Asynchronous variational integrators as a mechanical tool for dimensioning thin-shell structures

This is an interdisciplinary research project. This proposal presents research directions in the mechanics of thin-shell and rod theory by using the formalism of discrete mechanics applied to the study of structures in civil engineering. Its aims are to combine the domains of mathematics (Prof. Tudor Ratiu EPFL/DMA) and civil engineering (Prof. Yves Weinand EPFL/Ibois). The major objectives of this interdisciplinary group are the search and the development of a practical tool to study irregular surfaces. Thin shells have been a major subject of interest over the last four years at the Laboratory for timber constructions (IBOIS, Director Prof. Yves Weinand) at the EPFL. We use theory of AVIs (discrete mechanics) developped at Caltech by the team of J. Marsden and subdivision surfaces applied to irregular thin-shells in civil engineering to solve our problems. With these tools we shall study both dynamic and static phenomena conserving the symmetries of the problem. Moreover, the energy is conserved for nondissipative systems.