Cristina Padovani

Masonry-like solids with bounded compressive strength

Abstract This paper proposes a constitutive equation for masonry-like materials with bounded compressive strength. The general properties of this equation are proved and its solution is explicitly calculated. Subsequently, a numerical method is proposed in order to solve the equilibrium problem of masonry-like solids with bounded compressive strength. In particular the derivative of the stress with respect to the total strain is calculated; this derivative will be used for calculating the tangent stiffness matrix and then for solving the non-linear system, obtained with the discretisation into finite elements via the Newton-Raphson method. Finally, this numerical method is applied to the study of Moscas bridge in Turin and to the study of a three-dimensional circular reduced arch subjected to its own weight and a vertical load distributed along the extrados.

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.

On the Collapse of Masonry Arches

In this paper a constitutive equation for masonry arches is defined and its main properties are proven; in this equation to each pair of generalized strains (ε, κ), with ε the extensional strain and κ the curvature change of the centre line, is assigned the pair of generalized internal forces (N,M), where N is the normal force and M the bending moment. Subsequently, the collapse of masonry arches is characterized and the static and kinematic theorems proven. Finally, a method for determining the collapse load in the case of circular arches subjected to their own weight and a vertical point load applied at a point of the extrados is presented. The results obtained, of interest in some applications, are summarized in a series of graphs.

Strong Ellipticity of Transversely Isotropic Elasticity Tensors

The strong ellipticity of the elasticity tensor of a linearly hyperelastic, transversely isotropic material is investigated. The necessary and sufficient conditions for the elasticity tensor to be strongly elliptic are determined for the five constants characterizing it.

On the numerical solution of equilibrium problems for elastic solids with bounded tensile strength

Abstract This paper proposes a numerical method for the solution of equilibrium problems of elastic solids with bounded tensile strength. Some boundary-value problems are solved numerically and the solution obtained is compared to the exact one. Finally, a masonry spherical dome subjected to its own weight and to a point load at the crown is studied.

The Maximum Modulus Eccentricities Surface for Masonry Vaults and Limit Analysis

This paper presents a constitutive equation for masonry vaults which associates to each pair of generalized strains (A, K), where A are the strains, K are the curvature changes of the mean surface, the pair of generalized internal forces, (N, M) with N and M being the normal forces and bending moments per unit length, respectively The maximum modulus eccentricities surface is defined, and its main properties are proved. Subsequently, the limit analysis for masonry vaults is set forth and applied to the evaluation of the collapse load for a toroidal tunnel subjected to its own weight and an uniform load applied on the top circle.

An energetic view on the limit analysis of normal bodies

This note presents a limit analysis for normal materials based on energy minimization. The class of normal materials includes some of those used to model masonry structures, namely, no-tension materials and materials with bounded compressive strength; it also includes the Hencky plastic materials. Considering loads L(λ) that depend affinely on the loading multiplier λ ∈ R, we examine the infimum I 0 (λ) of the potential energy I(u,λ) over the set of all admissible displacements u. Since I 0 (λ) is a concave function of λ, the set A of all λ with I 0 (λ) > -∞ is an interval. Each finite endpoint λ c ∈ ℝ of A is called a collapse multiplier, and we interpret the loads corresponding to λ c as the loads at which the collapse of the structure occurs. We show that the standard definition of collapse based on the collapse mechanism does not capture all situations: the collapse mechanism is sufficient but not necessary for the collapse. We then examine the validity of the static and kinematic theorems of limit analysis under the present definition. We show that the static theorem holds unconditionally while the kinematic theorem holds for Hencky plastic materials and materials with bounded compressive strength. For no-tension materials it generally does not hold; a weaker version is given for this class of materials.

A numerical method for solving equilibrium problems of no-tension solids subjected to thermal loads

This paper starts out by recalling a constitutive equation of no-tension materials that accounts for thermal dilatation and the temperature dependence of the material parameters. Subsequently, a numerical method is presented for solving, via the finite element method, equilibrium problems of no-tension solids subjected to thermal loads. Finally, three examples are solved and discussed: a spherical container subjected to two uniform radial pressures and a steady temperature distribution, a masonry arch subjected to a uniform temperature distribution and a converter used in the steel and iron industry.

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.

Thermodynamics of no-tension materials

Abstract This paper presents a constitutive equation for no-tension materials in the presence of thermal expansion that accounts for the temperature-dependence of their material’s constants. Specifically, assuming that the symmetric part of the displacement gradient minus the thermal dilatation is small, an explicit expression is given for stress from which the free energy, internal energy, entropy and enthalpy are obtained. Then, the equilibrium energy equations of a no-tension solid are presented, and we observe that, under further suitable hypotheses, thermo-mechanical uncoupling occurs. Finally, the work lost during an adiabatic process by two spherical containers made of a linear elastic and a no-tension material are compared.