Masonry Constructions: Mechanical Models and Numerical Applications

Lucchesi, M.; Padovani, Cristina; Pasquinelli, Giuseppe; Zani, Nicola

doi:10.1007/978-3-540-79111-9

Cited by 66 publications

(94 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Particularly interesting is the use of polyhedral stress potentials to generate equilibrated force networks (Fraternali et al, 2002a,b). For a review of the available approaches to the statics of masonry vaults and domes we refer the reader to Di Pasquale (1975), Heyman (1995), Lucchesi et al (2008), Tomasoni (2008), Como (2010), and Block (2009).…”

Section: Introductionmentioning

confidence: 99%

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

Fraternali

2010

Mechanics Research Communications

154

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

Fraternali

2010

Mechanics Research Communications

154

View full text Add to dashboard Cite

“…The constitutive model is combined with the finite-element method in the code NOSA-ITACA (www.nosaitaca.it/en/software/) to provide a tool for studying the structural behaviour of existing masonry structures in both static and dynamical situations [11][12][13]. The code has been successfully applied to the analysis of some buildings of historical interest [14]. A substantial ingredient of the numerical solution of the equilibrium problem is the derivative of the stress-strain relation, allowing determination of the tangent stiffness matrix required by the Newton-Raphson method for solving the nonlinear algebraic system resulting from the discretization into finite elements.…”

Section: Introductionmentioning

confidence: 99%

“…A substantial ingredient of the numerical solution of the equilibrium problem is the derivative of the stress-strain relation, allowing determination of the tangent stiffness matrix required by the Newton-Raphson method for solving the nonlinear algebraic system resulting from the discretization into finite elements. In an isotropic material the derivative, as well as the solution to the constitutive equation, can be determined explicitly [14,Section 2.4].…”

Section: Introductionmentioning

confidence: 99%

On the derivative of the stress–strain relation in a no-tension material

Padovani

Šilhavý

2015

Mathematics and Mechanics of Solids

Self Cite

View full text Add to dashboard Cite

The stress-strain relation of a no-tension material, used to model masonry structures, is determined by the nonlinear projection of the strain tensor onto the image of the convex cone of negative-semidefinite stresses under the fourthorder tensor of elastic compliances. We prove that the stress-strain relation is indefinitely differentiable on an open dense subset O of the set of all strains. The set O consists of four open connected regions determined by the rank k = 0, 1, 2, 3 of the resulting stress. Further, an equation for the derivative of the stress-strain relation is derived. This equation cannot be solved explicitly in the case of a material of general symmetry, but it is shown that for an isotropic material this leads to the derivative established earlier by Lucchesi et al. (Int J Solid Struct 1996; 33: 1961-1994 and Masonry constructions: Mechanical models and numerical applications. Berlin: Springer, 2008) by different means. For a material of general symmetry, when the tensor of elasticities does not have the representation known in the isotropic case, only general steps leading to the evaluation of the derivative are described.

show abstract

“…No-tension (masonry-like) materials [Anzellotti 1985;Giaquinta and Giusti 1985;Del Piero 1989;Di Pasquale 1992;Lucchesi et al 2008a] cannot support all stresses: only negative semidefinite stresses are possible. Therefore, bodies made of no-tension materials cannot support all loads, certain loads lead to the collapse of the body.…”

Section: Introductionmentioning

confidence: 99%

On the choice of functions spaces in the limit analysis for masonry bodies

Lucchesi¹,

Šilhavý²,

Zani³

2012

J. Mech. Mater. Struct.

Self Cite

View full text Add to dashboard Cite

The kinematic and static problems of limit analysis of no-tension bodies are formulated. The kinematic problem involves the infimum of kinematically admissible multipliers, and the static problem the supremum of statically admissible multipliers. The central question of the paper is under which conditions these two numbers coincide. This involves choices of function spaces for the competitor displacements and competitor stresses. A whole ordered scale of these spaces is presented. These problems are formulated as convex variational problems considered by Ekeland and Témam. The static problem is unconditionally shown to be the dual problem (in the sense of the mentioned reference) of the kinematic problem. A necessary and sufficient condition, the normality, guarantees that the kinematic and static problems give the same result. The normality is not always satisfied, as examples show (one of which is presented here). The qualification hypothesis of Ekeland and Témam, sufficient for the equality of the static and kinematic problems, is never satisfied in the spaces of admissible displacements of bounded deformation or of functions integrable together with the gradient in the power p, 1 ≤ p < ∞. In the cases of lipschitzian displacements and of smooth displacements, the qualification hypothesis is equivalent to simple conditions that can be satisfied in the case of the pure traction problem. However, it is shown that then the space of admissible stresses must be enlarged to contain stress fields represented by finitely or countably additive tensor-valued measures.

show abstract

Masonry Constructions: Mechanical Models and Numerical Applications

Cited by 66 publications

References 0 publications

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions

On the derivative of the stress–strain relation in a no-tension material

On the choice of functions spaces in the limit analysis for masonry bodies

Contact Info

Product

Resources

About