An enhanced corotational Virtual Element Method for large displacements in plane elasticity

Abstract

An enhanced virtual element formulation for large displacement analyses is presented. Relying on the corotational approach, the nonlinear geometric effects are introduced by assuming nodal large displacements but small strains in the element. The element deformable behavior is analyzed with reference to the local system, corotating with the element during its motion. Then, the large displacement-induced nonlinearity is accounted for through the transformation matrices relating the local and global quantities. At the local level, the Virtual Element Method is adopted, proposing an enhanced procedure for strain interpolation within the element. The reliability of the proposed approach is explored through several benchmark tests by comparing the results with those evaluated by standard virtual elements, finite element formulations, and analytical solutions. The results prove that: (i) the corotational formulation can be efficiently used within the virtual element framework to account for geometric nonlinearity in the presence of large displacements and small strains; (ii) the adoption of enhanced polynomial approximation for the strain field in the virtual element avoids, in many cases, the need for ad-hoc stabilization procedures also in the nonlinear geometric framework.