Cameron Talischi

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Nonlinear elastic materials are of great engineering interest, but challenging to model with standard finite elements. The challenges arise because nonlinear elastic materials are characterized by non-convex storedenergy functions as a result of their ability to undergo large reversible deformations, are incompressible or nearly incompressible, and often(More)
We explore the recently-proposed Virtual Element Method (VEM) for the numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the linear elasticity equations in three-dimensions and elaborate upon the key concepts underlying the first-order VEM. While the point of departure is a conforming Galerkin(More)
Traditionally, standard Lagrangian-type finite elements, such as quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these elements exhibit the well-known "checkerboard" pathology in the solution of topology optimization problems. A feasible alternative to eliminate this(More)
1. Abstract Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. In general, finite element meshes with these elements exhibit the well-known checkerboard pathology in the iterative solution of topology optimization problems. Voronoi and(More)
We present a Matlab implementation of topology optimization for fluid flow problems in the educational code PolyTop (Talischi et al. 2012b). The underlying formulation is the well-established porosity approach of Borrvall and Petersson (2003), wherein a dissipative term is introduced to impede the flow in the solid (non-fluid) regions. Polygonal finite(More)
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