Massimiliano Lucchesi

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.

Stability of columns with no tension strength and bounded compressive strength and deformability. Part I: large eccentricity

This work concerns the stability of piles with rectangular cross section, made of a no-tension material with limited compressive strength and deformability, subjected to an axial load acting within the cross section but outside its middle third (large eccentricity). The differential equations obtained have been solved explicitly, and their solutions have allowed us to describe the stability characteristics of the pile through graphical representations.

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.

EXPLICIT SOLUTIONS FOR THE STABILITY OF NO-TENSION BEAM-COLUMNS

This work concerns the stability of rectangular cross-sectional piles made of a no-tension material and subjected to an axial load acting at the extremities within the middle third of the cross section. The resulting differential equations are solved, and an explicit relation between the load and a suitable deformability parameter obtained.

A note on equilibrated stress fields for no-tension bodies under gravity

We study the equilibrium problem for two-dimensional bodies made of a no-tension material under gravity, subjected to distributed or concentrated loads on their boundary. Admissible and equilibrated stress fields are interpreted as tensor-valued measures with distributional divergence represented by a vector-valued measure, as developed by the authors of the present paper. Such stress fields allow us to consider stress concentrations on surfaces and lines. Working in R n , we calculate the weak divergence of a stress field that is asymptotically of the form |x|-n+1To(x/|x|) for x → 0 on a region that is asymptotically a cone with vertex 0. Such stress fields arise as parts of our solutions for two-dimensional panels. Proceeding to problems in dimension two, we first determine an admissible equilibrated solution for a half-plane under gravity that underlies two subsequent solutions for rectangular panels. For the latter we give solutions for three types of loads.

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.

Energy dissipation of a thin elastoplastic tube under torsion and compression

An analytical computation is performed of the energy dissipated by a thin tube made of a work-hardening material, subjected to both a static compressive load and a dynamic torsional load.

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.