An energetic view on the limit analysis of normal bodies
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In this article, a limit analysis for normal materials based on energy minimization is presented, which includes no-tension materials and materials with bounded compressive strength; it also includes the Hencky plastic materials.Abstract:
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.read more
Citations
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Journal ArticleDOI
Bounded shear stress in masonry-like bodies
TL;DR: In this paper, a hyperelastic material with limited tensile and compressive strength is considered and the maximum value of the tangential component of the stress that can be attained on each plane depends on the intensity of the normal component.
Journal ArticleDOI
Masonry-like material with bounded shear stress
TL;DR: In this paper, the constitutive equation of masonry-like materials has been generalized in order to account for a limit to the tangential component of the stress, that is proportional to the normal component.
Book ChapterDOI
Mathematics of the Masonry–Like model and Limit Analysis
TL;DR: In this article, the authors present a brief introduction to the mathematics of equilibrium of no-tension (masonry-like) materials, and examine the question whether the total energy is bounded from below.
Journal ArticleDOI
Equilibrated divergence measure stress tensor fields for heavy masonry bodies
TL;DR: In this article, the equilibrium problem of rectangular panels made of no-tension material under gravity and undergoing a vertical load distributed on their top and a horizontal load on a lateral side was studied.
Numerical Methods for Slender Masonry Structures: A Comparative Study
Maria Girardi,Massimiliano Lucchesi,Cristina Padovani,Giuseppe Pasquinelli,Barbara Pintucchi,Nicola Zani +5 more
TL;DR: In this paper, two numerical approaches for modelling the dynamic behavior of masonry structures are compared for both three-dimensional bodies and one-dimensional structures, and a masonry tower with rectangular cross-section is analised.
References
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Book
Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.
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An introduction to continuum mechanics
Morton E. Gurtin,W. J. Drugan +1 more
TL;DR: In this paper, the NavierStokes Equations are used to define linear elasticity for tensor analysis, and the invariance of material response is established. But the analysis is restricted to finite elasticity and cannot be extended to infinite elasticity.
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Mathematical Theory of Elastic and Elasto Plastic Bodies: An Introduction
Jindřich Nečas,Ivan Hlaváček +1 more
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Modern Methods in the Calculus of Variations: L^p Spaces
Irene Fonseca,Giovanni Leoni +1 more
TL;DR: In this article, the Direct Method and Lower Semicontinuity of the Lp Spaces were studied. But they did not consider the direct method and lower semicontuity of Lp spaces.