Luciano Rosati

• University of Naples Federico II

We illustrate the performances of a brand new hysteretic model, recently proposed and denominated VRM+D, to characterize the nonlinear response of mechanical systems endowed with quite complex hysteretic behaviors. To this end, we combine the VRM+D with a continuation procedure based on Poincaré maps developed by Lacarbonara et al. in 1999. In this...

A recent analytical model of hysteresis, developed by the authors to simulate a great variety of complex uniaxial rate-independent mechanical hysteresis phenomena, is reformulated in a twofold manner. First, it is proposed an analytical reformulation that, compared to the current version of the model, does not require the evaluation of any internal...

In the present contribution a general formulation is proposed to account for general boundary conditions within the dynamic analysis of anisotropic laminated doubly-curved shell having arbitrary shape and variable thickness. Different analytical expressions are considered for the shell thickness variation along the geometrical principal directions,...

The accuracy of procedures for the analysis and design of hysteretic mechanical systems, in which both generalized rate-dependent and rate-independent hysteretic forces have a non-conservative nature, can be significantly improved by a straightforward computation of work and energy terms. Thus, with the aim of shedding light on the definition and e...

This paper illustrates the simulation of the complex hysteresis loops obtained by a cyclic experimental test carried out on an angular bracket; the related experimental data have been retrieved from the current scientific literature. In particular, the pinched and asymmetric hysteresis loop shapes are reproduced by using the recently formulated Vai...

An experimental campaign aiming to study the dynamic response of four different helical Wire Rope Isolators (WRIs) loaded along the axial direction is described in the paper. A total of seventy-one tests have been carried out by applying as input, to each of them, ten cycles of sinusoidal displacement. Specifically, the dynamic response of the WRIs...

The application of a recent beam model requires the evaluation of a suitably defined shear deformability tensor in order to ensure both energetic and geometric consistency with the 3D Saint Venant model subjected to non-uniform flexure and torsion. Actually, whatever is the position of the shearing force, the beam model provides the same elastic en...

The paper illustrates an extension of a solution algorithm required to evaluate the output variable of a modified Bouc-Wen model, namely a differential model capable of simulating generalized force-displacement hysteresis loops exhibiting cyclic softening and/or pinching. The proposed solution scheme has been derived by adopting the Backward Euler...

The number and nature of hysteretic responses typically exhibited by mechanical systems and materials are so huge that their modeling and identification are usually carried out on an ad-hoc basis. Thus, with the aim of proposing a unified approach to the modeling of rate-independent hysteretic behavior, we first perform a detailed classification of...

The fulfillment of the Drucker postulate applied to a phenomenological hysteretic constitutive model is hereby investigated. Such a material is defined in terms of analytical functions so that it is capable of determining the response and its tangent operator in closed form and does not require any iterative algorithm. Hence, the constitutive model...

This paper investigates the rocking behavior of rigid bodies seismically protected by means of lead rubber bearings and high damping rubber bearings, which are the most popular kinds of elastomeric isolators in the market. The complex nonlinear force–displacement relationship displayed by such devices is predicted by a phenomenological model based...

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling hig...

The paper addresses the theoretical framework and the numerical procedure developed to carry out the sectional analysis preliminary to the use of a recently formulated isotropic and homogeneous beam model consistently derived from the Saint Venant solid one. Specifically, in order to ensure the equivalence of the new beam model with the 3D solid on...

The complex response characterizing elastomeric isolation bearings is reproduced by employing a novel uniaxial hysteretic model that has been recently formulated and successfully implemented in OpenSees. Such a novel OpenSees material model offers several advantages with respect to differential models typically available in commercial software prod...

We extend a recently developed class of uniaxial symmetric rate-independent models to simulate complex asymmetric mechanical hysteresis phenomena. The main features of the novel formulation, that allows for the evaluation of the generalized force by solving a scalar equation and employing only one history variable, are illustrated by developing two...

