NURBS-based kinematic limit analysis of FRP-reinforced masonry walls with out-of-plane loading

A three-dimensional (3D) general upper-bound limit analysis procedure for the determination of the collapse load of out-of-plane loaded masonry walls with Fiber Reinforced Polymer (FRP) reinforcement strips is presented. The geometry of a given FRP reinforced masonry wall of arbitrary shape is represented by its Non-Uniform Rational B-Spline (NURBS) description in the three-dimensional Euclidean space. The NURBS parameter space is partitioned by means of a number of possible fracture lines and the original reinforced wall geometry is subdivided into an initial set of rigid elements, accordingly. An upper-bound limit analysis formulation, accounting for the main characteristics of both masonry material and FRP reinforcement by means of homogenization techniques, is deduced. Internal dissipation is allowed along element edges only and the effect of vertical loads and membrane stresses is considered as well. Numerical experiments show that a good estimate of the load bearing capacity is obtained provided that the initial arrangement of yield lines is adjusted by means of a suitable Genetic Algorithm (GA)

Novel non-linear static numerical model for curved masonry structures based on a combined adaptive limit analysis and discrete FE computations

A new procedure for a fast and comprehensive description of the collapse behavior of curved masonry structures is presented. The first step provides the identification of the exact collapse mechanism and the load-bearing capacity through adaptive NURBS limit analysis. This method is based on the discretization of the masonry vault through very few curved elements, assumed as rigid blocks with internal dissipation allowed only at interfaces, whose shape is iteratively modified until interfaces coincide with the correct position of cracks. On the obtained mechanism, a kinematic non-linear analysis with rigid-softening behavior can be also applied to better understand how the load-bearing capacity decreases during the evolution of the mechanism. A finite element (FE) non-linear static analysis is then applied to obtain the force-displacement curve according to the real elastic-softening behavior. The NURBS optimized model is converted into a discrete FE model composed of three-dimensional elastic units joint together by interfaces where the non-linear mechanical properties are lumped. Within this assumption, non-linear interfaces are applied along the cracks previously found through the limit analysis in a fully automatic way, preventing any mesh dependency effect. Furthermore, the combination of such approaches allows overcoming the respective drawbacks of the methods. Selected masonry arches and vaults are here studied to present the reliability of the presented coupled approach.NSFC - National Natural Science Foundation of China(51576043

Wavelength locking of silicon photonics multiplexer for DML-based WDM transmitter

We present a wavelength locking platform enabling the feedback control of silicon (Si) microring resonators (MRRs) for the realization of a 4 × 10 Gb/s wavelength-division-multiplexing (WDM) transmitter. Four thermally tunable Si MRRs are employed to multiplex the signals generated by four directly modulated lasers (DMLs) operating in the L-band, as well as to improve the quality of the DMLs signals. Feedback control is achieved through a field-programmable gate array controller by monitoring the working point of each MRR through a transparent detector integrated inside the resonator. The feedback system provides an MRR wavelength stability of about 4 pm (0.5 GHz) with a time response of 60 ms. Bit error rate (BER) measurements confirm the effectiveness and the robustness of the locking system to counteract sensitivity degradations due to thermal drifts, even under uncooled operation conditions for the Si chip

A Genetic Algorithm adaptive homogeneous approach for evaluating settlement-induced cracks in masonry walls

This paper presents a Genetic Algorithm adaptive homogeneous approach aiming at representing the crack patterns induced by ground settlements on masonry walls. This type of damage is a critical issue since it affects all masonry buildings, including those that are not located in seismic-prone areas. The GA-adaptive homogeneous approach here proposed is meant as a tool that overcomes the usual high computational costs requested by the traditional heterogeneous and homogeneous approaches. Here, the considered masonry wall is discretized into a low number of 2D polygonal elements; its displacement field is then determined through a linear programming problem. The actual position of cracks induced by the applied settlement is identified by modifying the initial mesh through an iterative mesh adaptation procedure performed with a Genetic Algorithm (GA); the iterations are carried on until the absolute minimum of the work performed by the reaction forces is attained. In this way, the computational effort needed for identifying the actual crack patterns is dramatically decreased due to the very few unknowns of the problem. The reliability of the GA-adaptive homogeneous approach here proposed is validated against selected benchmarks that come from experimental and numerical results, and is also compared with the traditional heterogeneous and homogeneous approaches. In all the three benchmarks, the GA-adaptive approach offers a satisfying computational efficiency and identifies the actual crack patterns with good accuracy, despite the low number of elements employed in the discretization of the masonry wall. This may pave the way for a broader use of this approach in the analysis of complex masonry structures affected by settlement-induced damages

Safety assessment of masonry bridges through a fast kinematic limit analysis procedure

In this contribution, the collapse behavior of masonry bridges is numerically analyzed by means of a fast and reliable limit analysis approach based on the upper-bound theorem. This approach relies on the description of the geometry of the bridge structure and backfill by means of NURBS approximating functions. A rigid body mesh starting from the assigned geometry can be generated, which is composed by very few elements still providing an exact representation of the original geometry. The main properties of masonry material are accounted for through homogenization and a kinematic formulation for the limit analysis of the obtained rigid block assembly is derived. The approach is capable of accurately predicting the load bearing capacity of masonry bridges with arbitrary geometry and load configuration, provided that the initial mesh is adjusted by means of a suitably meta-heuristic approach (i.e. a genetic algorithm) until element edges correctly approximate the actual failure mechanism. The approach proves to be both accurate and computationally inexpensive when compared to standard nonlinear finite element analyses and other more sophisticated numerical procedures proposed in the literature

