Homogenization techniques applied to structural analysis and tribology in extreme environment

The research group in applied mathematics with specialization in homogenization theory at Narvik University College (HiN) has recently started a very promising cooperation with the research institute Norut Narvik. We have found that there are many problem s where the fundamental understanding of the complex structures and tribological processes requires advanced mathematical modelling and analysis. In lubrication, for example, it is a challenging task to model the interaction between surface roughness and lubricant, in particular in cold environment. An other example, which is devoted to infrastructure, is the problem of modelling the dynamical behaviour of complex bridge structures in case of heavy wind load. We have found that modern homogenization tech niques developed in mathematics are extremely well suited for these purposes. We claim that the use of mathematical homogenization techniques in tribology and structural analysis is at an early stage of its development. Therefore we strongly believe that by combining the expertise in the fields structural analysis, tribology and mathematical modelling and analysis, we will be able to make a breakthrough in this interdisciplinary research field. In both institutions there are several researchers and stude nts who work with problems related to this interdisciplinary project. The main task will be to collaborate in order to develop the ideas described above and to expand our research field related to application to structural problems and industry. We also are convinced that this interdisciplinary project will make the computations more correct and cost-efficient that the methods used today by the engineers. An important part of the project, besides pure mathematical problems, will be to describe the mathe matical analysis in such a way that it will help engineers to understand how complex structures and surface roughness can be optimized from a structural, lubrication, friction and wear point of view.