報告題目：Modeling Size Effects at Small Length Scales Using Higher-Order and Surface Elasticity Theories

報告人： Prof. Xin-Lin Gao（Bobby B. Lyle School of Engineering, Southern Methodist University, Dallas, TX, USA）

報告時間：2016年5月24日（周二）下午 5:00-6:00

報告地點：明故宮校區9号樓506會議室

主辦單位：國際合作交流處、科協、機械結構力學及控制國家重點實驗室、航空宇航學院

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 higher-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.

 

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. 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.