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Structural topology optimization (STO) is usually treated as a constrained minimization problem, which is iteratively addressed by solving the equilibrium equations for the problem under consideration. To reduce the computational effort, several reduced basis approaches that solve the equilibrium equations in a reduced space have been proposed. In this work, we apply functional principal component analysis (FPCA) to generate the reduced basis, and we couple FPCA with a gradient-based optimization method for the first time in the literature. The proposed algorithm has been tested on a large STO problem with 4.8 million degrees of freedom. Results show that the proposed algorithm achieves significant computational time savings with negligible loss of accuracy. Indeed, the density maps obtained with the proposed algorithm capture the larger features of maps obtained without reduced basis, but in significantly lower computational times, and are associated with similar values of the minimized compliance.

The numerical modeling of compressible multiphase flows is of high interest for several engineering applications. In this work, we focus on the study of pyroclastic flows arising from volcanic eruptive events. An accurate evaluation of the effects of this multiphase flow is of crucial importance for the Civil Protection for the preservation of urban settlements in volcanic areas. In this work, we propose a Finite Element formulation for the simulation of pyroclastic flows at conditions of thermal and kinetic equilibrium. This analysis belongs to the class of advection dominated problems, which are known to suffer from numerical instabilities. The required stabilization is provided by using a Variational Multiscale Method, typically used for monophase compressible flows and extended here for the first time to multiphase flows. The stabilized formulation is validated with benchmark problems for compressible flows, which are solved for both monophase and multiphase cases. A throughout comparison of the numerical results of the two different flows is also presented. Moreover, the numerical formulation is applied to the simulation of representative cases of pyroclastic flows considering large-scale computational domains and realistic material properties and initial thermal-kinematic conditions. The numerical analyses presented show the accuracy of the proposed method for the simulation of compressible multiphase flows and its suitability for risk assessment studies of urban settlements prone to be affected by pyroclastic gravity currents. This work is partially funded by the Italian Ministry of University and Research (MUR) through the project PON-AIM “Attraction and International Mobility” CUP: E66C19000230005, and partially funded by the Spanish Ministry of Economy and Competitiveness (Ministerio de Economia y Competitividad, MINECO) through the project PRECISE (BIA2017-83805-R). Authors are also grateful to the CINECA consortium for the provision of computational utilities through the IsCRA project “Vulnerability and Risk Assessment” (IsC79-VRA).

We present a numerical model of a contactless test commonly used to assess the biomechanics of the human cornea. The test, consisting in a rapid air jet applied to the anterior surface of the cornea, is controversial. Although the numerous studies documented in the literature have not been able yet to clarify its relevance as a diagnostic tool, the test has the potential to be combined with inverse analysis procedures to characterize the parameters of numerical models of the cornea. With the final goal of employing the air puff test in advanced material identification algorithms, here we propose to model the cornea with standard finite elements and the fluids filling the anterior chamber of the eye with a meshfree discretization. The interaction between moving fluids and deforming cornea is accounted for by modifying the interface boundary conditions of both fluid and solid. The proposed model represents the first fully 3D example of an aqueous-cornea fluid-solid interaction analysis which uses a robust meshfree approach for the fluid. Although we restrict our scope to isotropic nonlinear materials, numerical results confirm the undeniable importance of including internal fluids in the simulation of the air puff test. Thus the proposed approach stands as a procedural paradigm for the identification of the mechanical parameters of the human cornea.

(1) Methods for checking the condition of monumental masonry structures can still be considered understudied. Among the different approaches available in the literature, the graphical ones have a special role, due to their simplicity and effectiveness. (2) In this work, a 2D method (Thrust Line Analysis (TLA)), the Modified Thrust Line Method (MTLM), and the 3D Membrane Equilibrium Analysis (MEA) method are compared. All methods have the same starting concept: no tensile strength, no sliding between the stone blocks, infinite compressive strength. (3) The methods are compared in terms of stress distribution (for the same—or similar—thrust line), and in terms of the Geometrical Safety Factor ensured. (4) The work shows that these theories, if properly conveyed in a scientific methodology (as many authors are doing currently and have done in the past) demonstrate the effectiveness and the advantages of graphical methods for simple structures.

Masonry domes constitute a large part of the international architectural heritage. The issue of its conservation has long been a challenge both for architects and engineers. To limit any problems related to degradation, arising from structural damage or external factors, historical buildings are continuously restored and strengthened. Reliable tools are therefore needed to assess their structural safety. The present work discusses how modern methods can be used to understand ancient structures addressing the comparison between different methods of structural analysis, exploring the range of applications of limit analysis and finite element analysis in the stability assessment of masonry domes, focusing on the pros and cons of each approach. By applying equilibrium approaches and deformation-based models (finite element method), this paper provides two demonstration examples to compare the utility of each of them within a longstanding debate on the most proper way to evaluate traditional structures in masonry.

