Andrea Pagni

A numerical method for solving equilibrium problems of masonry-like solids

This paper proposes a numerical method for the solution of equilibrium problems of solids which do not support tension. Some boundary-value problems are solved numerically and the solution obtained is compared to the exact one.SommarioIn questo lavoro viene proposto un metodo numerico per la soluzione di problemi di equilibrio di solidi non resistenti a trazione. Vengono successivamente risolti numericamente alcuni problemi di equilibrio e la soluzione ottenuta è confrontata con quella esatta.

A Thermomechanical Solver for Multilayer Power Electronic Assemblies Integrated Into the DJOSER Thermal Simulator

The DJOSER analytical thermal solver for multilayer mounting structures has been tested as a useful and friendly tool for the thermal analysis of power electronic devices and their packages, able to replace the onerous programs based on the finite element method (FEM) calculations. The other problem connected with the packaging evaluation is the calculation of the thermally induced stresses and strains in the various layers composing the assembling structures. This paper deals with the first step of the implementation of a thermomechanical solver to be connected with the DJOSER program, which is able to calculate the stresses at the layer interfaces, using the same strategy, i.e., a semianalytical mathematical approach, as well as the same structural models (stepped pyramidal structures and homogeneous layers). The basic theory is briefly exposed and the method is applied to some two-layer virtual structures. The obtained results are compared with those obtained using standard FEM analysers.

LONGITUDINAL OSCILLATIONS OF BIMODULAR RODS

In this paper we consider the longitudinal vibrations of bimodular rods. After proving the equivalence between the entropy condition and Lax condition (whenever this latter is applicable), we go on to consider the Riemann problem and prove that a unique solution always exists except for the special case of no-tension materials. This procedure allows for easy determination of the explicit solution.

FREE LONGITUDINAL VIBRATIONS OF BIMODULAR BEAMS: A COMPARATIVE STUDY

In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Youngs modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.

Materials with elastic range and plastic change of volume

Following the lines of Lucchesi and Podio-Guidugli, Lucchesi and Silhavý, and Lucchesi et al. we sketch a theory of materials with elastic range that, unlike the treatment in those papers, places no restrictions on plastic changes of volume or on related quantities. We then describe with some detail the constitutive behavior of two important classes of materials with elastic range that, by analogy with the terminology used in classical plasticity, we call v. Mises materials and ideally plastic materials. Finally, for a specific ideally plastic v. Mises material, we present a numerical computation that shows how, when plastic change of volume is allowed, the shear stress maintaining a simple shear flow need not have constant value.

Hadamard-V. Mises ideally plastic materials

Abstract For a Hadamard-v. Mises ideally plastic material the authors consider three nested classes of histories; each class is defined by means of bounds placed on deformations and deformation rates, or on elastic and plastic deformations. They establish, in certain simple but significant cases, the error committed in evaluating the stress response by assuming that a history belongs to one of the above-mentioned classes.

Integrating a thermo-mechanical solver into the DJOSER analytical thermal simulator for multilayer power electronic assemblies. Preliminary results

The DJOSER analytical thermal solver for multilayer mounting structures has been tested as a useful and friendly tool for the thermal analysis of power electronic devices and their packages, able to replace the onerous programs based on the finite element (FEM) calculations. The other problem connected with the packaging evaluation is the calculation of the thermally induced stresses and strains in the various layers composing the assembling structures. This paper deals with the first step of the implementation of a thermo-mechanical solver to be connected with the DJOSER program, which may be able to calculate the stresses at the layer interfaces, using the same strategy, i.e. a semi-analytical mathematical approach, and the same DJOSER structural constrains (stepped pyramidal structures, homogeneous layers). The basic theory is briefly exposed and the method is applied to some two-layers virtual structures. The obtained results are compared with those obtained using standard FEM analyses, revealing a substantial agreement but also some local disagreements.