Static Analysis of a Double-Cap Masonry Dome

Babilio, Enrico; Ceraldi, Carla; Lippiello, Maria; Portioli, Francesco; Sacco, Elio

doi:10.1007/978-3-030-41057-5_165

Cited by 5 publications

(6 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…to be solved with respect to the collapse multiplier λ, the normal-force tensor N , the shear-force vector Q, and the bending-moment tensor M . In the next section, a discretization approach will be discussed for achieving an efficient computational solution strategy of problem (20).…”

Section: Lower-bound Limit Analysismentioning

confidence: 99%

“…That is accomplished by a procedure resembling finite-volume discretizations (e.g., see [54]). In particular, the following three steps are involved: (i) a mesh is considered on the mid-surface Σ of the dome, which induces its decomposition into elements (or control volumes, as in the customary notation in finite-volume methods); (ii) a suitable approximation of the shell stress tensors N , Q, and M is introduced by interpolation with nodal values; (iii) the optimization constraints in problem (20) are relaxed by requiring the equilibrium equations (12) and the admissibility inequalities ( 18)-( 19) respectively to hold for the elements and at the nodes of the mesh. Concerning step (i), a mesh is constructed on the mid-surface Σ of the dome as the image, through the map x, of a rectangular mesh in the parameter domain Ω = [a, b] × [0, 2π], as shown in Figure 3.…”

Section: Problem Discretizationmentioning

confidence: 99%

“…where F i c is a 3 × 9I friction admissibility matrix. Finally, the discretized version of the lower-bound limit analysis problem (20) results to be:…”

Section: Problem Discretizationmentioning

confidence: 99%

“…In turn, the computational translation of membrane formulations has been pursued along two different directions. A continuous description of the unknown thrust membrane (parameterized as the graph of a function by its elevation) and of the relevant membrane forces (generated by an Airy potential in Pucher's form [17]) is adopted in the thrust surface analysis method [18][19][20][21]. Conversely, a discrete description of the unknown thrust membrane as a 3D network of truss elements, with the stress state being represented by normal forces in the truss elements, is the rationale for the thrust network analysis method (e.g., see [22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

Nodargi¹,

Bisegna²

2021

Preprint

View full text Add to dashboard Cite

A static limit analysis approach is proposed for assessing the collapse capacity of axisymmetric masonry domes subject to horizontal forces. The problem formulation is based on the sound theoretical framework provided by the classical statics of shells. After introducing the shell stress tensors on the dome mid-surface, integral equilibrium equations are enforced for its typical part. Heyman's assumptions of infinite compressive and vanishing tensile strengths are made, with cohesionless friction behavior governing the shear strength, to characterize the admissible stress states in the dome. An original computational strategy is developed to address the resulting static limit analysis problem, involving the introduction of a mesh on the dome mid-surface, the interpolation of the physical components of the shell stress tensors on the element boundaries, and the imposition of equilibrium and admissibility conditions respectively for the elements and at the nodes of the mesh. The descending discrete convex optimization problem is solved by standard and effective optimization tools, automatically providing collapse multiplier of horizontal forces, incipient collapse mechanism and expected crack pattern. Convergence analysis, validation with experimental results available in the literature, and parametric analyses with respect to geometric parameters and friction coefficient, are presented for spherical and ellipsoidal masonry domes, proving the reliability of the proposed approach for estimating the pseudo-static seismic resistance of masonry domes.

show abstract

Section: Lower-bound Limit Analysismentioning

confidence: 99%

Section: Problem Discretizationmentioning

confidence: 99%

“…where F i c is a 3 × 9I friction admissibility matrix. Finally, the discretized version of the lower-bound limit analysis problem (20) results to be:…”

Section: Problem Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

Nodargi¹,

Bisegna²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Following the initial idea proposed in [35,36], blockbased methods have been broadly used for the limit analysis of both 2D and 3D masonry structures in the last twenty years (e.g., see [32,39,56,57]), also assuming non-associative friction flow law (e.g., see [5,12,19,25,49,53]). An extension to masonry domes under horizontal forces has been discussed in [4,13], taking advantage of a point contact model which simplifies the imposition of the failure conditions at block interfaces and results in a cone programming problem.…”

Section: Introductionmentioning

confidence: 99%

A finite difference method for the static limit analysis of masonry domes under seismic loads

Nodargi

Bisegna

2021

Meccanica

View full text Add to dashboard Cite

The static limit analysis of axially symmetric masonry domes subject to pseudo-static seismic forces is addressed. The stress state in the dome is represented by the shell stress resultants (normal-force tensor, bending-moment tensor, and shear-force vector) on the dome mid-surface. The classical differential equilibrium equations of shells are resorted to for imposing the equilibrium of the dome. Heyman’s assumptions of infinite compressive and vanishing tensile strength, alongside with cohesive-frictional shear response, are adopted for imposing the admissibility of the stress state. A finite difference method is proposed for the numerical discretization of the problem, based on the use of two staggered rectangular grids in the parameter space generating the dome mid-surface. The resulting discrete static limit analysis problem results to be a second-order cone programming problem, to be effectively solved by available convex optimization softwares. In addition to a convergence analysis, numerical simulations are presented, dealing with the parametric analysis of the collapse capacity under seismic forces of spherical and ogival domes with parameterized geometry. In particular, the influence that the shear response of masonry material and the distribution of horizontal forces along the height of the dome have on the collapse capacity is explored. The obtained results, that are new in the literature, show the computational merit of the proposed method, and quantitatively shed light on the seismic resistance of masonry domes.

show abstract

Masonry Domes Under Complex Loading Conditions: A Shell-Based Static Limit Analysis Approach

Nodargi,

Bisegna

2023

Lecture Notes in Applied and Computational Mechanics

View full text Add to dashboard Cite

Static Analysis of a Double-Cap Masonry Dome

Cited by 5 publications

References 20 publications

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

A finite difference method for the static limit analysis of masonry domes under seismic loads

Masonry Domes Under Complex Loading Conditions: A Shell-Based Static Limit Analysis Approach

Contact Info

Product

Resources

About