This paper intends to show basic strategies and technical solutions that may reduce the consequence of a volcanic eruption on buildings. One of the most dangerous eruptive phenomena is pyroclastic flow, a gas-solid mixture which can flow slope down up to reach considerable distances from the point of emission, with a speed that can easily exceed 100 km/h (~30 m/s). The damage caused by the impact on buildings depends on the combination of several factors: the duration of phenomenon, the temperature of flow and the pressure produced by the impact. The study tries to define a design-oriented approach of retrofitting and new construction with specific reference to the possible eruption of Vesuvio or Campi Flegrei in the Campania Region of Italy. For both red areas, which are directly affected by the flows, the Department of Civil Protection defined only one solution, that is the preventive evacuation. Whilst through the proposed mitigation strategy, the task is to establish a resilient sector within the red areas where buildings can withstand pressure and temperature in order to achieve both economic benefits and make reconstruction easier.

This research work provides a stability study for a double masonry dome during its construction process and, a consideration of the possible effects that the procedure followed for building the structure has on its current mechanical behaviour. In particular, the analysis is carried out on the Baroque dome of Santa Maria alla Sanita in Naples, a relatively small dome with a span of 12 m. The main contribution of the paper consists of making a hypothesis about the different phases of construction and demonstrating that the dome was in equilibrium during these different phases. This aspect has been rarely considered when analysing historical structures. The theoretical framework assumed refers to Limit Analysis in which the masonry is modelled as composed of rigid-unilateral material. To assess the stability of the dome, the study proposes an equilibrium analysis performed both graphically and analytically, by using the graphic statics and the membrane analysis. The results obtained from the two methods are also compared, at each stage of construction. Besides the classical graphical methodology based on the slicing technique, the membrane equilibrium solution provides a wider repertoire of equilibrium states, since it allows for biaxial stress fields and is here implemented with a new method for which the surface and the stress potential are both approximated through simplicial surfaces based on the same triangulation. This more refined analysis confirms the results obtained through graphic statics giving wider geometrical safety margins and a more detailed interpretation of the non-axisymmetric loading cases

Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.

A coupled hydromechanical code based on a distributed brittle damage material model has been developed in order to simulate hydraulic fracturing processes. As specific feature, the code does not assume the development of a discrete number of sharp cracks but considers a diffused damage that takes place under overall confinement of the system. The code is validated against a laboratory test reproducing the local effects of a hydraulic fracturing procedure. The numerical model of the laboratory test is then used to conduct a parametric analysis where the influence of the principal hydromechanical parameters on the hydraulic fracturing performance is assessed. Finally, the code is applied to simulate multiple hydraulic fracturing interventions in a large scale shale reservoir. In all applications considered, the model shows a good predictive capability in terms of damage extension.

The objective of the present work is to develop an automated numerical method for the analysis of thin masonry shells. The material model for masonry that we adopt is the so-called "normal rigid no-tension" (NRNT) material; and for such a material, the kinematical and the safe theorems of limit analysis are valid. The present study focuses on the application of the second theorem to masonry vaults and domes, being devoted to the determination of a class of purely compressive stress regimes, which are balanced with the load. The mere existence of such a class is a proof that the structure is safe, and members of this class may be used to assess the geometric degree of safety of the structure and to estimate bounds on the thrust forces exerted by the structure on its boundary. The problem is reduced to the equilibrium of a membrane S and can be formulated in terms of projected stresses defined on the planform Ω of S. The search of the stress reduces to the solution of a second-order pde, in terms of the stress potential F. In order that the membrane stress on S be compressive, the potential F must be concave. As for the thrust line in an arch, the surface S is not fixed and may be changed, given that it remains inside the masonry. Under these simplifying assumptions, the whole class of equilibrated stress regimes for a masonry shell is obtained by moving and deforming S inside the masonry, and also, for any fixed shape, by changing the boundary data for F, that is the distribution of thrust forces along the boundary. The search for a feasible stress state on a convenient membrane surface, to be chosen with a trial and error procedure, requires a substantial effort and may be unrewarded. Then, the main object of the present work, is to produce a computer code that can handle numerically the interplay of the shape controlled by a function f, and of the stress potential F, by developing a convergent optimization scheme able to give a safe state under the given material and geometrical constraints, namely the concavity of F and the inclusion of f within the masonry. Two simple cases, are exposed in detail to illustrate the method.

