Events Calendar

Aerospace and Mechanical Engineering Seminar Series

Speaker: Xianyi Zeng, Postdoctoral Associate in the Department of Civil and Environmental Engineering at Duke University, Durham, NC

Talk Title: Multi-Robot Systems for Monitoring and Controlling Large Scale Environments A Variational Multiscale Finite Element Method for Nearly Incompressible Solids and Fluid-Structure Interactions

Series: Aerospace and Mechanical Engineering Seminar Series

Abstract: We present a new approach to stabilize the finite element methods for explicit transient solid mechanics in the nearly incompressible regime using linear simplicial finite elements, and present its extension to fluid-structure interactions. In these problems, triangular/tetrahedral elements are usually preferred because they allow efficient and automated mesh generation for complicated geometries. However, standard Galerkin formulation typically leads to volume locking or instability on these elements in the case of nearly incompressible solid dynamics.

To overcome these difficulties, we describe a stabilized method that is based on a mixed formulation, in which the usual momentum equation is complemented by a rate equation for the evolution of the pressure field. The stabilization term is derived using a variational multiscale approach for isotropic linear elastic materials, and it is shown to greatly improve the stability of the methods without decreasing the order of the accuracy. Next we extend the methodology to nonlinear elastic materials by properly linearizing the variational form, and then to viscoelastic materials by introducing internal variables. Extensive numerical results in these contexts are presented to assess the accuracy and stability properties of the proposed methods for general solid mechanics.

Finally, we describe a similar VMS-based finite element method for shock hydrodynamics, and conclude the presentation by coupling the two methods to perform challenging shock-solid interaction computations.

Biography: Xianyi Zeng obtained a BS in mathematics and applied mathematics from Peking University, and a PhD in computational and mathematical engineering from the Stanford University. Before joining the Civil and Environmental Engineering Department at Duke University as a postdoc, he worked on his dissertation in the Department of Aeronautics and Astronautics at Stanford University while pursuing the doctoral degree. Dr. Zeng has broad interests in computational mechanics and their applications, including computational gas dynamics, computational solid mechanics, fluid-structure interactions, and numerical modeling of inelastic materials, among others.

Host: Paul Ronney

Location: Seaver Science Library (SSL) - 150

Audiences: Everyone Is Invited

Contact: Valerie Childress