Achille Paolone

• Full Professor
• Sapienza University of Rome

Even local small cracks may induce instability and failure or operativity loss before the crisis for the intact material is actually attained. Thus, damage models and the possibility of their identification have become trendy subjects in structural mechanics. We previously studied buckling and post-buckling of parabolic arches with a local transver...

Reinforced concrete structures are often subject to significantly non‐uniform corrosion patterns. In real situations, the information available about deterioration is incomplete and sometimes is reduced to qualitative judgments formulated by inspectors based on in‐situ surveys. This work proposes a practice‐oriented fiber‐based modeling approach ca...

Reinforced concrete bridge piers are often subject to spatially non-uniform deterioration which typically produces strength and ductility degradation. When piers are subject to deterioration, the sectional response is no longer uniform and the determination of the pushover curves from sectional response is no longer immediate. This paper proposes a...

The current basic OpenSees distribution includes several uniaxial models for concrete. Among them, the model proposed by Chang and Mander in 1994 offers a comprehensive setting applicable both to confined and unconfined concrete, by a proper selection of material parameters. The model offers the possibility to smoothly combine Tsai equation, for th...

Existing reinforced concrete (RC) bridge piers are often subject to complex spatially non-uniform steel corrosion patterns typically due to water percolation and exposition to environmental agents. This produces degradation of strength and ductility of the pier, which may significantly influence the seismic performances of bridges. The computation...

Historical masonry structures represent a conspicuous part of the European architectural heritage. However, these often are more vulnerable to damage risk than other constructions due to their peculiar mechanical properties. This justifies the lively interest in the development of efficient and reliable approaches for their structural capacity asse...

Since most of the historical building heritage of many countries consists of masonry, such structures are of great interest in civil engineering. Unfortunately, the intrinsic chaotic nature of the masonry material results in poor tensile strength and poor ductility, from the mechanical point of view, and great modeling difficulties, from the engine...

The response of slender bridge piers to horizontal actions may be significantly influenced by geometric nonlinearities. In such conditions, the use of sophisticated models implemented in complex structural analysis software can be economically disadvantageous, especially in the preliminary design phases. This paper proposes a simple numerical proce...

Steel corrosion in Reinforced Concrete (RC) bridge piers may occur due to particular environmental expositions or percolation of aggressive water from superstructures. In some cases, the causes of corrosion are non-uniformly distributed and produce non-homogeneous spatial deterioration patterns that can modify the capacity of the piers both in term...

Most studies on cracked one-dimensional structural elements deal with their statics and free dynamics, while their stability is only given marginal consideration, especially arches. This chapter investigates buckling and post-buckling of parabolic arches with crack-like damages. The environment acts on the arch by: a vector force field, power dual...

Structural monitoring plays a central role in civil engineering; in particular, optimal sensor positioning is essential for correct monitoring both in terms of usable data and for optimizing the cost of the setup sensors. In this context, we focus our attention on the identification of the dynamic response of beam-like structures with uncertain dam...

Damage, be it a material or a geometric degradation, modifies some features of the response foreseen by the original structural design. These variations, once the dependence on the damage causing them is established, can be used for identification purposes. In the literature, vibration‐based approaches usually compare some responses of linear elast...

The statics of fully deformable parabolic arches affected by a small crack at opposite sides of a damaged cross section is studied. The finite governing equations are linearized; the mechanical response for ‘small’ displacements and rotation is assumed. The effect of the crack is modelled by springs with stiffnesses calculated through linear elasti...

This paper addresses the problem of identifying structural damage affecting one element of a steel truss. The purpose is to detect damages in relation to their magnitude, location and extension. A planar model of a damaged steel truss is used to illustrate the procedure. The direct problem is addressed by FEM, proposing the local stiffness of a dam...

This paper is dedicated to the identifiability of vibrating beam structures with uncertain damages. The probability of damage occurrence is computed assuming a Gaussian distributed random damage parameter. Then, we propose a technique for selecting an optimized solution of sensors placement based on the comparison among the probability of damage oc...

This work investigates the capabilities of two different approaches for the analysis of thin-walled structures, both based on enriched beam theories that include out-of-plane cross-section warping, being the in-plane deformations neglected. First approach relies on a three-dimensional beam finite element based on a four-field mixed formulation, whe...

This book gathers the peer-reviewed papers presented at the XXIV Conference of the Italian Association of Theoretical and Applied Mechanics, held in Rome, Italy, on September 15-19, 2019 (AIMETA 2019). The conference topics encompass all aspects of general, fluid, solid and structural mechanics, as well as mechanics for machines and mechanical syst...

A structural damage identification technique hinged on the combination of orthogonal empirical mode decomposition and modal analysis is proposed. The output-only technique is based on the comparison between pre- and post-damage free structural vibrations signals. The latter are either kinematic (displacements, velocities or accelerations) or deform...

Dissipative properties of a structural system are difficult to be characterized in real structure. Nevertheless, damping features may be dominant in several operating conditions of railway bridges influencing fatigue life or passenger comfort during train passage. Observations treating real data acquired in operational condition on steel and concre...

We propose a mixed variational principle for deducing the generalized Marguerre–von Kármán equations, governing the relatively large deflections of thin elastic shallow shells. These equations account for both non-flat stress-free configurations of the shell and inelastic strains. We implement this formulation by using \(C^0\) interior penalty meth...

A mixed variational principle is proposed for deducing the Föppl–von Kármán equations governing the large deflections of thin elastic plates or shallow shells. Proper boundary conditions are found for the case of applied in-plane tractions and displacements, and simple mechanical interpretations are achieved. Numerical implementation is carried out...