The equilibrium of cloister masonry vaults, treated as composed of unilateral material in the sense of Heyman, is the topic of the present work. For such a material, the safe and the kinematic theorems of limit analysis can be employed to detect equilibrium and nonequilibrium. In the spirit of the safe theorem, the structure is stable if a statically admissible stress field can be detected. On allowing for singular stresses, here we consider statically admissible stress fields concentrated on surfaces or lines lying inside the masonry vault. Such structures are unilateral membranes, whose geometry is described a la Monge, and the equilibrium of them is formulated in Pucher form, that is, in terms of the so-called projected stresses over the planform Ω. The problem, under purely parallel loads, is reduced to a single partial differential equation of the second-order, in two space variables, where the shape function f and the stress function F appear symmetrically. The unilateral restrictions require that the membrane surface S lies in between the extrados and intrados surfaces of the vault and that the stress function be concave. In the present work, by starting with a sensible choice of a concave stress function F, the transverse equilibrium equation is solved for f by imposing suitable boundary conditions. A cloister vault of Palazzo Caracciolo di Avellino, a XIV century building located along via dell'Anticaglia in Naples, is the case study. For two load conditions, membrane surfaces and geometrical safety factors are identified.

The Modified Finite Particle Method (MFPM) is a meshless method belonging to the class of meshless method. Given the absence of a pre-determined connectivity among nodes, such methods are mainly used in applications where large deformations are involved, such as fluid-dynamics. In the present work we combine the Modified Finite Particle Method with a Weighted Least Square Residual Method, and use the combined version of the method for the solution of saddle point problems, such as the Stokes and Navier–Stokes equations for incompressible fluid flow simulations. The use of MFPM derivative approximation techniques in the framework of Least Square Residual Method permits a simple handling of the numerical difficulties typical of incompressible fluid simulations, avoiding problems such as pressure spurious oscillations, and preserving the convergence properties of the Modified Finite Particle Method also in presence of random collocation point distributions.

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

In the present paper we propose a new class of analytical solutions for the equilibrium problem of a prismatic sand pile under gravity, capturing the effects of the history of the sand pile formation on the stress distribution. The material is modeled as a continuum composed by a cohesionless granular material ruled by Coulomb friction, that is a material governed by the Mohr-Coulomb yield condition. The closure of the balance equations is obtained by considering a special restriction on stress, namely a special form of the stress tensor relative to a special curvilinear, locally non-orthogonal, reference system. This assumption generates a class of closed-form equilibrium solutions, depending on three parameters. By tuning the value of the parameters a family of equilibrium solutions is obtained, reproducing closely some published experimental data, and corresponding to different construction histories, namely, for example, the deposition from a line source and by uniform raining. The repertoire of equilibrated stress fields that we obtain in two special cases contains an approximation of the Incipient Failure Everywhere (IFE) solution and a closed-form description of the arching phenomenon. © 2016, Elsevier Ltd. All rights reserved.

The air puff test is an in-vivo investigative procedure commonly utilized in ophthalmology to estimate the intraocular pressure. Potentially the test, quick and painless, could be combined with inverse analysis methods to characterize the patient-specific mechanical properties of the human cornea. A rapid localized air jet applied on the anterior surface induces the inward motion of the cornea, that interacts with aqueous humor-the fluid filling the narrow space between cornea and iris-with a strong influence on the dynamics of the cornea. While models of human cornea reproduce accurately patient-specific geometries and have reached a considerable level of complexity in the description of the material, yet scant attention has been paid to the aqueous humor, and no eye models accounting for the physically correct fluid-solid interaction are currently available. The present study addresses this gap by proposing a fluid-structure interaction approach based on a simplified two-dimensional axis-symmetric geometry to simulate the anterior chamber of the eye undergoing the air puff test. We regard the cornea as a membrane described through an analytical model and discretize the fluid with a mesh-free particle approach. The membrane is assumed to be nonlinear elastic and isotropic, and the fluid weakly compressible Newtonian. Numerical analyses reveal a marked influence of the fluid on the dynamics of the cornea. We perform a parametric analysis to assess the quantitative influence of geometrical and material parameters on the mechanical response of the model. Additionally, we investigate the possibility to use the dynamics of the test to estimate the intraocular pressure.

The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.

We present a numerical procedure for the simulation of the air puff test, a medical procedure used by ophtalmologists for the identification of the Intra Ocular Pressure, and potentially useful for the identification of material properties of the human cornea. The problem involves the modeling of the cornea, that is a biological tissue, modelled as an hyperelastic material, and the aqueous humor, that is, the fluid filling the anterior chamber of the eye, that is treated as a Newtonian fluid, and modelled using a meshfree formulation, useful for the solution of a Fluid-Structure Interaction problem. Fluid and Structure are coupled using a Dirichlet-Neumann iterative approach, which permits the adoption of a partitioned coupling approach and explicit, fast solvers for the different subproblems.