Mathematical modeling of hybrid soft robots is complicated by the description of the complex shape that they undergone when subject to actuation and external loads. It might be noticed that several approaches have been used so far in robotics, and the problem is not yet fully solved. This short paper aims at presenting an overview of modeling and s...

Influence of non-structural elements on the seismic response of nonlinear systems is hereby investigated. In particular, tail-equivalent linearization has been adopted because of its capability of determining the statistics of stochastic response processes in order to characterize secondary excitation. A random vibration analysis determined a param...

In this work we investigate the rocking response of the Riace bronze A, a slender statue modelled as an equivalent rigid body freestanding on an isolated base supported on: (a) Steel Reinforced Elastomeric Bearings, (b) Fiber Reinforced Elastomeric Bearings, (c) Flat Surface Sliding Bearings, and (d) Curved Surface Sliding Bearings. The dynamic res...

We present a systematic approach to the derivation of complete solutions for three-dimensional transversely isotropic elastic problems. The class of solutions derived in the paper is obtained by exploiting the entire kernel of the differential operator \(\mathcal {C}\) expressing the elastic equilibrium problem of transversely isotropic media. In p...

The paper illustrates the numerical procedure, based upon a Boundary Element (BE) approach, developed to efficiently evaluate the warping functions in the Saint Venant theory of beam-like solids having both compact and thin-walled sections. Specifically, Chebyshev nodes are selected as collocation points of the BE formulation associated with the re...

Nonlinear time history analysis represents the most appropriate structural analysis procedure to accurately analyze seismically base-isolated structures since their dynamic response is typically governed by a system of coupled nonlinear ordinary differential equations of the second order in time. The selection of a suitable phenomenological model,...

We discuss the energetic and geometric consistency of a one-dimensional (1D) beam model based on the Saint-Venant three-dimensional (3D) solution of a beam-like solid, with a focus on the effects associated with shear stresses. In particular we prove that a geometric model of the beam can be defined so as to provide the same elastic energy of the S...

Starting from the recent reformulation of the Thrust Network Analysis (TNA) developed by the authors, we further generalize the method in order to include triangular stress elements, used to model membrane thrusts within the analysis process. These elements substitute the classical network branches so that the correspondence between thrust stresses...

An inverse strategy is developed for identifying the parameters of the hysteretic phe-nomenological constitutive model presented in Vaiana et al. (2019) and belonging to a wider class of hysteretic models. The model, differently from the celebrated Bouc-Wen one, permits the definition of either stress-strain or load-displacement relationships by cl...

This paper reports on a collaborative activity developed as part of the DPC-ReLUIS Research Project, year 2017. It aims at comparing the results obtained by considering alternative options in the definition of the nonlinear FEM model employed in pushover analyses for seismic assessment of existing RC frames. Specifically, the RC frame structure of...

This paper presents a computational strategy that combines a novel rate-independent phenomenological model with an explicit time integration method to efficiently perform nonlinear dynamic analyses of non-stiffening hysteretic mechanical systems. The novel rate-independent model, developed by specializing a general class of uniaxial phenomenologica...

The bridge over the Basento river in Potenza, Italy, designed by Sergio Musmeci, is supported by a continuous double-curvature RC shell optimized to reduce bending forces. This 300 m long bridge can be considered as a unique representative example of pioneering research on the design and construction of optimized structures. First, the design proce...

Capacity domains of reinforced concrete elements, computed according to Eurocode 2 provisions, have been investigated from a probabilistic perspective in order to examine the variability of the failure probability over different regions of the domain boundary. To this end, constitutive parameters, such as limit stresses and strains, have been defin...

Through-the-thickness (TT) confinement of masonry and concrete panels by composite or steel reinforcements, aiming at seismic retrofit of existing structures, has recently growth in popularity. However, structural design of transversal reinforcements, modelled as an homogeneized material, is often performed by neglecting the cyclic nature of seismi...

