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On the Use of Variational Inequalities in Dynamic Computational Contact Mechanics

日時:2013年11月13日(水)13:00から14:30
場所:工学研究科2号館 232講義室
講師:Prof. Shaker Meguid (Director of Mechanics and Aerospace Design Laboratory, University of Toronto)

概要:
Dynamic contact plays an important role in dictating the integrity, performance and safety of many engineering systems/components. Despite their importance to the mechanical integrity of the systems examined, dynamic contact effects are frequently treated using oversimplifying assumptions, which neglect the main features of the problem. The reason is that modeling dynamic contact in solids poses mathematical and computational difficulties. With the application of loads to the bodies in contact, the actual surface on which these bodies meet, change with time, and the stresses at the surfaces are generally unknown and complex to determine.
Analytical closed form solutions for contact problems were developed by Hertz in 1882. Hertz classical theory of contact was developed for elastic quasi-static frictionless bodies with the contact region being small compared with the dimensions of the contacting bodies. In spite of the fact that Hertz's theory of contact bas stood the test of time and has been a landmark in applied mechanics for many decades, it suffers from the above- mentioned severe restrictions.
In this lecture, we will develop the formulations for dynamic contact using variational inequality. Three aspects of the work are examined to overcome existing contact challenges; these include:
(i) the development of the appropriate dynamic variational inequalities expressions to accurately and consistently represent dynamic contact problems,
(ii) the development of robust solution algorithms that guarantee the accurate imposition of the kinematic contact constraint and avoid interpenetration of the mating bodies, and
(iii) evaluate the integrity of realistic design problems using the newly developed variational inequalities algorithms.
The design problems include aeroengine compressor disc assembly, shot-peening, crush of thin walled tubular columns and finger implants.

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