SUMMARY Particle methods are a class of numerical methods that belong to the family of meshless methods and are not based on an underlying mesh or grid, but rather on any general distribution of particles. They are nowadays widely applied in many fields, including, for example, solid mechanics, fluid dynamics, and thermodynamics. In this paper, we start from the original formulation of the so-called modified finite particle method (MFPM) and develop a novel formulation. In particular, after discussing the position of the MFPM in the context of the existing literature on meshless methods, and recalling and discussing the 1D formulation and its properties, we introduce the novel formulation along with its extension to the approximation of 2D and 3D differential operators. We then propose applications of the discussed methods to some elastostatic and elastodynamic problems. The obtained results confirm the potential and the flexibility of the considered methods, as well as their second-order accuracy, proposing MFPM as a viable alternative for the simulation of solids and structures. Copyright © 2014 John Wiley & Sons, Ltd.

The idea of a no-tension (NT) material underlies the design of masonry structures since antiquity. Based on the NT model, the safety of the structure is a problem of geometry rather than of strength materials, in the same spirit of the “rules of proportion” of the medieval building tradition. The use of singular stress fields for equilibrium problems of NT materials in 2d, has been recently proposed by Lucchesi et al. to produce statically admissible stress fields; here we introduce a simple way to construct singular stresses, based on the Airy’s stress formulation. We interpret the singular part of such stress fields as axial contact forces acting on ideal 1d structures arising inside the body, in the same spirit of Strut and Tie methods. A number of simple problems of equilibrium concerning typical walls, arches and portals, is solved in terms of stress fields having regular and singular parts, by adopting the direct and the stress function formulation. The validity of the rules of proportion described by Derand and Gil is also verified.

In this paper, we study the fluid-structure interaction in a weakened basilar artery. The aim is to study how the wall shear stress changes in space and time because of the weakening, because spatial and temporal changes are thought to be possible causes of aneurysm and vascular deseases. The arterial wall, in its natural configuration, is modeled as a hyperelastic cylinder, inhomogeneous along its axis, in order to simulate the axis-symmetric weakening. The fluid is studied exploiting a recent approach for quasi-one-dimensional flows in slowly varying ducts, which allows to write the averaged equations of mass and energy balance on the basis of the velocity profile in a straight duct. The unknowns are the wall pressure, the average velocity, and the wall radial displacement. The problem is solved in two parts: first, the stationary non-linear coupled problem is solved, and an intermediate configuration is obtained. Then, we study the variation of the basic unknowns about the intermediate configuration, considering time dependence over the cardiac cycles. The results suggest that, with a 10% reduction of the main elastic modulus, the shear stress in the weakened zone changes its sign and doubles the maximum stress value detected in the healthy zone. Copyright © 2015 John Wiley & Sons, Ltd.

This paper analyses the demographic and institutional influences underlying public spending on education, as well as the consequences for average educational attainment and economic growth. The issues are topical given, on one hand, EU objectives for increased investment in human resources and, on the other, increasing concerns about the sustainability of public finances, particularly in view of ageing populations. The paper presents methodologies for projecting educational attainment and public expenditure on education. Tentative numerical results suggest that the growth of average educational attainment is likely to slow slightly, compared to recent decades. Nevertheless, education is set to continue making a substantial contribution to economic growth in the EU as a whole, though the impact varies widely among Member States. As regards public expenditure, although demographic trends mean a reduction in the potential number of students, this is offset by two factors: increasing enrolment rates at upper-secondary and tertiary level (projected taking into consideration either past developments in enrolment or the expected future evolution of labour force); and increasing expenditure per student (projected on the basis of recent trends). Thus, few savings - if any - are expected from reductions in expenditure on education due to changes in the demographic structure.

In this paper, we study the equilibrium of masonry vaults, assuming that the material has infinite friction and no cohesion (i.e. it is No-Tension in the sense of Heyman). With Heyman's assumptions, the equilibrium of a structure composed of this ideal masonry material, can be studied with limit analysis. In particular, the present study is concerned with the application of the safe theorem of limit analysis to masonrylike vaults, that is, curved constructions modelled as continuous unilateral bodies. On allowing for singular stresses in the form of line or surface Dirac deltas, statically admissible stress fields concentrated on surfaces (and on their folds) lying inside the masonry, are considered. Such surface and line structures are unilateral membranes/ arches, whose geometry is described a la Monge, and their equilibrium can be formulated in Pucher form. It is assumed that the load applied to the vault is carried by such a (possibly folded) membrane structure S. The geometry of the membrane S, that is of the support of the singularities, is not fixed, in the sense that it can be displaced and distorted, provided that one keeps it inside the masonry. Two particular case studies are analyzed to illustrate the method: A cross vaults of the Gothic Cathedral of Caserta, and a modern timbrel spiral stair built by the Guastavinos in New York. © Civil-Comp Press, 2015.

This paper focuses on the application of the Modified Finite Particle Method (MFPM) on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.