Dear Colleagues, within the International Conference on Nonlinear Solid Mechanics, to be held in Rome on June 16-19 2019, we are organizing a Mini-Symposium on Mathematical Models and Numerical Methods for Hysteretic Mechanical Systems and Materials (http://www.memocsevents.eu/iconsom2019/mini-symposia/). We are pleased to invite you to participa...

A procedure is presented for performing Eurocode 8-compliant spectral analyses of reinforced concrete structures by means of seismic response envelopes. To account for global torsion effects in the computation of the supreme envelope an algorithmic rotational response spectrum is defined. The presented strategy turns out to be particularly appropri...

We present a uniaxial phenomenological model to accurately predict the complex hysteretic behavior of bolted steel reinforced elastomeric bearings and unbonded fiber reinforced elastomeric bearings. The proposed model is based on a set of only five parameters, directly associated with the graphical properties of the hysteresis loop, leads to the so...

We illustrate the consistent derivation of a one-dimensional (1D) beam model from the Saint Venant three-dimensional (3D) solution of a beam-like solid that aims at the formulation of a 1D finite element able to reproduce the 3D elastic solution. The derivation is achieved by enforcing the equivalence between the 3D solid model and the 1D beam both...

We present a general formulation of a class of uniaxial phenomenological models, able to accurately simulate hysteretic phenomena in rate-independent mechanical systems and materials, which requires only one history variable and leads to the solution of a scalar equation for the evaluation of the generalized force. Two specific instances of the cla...

Starting from the recent reformulation of the Thrust Network Analysis (TNA) developed by the authors, we further generalize the method in order to include triangular stress elements, used to model membrane thrusts within the form-finding process. These elements substitute the classical network branches so that the correspondence between thrust stre...

The efficiency of a structure is strongly affected by its form and therefore its optimization is essential. The aim of this study is to investigate and discuss the form of the Musmeci bridge over Basento river in Potenza (Italy). This bridge can be considered a paradigmatic example of the form optimization of reinforced concrete shell structures. A...

This paper reports on a collaborative activity developed as part of the DPC-ReLUIS Research Project, year 2017. It aims at comparing the results obtained by considering alternative options in the definition of the nonlinear FEM model employed in pushover analyses for seismic assessment of existing RC frames. Specifically, the RC frame structure of...

We report on a historical study and on the evaluation of the structural performance of an innovative vaulting system developed in the 17th and 18th centuries. This peculiar construction technique, which employed clay hollow cylinders as construction blocks, was used to reduce erection times and costs as well as to guarantee several static and funct...

In recent years, considerable attention has been paid to research and development methods able to assess the seismic energy propagation on the territory. The seismic energy propagation is strongly related to the complexity of the source and it is affected by the attenuation and the scattering effects along the path. Thus, the effect of the earthqua...

Through-the-Thickness Jacketing (TTJ) is a technique for repairing and retrofitting shell structures by inducing in the shell core a beneficial confining stress state created by a net of broadly distributed retrofitting links crossing the shell thickness and tying externally applied layers. The paper presents the derivation, the algorithmic impleme...

We derive the analytical expression of the Eshelby tensor field for inclusions of arbitrary polyhedral shape. The formula contributed in the paper is directly expressed as function of the coordinates defining the vertices of the polyhedron thus avoiding the use of complex variables and anomalies exploited in previous contributions on the subject. I...

We exploit a recent generalization of the Thrust Network Analysis (TNA) to analyse masonry structures of extremely complicated and audacious geometry such as helicoidal staircases. Actually, differently from available methods, based on ad-hoc solutions holding for each particular structure, the TNA allows for studying the equilibrium of structures...

Through-the-Thickness Jacketing (TTJ) is a technique for repairing and retrofitting shell structures by inducing in the shell core a beneficial confining stress state created by a net of broadly distributed retrofitting links crossing the shell thickness and tying externally applied layers. The paper presents the derivation, the al-gorithmic implem...

