The virtual element method has been developed over the last decade and applied to
problems in solid mechanics. Different formulations have been used regarding the order of …

In this paper, a hybrid variational framework for the Virtual Element Method (VEM) is
proposed and a family of polygonal elements for plane elasticity is developed. Under …

A plasticity formulation for the Hybrid Virtual Element Method (HVEM) is presented. The
main features include the use of an energy norm for the VE projection, a high-order …

This paper develops a family of new weak Galerkin (WG) finite element methods (FEMs) for
solving linear elasticity in the primal formulation. For a convex quadrilateral mesh, degree …

This article revolves around shape and topology optimization, in the applicative context
where the objective and constraint functionals depend on the solution to a physical …

We develop a lowest-order nonconforming virtual element method for planar linear elasticity,
which can be viewed as an extension of the idea in Falk (1991) to the virtual element …

One of the first applications of virtual elements in engineering was related to elasticity. It had
the aim to construct a general methodology that could be applied to problems involving two …

We discuss the design and implementation details of two conforming virtual element
methods for the numerical approximation of two partial differential equations that emerge in …

This paper devises a novel lowest-order conforming virtual element method (VEM) for planar
linear elasticity with the pure displacement/traction boundary condition. The main trick is to …

Discrete approaches to mechanics and physics of solids Page 1 Discrete approaches to
mechanics and physics of solids A thesis submitted to the University of Manchester for the …