研究中心会议室）

报告人简介：

Xin-Lin Gao，美国南卫理公会大学机械工程系教授，1998年在威斯康辛-麦迪逊大学获得机械工程博士学位，曾任教于德克萨斯大学、德州农机大学、密西根技术大学，同时是巴黎东大学和华东理工大学客座教授，发表期刊论文109篇，2011年当选美国机械工程师学会会士，2014年入选上海市人才计划。

Higher-Order and Surface Elasticity Theories and

Their Applications at Small Length Scales

Xin-Lin Gao

Bobby B. Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA

ABSTRACT

Classical elasticity cannot interpret microstructure and/or surface energy dependent size effects observed in numerous experiments at the micron and nanometer scales. Higher-order and surface elasticity theories contain additional material parameters and are capable of explaining these size effects. Two high-order elasticity theories and one surface elasticity theory along with their applications in solving beam, plate, and shell problems exhibiting size effects will be discussed in this seminar.

One higher-order elasticity theory is a modified couple stress elasticity theory, which involves two Lamé’s constants and one material length scale parameter. By applying this theory and Hamilton’s principle, a non-classical third-order shear deformation plate model is developed, which captures size effects and recovers the classical Mindlin and Kirchhoff plate models as special cases.

The other is a simplified strain gradient elasticity theory that contains one length scale parameter in addition to the two classical elastic constants. As a direct application of the theory, an analytical solution for the pressurized thick-walled cylindrical shell problem is obtained, which reduces to Lamé’s classical solution when the strain gradient effect is not considered.

The surface elasticity theory is that of Gurtin and Murdoch, which contains three surface elastic constants. Based on this theory and the modified couple stress theory, a new Bernoulli-Euler (B-E) beam model is developed using a variational formulation, which reduces to the classical B-E beam model when the microstructure-dependence, surface energy, and Poisson’s effect are all suppressed.

Biographical Sketch

Dr. Xin-Lin Gao is currently a professor of mechanical engineering and the mechanics and manufacturing area director at Southern Methodist University located in Dallas, Texas. His other experience includes teaching at University of Texas-Dallas for 3 years, at Texas A&M University for 7 years, and at Michigan Technological University for 4 years. In addition, he was a visiting professor at University of Paris-East and has been a visiting chair professor at East China University of Science and Technology in Shanghai since September 2010. He received an M.Sc. degree in Engineering Mechanics in May 1997 and a Ph.D. degree in Mechanical Engineering (with a minor in Mathematics) in May 1998, both from the University of Wisconsin-Madison. He has conducted research in a variety of areas in mechanics and materials and has authored 109 journal papers, 2 book chapters, and 126 conference and other publications. He has been a PI or Co-PI of funded research projects worth about $9.6M. He has been a reviewer for 105 journals, 9 publishers and 14 funding organizations and has organized 25 symposia at major international technical conferences. He has been an editor/guest editor of one book, proceedings of one conference, and four special journal issues. He currently serves on the editorial boards of seven journals. He was elected an ASME Fellow in January 2011. He was selected as an expert by the Shanghai Thousand Talents Program in June 2014.