The classical Eurocode-compliant ultimate limit state (ULS) analysis of reinforced concrete sections is investigated in the paper with the aim of verifying if and how this well-established design procedure can be related to plasticity theory. For this reason, a comparative analysis concerning capacity surfaces of reinforced concrete cross sections,...

A general procedure for the numerical solution of three-dimensional normal and tangential contact problems for non-conforming bodies of arbitrary shape is presented. The proposed procedure is based on the interpolation of known analytical solutions relating surface displacements of an elastic half-space subjected to pyramidal distributions of norma...

Jacketing of masonry walls employing Through-the-Thickness ties (TTJ) represents a widespread and effective technique for seismic retrofit of historical structures since confinement induced by these elements can increase structural ductility and strength. In this respect the authors have recently proposed a deterministic Equivalent Single Layer (ES...

An effective strategy for seismic retrofit of existing structures [1], such as reinforced concrete or masonry shear walls, vaults and shells, is represented by Through-the-Thickness Jacketing (TTJ) that amounts to employing steel, FRP, glass or aramidic ties crossing the thickness of the original structure. In particular this reinforcing technique...

Gustav Kirchhoff has been credited, among many other renowned achievements, as the first scientist who tackled and solved the problem of studying the transversal vibrations of beams with variable cross-section. His contribution, which was presented in 1879 and published in the following year, is nowadays almost forgotten in the international scient...

We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O’Dwyer and fully developed by Block and coworkers. Reducing the bias by the quoted authors in favor of a graphical interpretation of the method, we reformulate...

The paper proposes a generalized shell formulation devised for the triaxial stress analysis of Through-the-Thickness (TT) confining mechanisms induced by TT Jacketing (TTJ) devices in laminated composite structures, such as masonry walls retrofitted by stirrups-tied FRP sheets and TT jacketed concrete sandwich panels. Assuming a smeared descripti...

We generalize a recent application of the equivalent inclusion method, Jin et al. (2011), to derive the elastic field induced by a constant eigenstrain applied to an elliptic inclusion whose boundary is approximated by a polygon, the number of sides being assigned so as to recover the analytical values of the entries of the Eshelby tensor. The gene...

We outline a general methodology for proving the equivalence between several solutions available in the literature for the elastic problem of transversely isotropic materials. The proposed methodology is mathematically supported by a novel solution strategy yet arriving at the same expression of the displacement field contributed by Ding et al. (20...

The Eshelby tensor field is evaluated analytically for polygonal inclusions of arbitrary shape. The formula contributed in the paper is directly expressed as function of the coordinates defining the vertices of the polygon, thus avoiding the use of complex variables and anomalies exploited in previous contributions on the subject. It has been obtai...

We derive the analytical expression of the Eshelby tensor field for inclusions of arbitrary polygonal shape. Differently from previous contributions in the literature, the formula proved in the paper has a particularly compact expression since it is based on the analytical evaluation of integrals depending by lower exponents of the scalar product o...

The classical Cerruti problem of an isotropic homogeneous half-space subject to a concentrated load tangential to its surface is extended to cope with linear distributions of loads acting over a polygonal domain. The approach is based upon a generalized version of the Gauss theorem and recent results of potential theory which consistently take into...

We outline a general approach for extending the classical Boussinesq’s solution to the case of pressures distributed according to a polynomial law of arbitrary order over a polygonal domain. To this end we exploit a generalized version of the Gauss theorem and recent results of potential theory which consistently take into account the singularities...

We provide analytical formulas and design charts for computing displacements, strains and stresses in transversely isotropic half-spaces subject to linearly distributed vertical pressures. The domain integrals extended to the loaded region, resulting from the solution associated with a vertical point load, are first transformed into boundary integr...

We derive a design chart for the analysis of masonry gravity walls in the archeological area of Pompei. The proposed methodology, based on the prescriptions of the Italian seismic code, can be used as well for a rapid dimensioning.

A comprehensive survey is presented on two-phase and multi-phase continuum poroelasticity theories whose governing equations at a macroscopic level are based, to different extents, either on the application of classical variational principles or on variants of Hamilton’s least Action principle. As a focal discussion, the ‘closure problem’ is recall...