Masonry structures in the presence of foundation settlements and unilateral contact problems

This paper aims at presenting a new perspective on the modeling of the influence of foundation settle- ments in masonry structures. We show that it is possible to model in a consistent way the crack pat- tern and the associated mechanism induced by applied settlements starting from a proper treatment of unilateral contact constraints between contiguous blocks, in which the structure is partitioned after the onset of settlements. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a complementary boundary formulation, to the case of contact between multiple no-tension rigid bodies satisfying Heyman’s hypotheses for the limit analysis of masonry structures. The discretization of the proposed variational formulations directly entails two dual linear programming problems. The proposed formulations allow to correctly evaluate the effects of foundation settlements and their influence on the ultimate load bearing capacity of masonry structures

On Collapse Behavior of Reinforced Masonry Domes under Seismic Loads

In this paper, the first result on the collapse behavior of reinforced masonry domes under seismic loads is presented. A certain masonry dome is modeled through NURBS surfaces, which have the great advantage to represent accurately complex geometries. The obtained NURBS model is imported in the MATLAB® environment, in which an initial NURBS mesh is defined. An upper bound limit analysis is applied: each element is idealized as rigid block and eventual plastic dissipation is allowed only along element edges. The minimum of the kinematic multipliers is found by optimizing the NURBS mesh (i.e. modifying the position of fracture lines) through a meta-heuristic algorithm (e.g. a Genetic Algorithm). A reinforcing system made by FRCM fibers is included through additional NURBS surfaces: each new surface represents a strip and exhibits only a tensile contribute in the evaluation of plastic dissipation. The dome of the church of Anime Sante, which collapsed during the L’Aquila earthquake in 2009, is considered as meaningful case study. A standard disposition of FRCM fibers, typically designed for incrementing the vertical load bearing capacity, has been hypothesized. The reinforced dome is analyzed under a horizontal acceleration linear in height and constant in plane and a comparison between the unreinforced and the reinforced case is presented

A fast and general upper-bound limit analysis approach for out-of-plane loaded masonry walls

A new general approach for the limit analysis of out-of-plane loaded masonry walls based on an upper bound formulation is presented. A given masonry wall of generic form presenting openings of arbitrary shape is described through its Non-Uniform Rational B-Spline (NURBS) representation in the three-dimensional Euclidean space. A lattice of nodes is defined in the parameters space together with possible fracture lines. An initial set of rigid elements initially subdividing the original wall geometry is identified accordingly. A homogenized upper bound limit analysis formulation, which takes into account the main characteristics of masonry material such as very low resistance in traction and anisotropic behavior is deduced. Moreover the effect of vertical loads and membrane stresses is considered, assuming internal dissipation allowed exclusively along element edges. A number of technically meaningful examples prove that a good estimate of the collapse load multiplier is obtained, provided that the initial net of yield lines is suitably adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism

Fast and reliable limit analysis approach for the structural assessment of FRP-reinforced masonry arches

This contribution is devoted to assess the capability of a new upper-bound approach for the limit analysis of FRP-reinforced masonry arches by comparing it to both experimental tests and a number of existing numerical procedures. The approach is based on an idea previously presented by the Authors and relies on the representation of the geometry of both the arch and of FRP reinforcement through Non Uniform Rational B-Spline (NURBS) functions. This allows generating a rigid body assembly starting from the assigned geometry composed by very few elements which still provide an exact representation of the original shape. A homogenized kinematic formulation for the limit analysis of the obtained rigid blocks assembly is derived, which accounts for the main properties of masonry material. FRP material is included exploiting the Italian CNR Recommendations for the design of FRP based reinforcing interventions. The approach is capable of accurately predicting the load bearing capacity of masonry arches of arbitrary geometry, provided that the initial mesh is adjusted by means of a suitably devised Genetic Algorithm (GA) until the active interfaces among blocks (e.g. hinges) closely approximate the actual failure mechanism

NURBS-Based Upper Bound Limit Analysis of FRP Reinforced Masonry Vaults through an Efficient Mesh Adaptation Scheme

Masonry vaults represent one of the typical structural typologies in historical masonry buildings. The study of the ultimate behavior of masonry vaults, together with the need to design adequate retrofitting techniques, is of high relevance in the optics of the preservation of the cultural heritage. In this paper, a new approach for the limit analysis of masonry construction is applied to FRP reinforced masonry vaults. This approach relies on the representation of geometry through NURBS surfaces, upper bound formulation of limit analysis, idealization of the structure as an assembly of rigid bodies with dissipation allowed only along interfaces, and optimization by means of a mesh adaptation scheme. The presence of FRP strips can be taken into account in easy way, because they can be included simply by adding NURBS surfaces and assigning them an adequate delamination stress value. The efficient mesh adaptation is performed by means of a Prey Predator Algorithm, which has been proven to be very suited for these problems. The strength of the proposed method lies in an accurate estimation of load-bearing capacity and collapse mechanism obtained with a model which requires a very low computational effort