Edoardo Artioli

Free vibration analysis of spherical caps using a G.D.Q. numerical solution

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

A stress/displacement Virtual Element method for plane elasticity problems

Abstract The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger–Reissner variational formulation. A low-order Virtual Element Method (VEM) with a priori symmetric stresses is proposed. Several numerical tests are provided, along with a rigorous stability and convergence analysis.

Free vibrations for some Koiter shells of revolution

Abstract The asymptotic behaviour of the smallest eigenvalue in linear Koiter shell problems is studied, as the thickness parameter tends to zero. In particular, three types of shells of revolution are considered. A result concerning the ratio between the bending and the total elastic energy is also provided, by using the general theory detailed in [L. Beirao da Veiga, C. Lovadina, An interpolation theory approach to Shell eigenvalue problems (submitted for publication); L. Beirao da Veiga, C. Lovadina, Asymptotics of shell eigenvalue problems, C.R. Acad. Sci. Paris 9 (2006) 707–710].

VEM for Inelastic Solids

The virtual element method (VEM) is a generalization of the finite element method recently introduced.

State update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization

This work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in a unified manner a wide class of deviatoric yield functions with linear or nonlinear strain-hardening. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free energy and dissipation potential. An efficient algorithm for the computation of the latter, its gradient and its Hessian is provided, using Haigh-Westergaard stress invariants. Numerical results on a single material point loading history and finite element simulations are reported to prove the effectiveness and the versatility of the method. Its merit turns out to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to high curvature points of the yield surface.

SMA Constitutive Modeling and Analysis of Plates and Composite Laminates

The study of polycrystalline shape memory alloys (SMAs) has been a scientific research topic of the utmost importance during the last 5 decades. The mathematical modeling of the very special thermomechanical response of SMAs represent an important issue for designing new applications and performing virtual testing of SMA devices. Literature devoted to the subject of modeling the pseudoelasticity (PE), the shape memory effect (SME), and the two-way effect (TWE) has reached considerable dimensions. Several approaches have been proposed in literature for modeling the SMA behavior which will be discussed in this chaper.

A family of virtual element methods for plane elasticity problems based on the Hellinger–Reissner principle

Abstract In the framework of 2D elasticity problems, a family of Virtual Element schemes based on the Hellinger–Reissner variational principle is presented. A convergence and stability analysis is rigorously developed. Numerical tests confirming the theoretical predictions are performed.

A New Integration Algorithm for the von-Mises Elasto-Plastic Model

We introduce a new numerical time integration scheme, in the framework of associative von-Mises plasticity with linear kinematic and isotropic hardening. The new procedure is based on the model reformulation in terms of an augmented stress tensor and on the adoption of an integration factor; the integration of the model makes use of exponential maps. A consistent number of numerical tests enlighten the superior behaviour of the new exponential-based technique, by means of comparison with classical return map algorithms based either on backward Euler or generalized midpoint integration rules.

Numerical Testing on Return Map Algorithms for von-Mises Plasticity with Nonlinear Hardening based on a Generalized Midpoint Integration Scheme

We consider an associative von-Mises elastoplastic constitutive model in the realm of small deformations [1]. The model takes into account both linear isotropic hardening and linear/nonlinear kinematic hardening. The aim of the work is to test integration algorithms based on a return mapping concept and adopting a generalized midpoint integration rule. The method under consideration was originally proposed by Ortiz and Popov [2] and further studied in the simpler case of nonhardening materials by Simo [3]. The tested method guarantees yield consistency at the end of the time step and results linearly or quadratically accurate depending on the choice of the integration parameter. The numerical algorithm adopts a return map update based on a projection along the midpoint normal-to-yield-surface direction onto the endpoint limit surface.