This study presents an analysis of the stress-partitioning mechanism for fluid saturated poroelastic media in the transition from drained (e.g. slow deformations) to undrained (e.g. fast deformation) flow conditions. The goal of this analysis is to derive fundamental solutions for the general consolidation problem and to show how Terzaghi’s law is...

By exploiting the theory of the response envelopes formulated by Menun and Der Kiureghian [Envelopes for seismic response vectors. I–Theory, J. Str. Engrg. 2000; 126(3); 467–473], an algorithmic approach for seismic analysis of reinforced concrete frames is presented. It aims to fill a gap between research on spectral analysis of structures and cur...

The mechanics of stress partitioning in two-phase porous media is predicted on the basis of a variational purely-macroscopic theory of porous media (VMTPM) with compressible constituents. Attention is focused on applications in which undrained flow (UF) conditions are relevant, e.g., consolidation of clay soils and fast deformations in cartilagineo...

The linearized version of a recently formulated Variational Macroscopic Theory of biphasic isotropic Porous Media (VMTPM) is employed to derive a general stress partitioning law for media undergoing flow conditions under prevented fluid seepage and negligible inertia effects, typically met in biphasic specimens subjected to jacketed tests. The pr...

We outline a general approach for evaluating the displacement, stress and temperature fields within an isotropic elastic half-space subject to a uniform heat source acting over an arbitrary region of its free surface. To this end we make systematic use of the Gauss theorem and exploit recent results in potential theory.

The paper illustrates a solution approach for the Saint-Venant flexure problem which preserves a pure objective tensor form, thus yielding, for sections of arbitrary geometry, representations of stress and displacement fields that exploit exclusively frame-independent quantities. The implications of the availability of an objective solution to the...

It has been shown in a previous paper that the normal stress resultants for an arbitrary polygonal section endowed with a uniaxial elastoplastic law can be computed exactly by means of a general approach; it has been denominated fiber free as no fiber discretization of the section is required. The aim of this paper was to extend the fiber-free appr...

We present a family of algorithms for evaluating the ultimate limit state of composite and reinforced concrete (RC) sections of arbitrary polygonal or circular shape, either simple or multicell, subject to axial force and biaxial bending. All algorithms are based upon a secant strategy for computing the stiffness matrix used in the equilibrium iter...

Within the framework of flexibility formulations we present a frame element which enhances the performances of previously formulated elements in a threefold manner. First, the analytical evaluation of the section integrals is carried out by means of the fiber-free approach, what avoids the use of the inaccurate fiber method; second, a variationally...

We present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto-plastic uniaxial constitutive laws. By means of a suitable application of Gauss theorem, we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely a...

The paper illustrates a biphasic formulation which addresses the dynamic response of fluid saturated porous biphasic media at finite deformations with no restriction on the compressibility of the fluid and of the solid skeleton. The proposed model exploits four state fields of purely kinematic nature: the displacements of the solid phase, the veloc...

A secant approach is illustrated for the ultimate limit state (ULS) analysis of prestressed reinforced concrete sections subjected to axial load and biaxial bending in presence of softening stress–strain laws. The stiffness matrix and the resultant loads are evaluated analytically by a novel methodology, termed fiber-free, which represents a comput...

In the present contribution a novel model for the description of the dynamic response of biphasic media at finite deformations is illustrated. The model is formulated by means of eight kinematic scalar fields: the displacement field of the solid phase, the velocity of the fluid, the density of fluid and an additional scalar field associated with th...

The implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three-invariant elastoplastic models under plane stress conditions discussed in Part I of this paper [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part I: Theoretical...

A derivation of the projected algorithm for general isotropic three-invariant plasticity models under plane stress conditions is presented. It is obtained by consistently specializing the 3D formulation to the 2D subspace defined by the plane stress condition. Closed-form intrinsic algorithm linearization and a novel expression of the consistent ta...