Numerical Analysis and Scientific Computing Seminar | Diane Guignard, Discontinuous Galerkin method for large deformations of plates

MC 5501 and Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link) 

Speaker

Diane Guignard, Assistant Professor, University of Ottawa, Department of Mathematics and Statistics

Title

Discontinuous Galerkin method for large deformations of plates

Abstract

We study the elastic behavior of prestrained and bilayer thin plates which can undergo large deformations and achieve non-trivial equilibrium shapes even without external forces or prescribed boundary conditions. These phenomena can be observed in nature or be manufactured. Being able to simulate the deformation of such plates can be benecial for many engineering applications, for instance to develop micro-mechanical devices or to design climate-responsive architecture. We are mainly interested in the bending regime, namely when the three-dimensional hyper-elastic energy scales like the third power of the thickness of the plate. From a mathematical point of view, the dimensionally reduced problem consists of a fourth order minimization problem subject to a nonlinear and nonconvex metric constraint.

In this talk, we introduce a numerical method based on a discontinuous Galerkin finite element method for the space discretization and a discrete gradient flow for the energy minimization. We discuss the properties of the method and present numerical experiments showcasing the large variety of shapes that can be achieved.