In the present work we generalize curvilinear Virtual Element technology, introduced for a simple linear scalar problem in previous work, to generic 2D solid mechanic problems small deformations. Such generalization also includes development of novel space displacements that contains rigid body motions. Our approach can accept black-box (elastic or inelastic) constitutive algorithm and, addition, make use curved edges thus leading an exact approximation geometry. Rigorous theoretical...

The virtual element method (VEM) for curved edges with applications to contact mechanics is outlined within this work. VEM allows the use of non-matching meshes at interfaces advantage that these can be mapped a simple node-to-node formulation. To account exact approximation complex geometries interfaces, we developed technology considers edges. A number numerical examples illustrate robustness and accuracy discretization technique. results are very promising underline advantages new...

Abstract In this communication we propose a new exponential‐based integration algorithm for associative von‐Mises plasticity with linear isotropic and kinematic hardening, which follows the ones presented by authors in previous papers. first part of work develop theoretical analysis on numerical properties developed schemes and, particular, address yield consistency, exactness under proportional loading, accuracy stability methods. second contribution, show detailed comparison between method...

In this paper we present the frequency evaluation of spherical shells by means generalized differential quadrature method (G.D.Q.M.), an effective numerical procedure which pertains to class collocation methods. The shell theory used in study is a first-order shear deformation with transverse shearing deformations and rotatory inertia included. governing equations terms mid-surface displacements are obtained and, after expansion partial Fourier series circumferential coordinate, solved...

Summary Within the framework of displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is development optimal techniques evaluation stress field. In fact, in classical VEM formulation, same projection operator used to approximate strain field (and then evaluate stiffness matrix) employed recover, via constitutive law, Considering a first‐order strains are locally mapped onto constant functions, and stresses piecewise constant. However, displacements...

We propose an adaptive curved virtual element method (ACVEM) which is able to combine exact representation of the involved computational geometry and a dynamic tuning optimal mesh resolution through robust efficient residual-based a-posteriori error estimator. A theoretical analysis on reliability estimator gallery numerical tests supports efficacy proposed approach. The ACVEM combined with Monte Carlo simulations, methodology developed determine homogenized material moduli representative...

This work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in unified manner wide class of deviatoric yield functions with linear or nonlinear strain-hardening. The is based on an incremental energy minimization approach, the framework generalized standard materials convex free and dissipation potential. An efficient method computation latter, its gradient Hessian provided, using Haigh-Westergaard stress invariants. Numerical...

We consider three different exponential map algorithms for associative von-Mises plasticity with linear isotropic and kinematic hardening. The first scheme is based on a formulation of the time continuous model, which automatically grants yield consistency method in numerical solution. second one quadratically accurate but non-yield consistent already proposed Auricchio Beirão da Veiga (Int. J. Numer. Meth. Engng 2003; 56: 1375–1396). third an improved version one, condition enforced...

This paper deals with the modal analysis of rotational shell structures by means numerical solution technique known as Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within Reissner first order shear deformation theory (F. S. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, compatibility equations via Principle Virtual Works are obtained, general structure, given internal equilibrium in terms stress resultants and couples....

Abstract We consider four schemes based on generalized midpoint rule and return map algorithm for the integration of classical J 2 plasticity model with linear hardening. The comparison, aiming to establish which is preferable scheme among considered, both theoretical numerical. On one side, extending completing existing results in literature, we investigate from viewpoint, addressing particular existence solution, long‐term behaviour, accuracy stability. other hand, develop an extensive set...