This paper presents the formulation of a three-dimensional beam finite element (FE) that accounts for cross-section warping and dynamic inertia effects. The model is the extension of an existing mixed formulation, originally developed for the static analysis of thin-walled beams, to the case of dynamic loading conditions. Four independent fields ar...

The papers focusing on dynamic identification of structural damages usually rely on the comparison of two or more responses of the structure; the measure of damage is related to the differences of the vibration signals. Almost all literature methods assume damping proportionality to mass and stiffness; however, this is acceptable for new, undamaged...

Structural damping in high-speed railway bridges is a key parameter that affects significantly the performance of the structure in terms of fatigue life and comfort of the passengers and hence has a significant impact on the design procedures. For these reasons its accurate assessment is a paramount task to be performed and hence the results of an...

Damage detection and localization in structural systems is experimentally studied. A novel pseudo-modal approach, recently proposed by some of the authors, is adopted. It is based on the comparison between free vibrations of the undamaged and damaged states, and aims to maximize the damage signature embedded in the data by exploiting the energy con...

The seismic vulnerability assessment of masonry buildings reinforced with FRP was investigated by means of random sampling of their mechanical properties and repeated nonlinear static analyses. To this aim, the Monte Carlo simulation method was adopted to account for the uncertainty of the mechanical parameters characterizing the analytical model r...

The evaluation of physical models able to properly reproduce the dissipative properties of railway bridges is a crucial task for fatigue life and comfort analyses. In this work a parametric model of a usual structural system (beam bridge) is adopted to determine the main damping features of real-life bridges. The results of several experimental cam...

The evaluation of the residual stresses in prestressed concrete structures is nowadays a significant target. Road and rail bridges are ones of the meaningful cases of interest; indeed, the growth of traffic, for the actions, and long-term phenomena and age degradation, for the resistances, often imply for such structures a strong reduction of the i...

We present the use of piezoelectric disk buzzers, usual in stringed musical instruments to acquire sound as a voltage signal, for experimental modal analysis. These transducers helped in extracting natural frequencies and mode shapes of an aluminium beam and a steel arch in the laboratory. The results are compared with theoretical predictions and e...

The hybridisation of fibres reinforced laminates, i.e., the combined use of two or more families of fibres, is an effective technique to achieve a pseudo-ductile response and overcome the inherent brittleness which limits the wider use of composite materials. In this paper, a one-dimensional analytical model for unidirectional hybrid laminates is d...

Piezoelectric disk buzzers are commonly used on stringed musical instruments to acquire the sound in the form of a voltage signal. Aim of the present investigation is to assess the possibility of using these transducers for experimental modal analysis. Piezoelectric disks were therefore used in the laboratory to extract the natural vibration freque...

The detection of structural damping is a crucial point in structural identification. Classic techniques usually refer to deterministic systems, since the assumption of randomness in the mechanical quantities implies non-trivial analytical difficulties in the development of both the direct and the inverse problem. In some recent works, starting from...

Uncertainty characterization plays a key role in the safety assessment of many engineering structures. Nevertheless, the inverse problem for structures with uncertain parameters has received less attention than the relevant direct one, since one deals with stochastic structural system identification. This paper discusses the dynamic identification...

Localization of damages becomes rather challenging when the associated stiffness reduction is small in presence of structural uncertainties. This work presents a sensitivity analysis and an improvement of a novel pseudo-modal approach, recently proposed by the authors. Starting from free vibrations of the undamaged and damaged states, the method ai...

Time-frequency vibration signals processing technique and modal-based properties are combined to localize structural damage. The approach is devised to detect and locate damaged areas in the structure from its free vibrations and relies on the comparison between information gathered for the undamaged and damaged states. Extending previous studies b...

This paper deals with the identification of linear structural systems with random parameters. The stiffness matrix of a four-storey shear frame structure is assumed to be linearly dependent on a random parameter ruling the damage evolution of the columns. The evaluation of natural frequencies and the mode-shapes is in the context of random eigenval...

We investigate the effects of warping on the dynamic stability of non-trivial equilibrium configurations for non-symmetric open thin-walled beams. We use a direct one-dimensional model coarsely describing warping; the rest of the kinematics is exact. Dynamic derives from the balance of power; constitutive relations are non-linear, hyper-elastic, an...

The aim of the paper is to propose and assess a simplified FE modeling strategy to simulate the global behavior of masonry structures externally reinforced with FRP composite strips applied with a grid configuration and anchored properly at their ends. The nonlinear behavior of the masonry is represented by a mascroscopic smeared crack approach. Th...

A direct model coarsely describing warping, endowed with nonlinear constitutive relations, yields field equations for open thin-walled beams. They are numerically integrated by an in-house numerical code, providing non-trivial equilibria and examining their stability. We investigate warping effects on critical loads and natural frequencies for gene...

We report about the experimental identification of viscoelastic constitutive models for frequencies ranging within 0–10 Hz. Dynamic moduli data are fitted for several materials of interest to medical applications: liver tissue (Chatelin et al., 2011), bioadhesive gel (Andrews et al., 2005), spleen tissue (Nicolle et al., 2012) and synthetic elastom...

Localized damage in a parabolic arch is identified by combining a time-frequency vibration signals processing technique and modal-based properties. The approach is devised to detect and locate damaged areas in the structure from its free vibrations and relies on the comparison between information gathered for the undamaged and damaged states. The n...

This work investigates the in-plane behaviour of a masonry building facade before and after structural interventions with epoxy-based unidirectional FRP strips. To this end, a simple macro-modeling approach is proposed for the simulation of the XVIII century Camponeschi Palace facade in the city of L'Aquila, Italy, damaged by the 2009 earthquake. T...

The seismic capacity of masonry arches with circular shape is studied in this paper. The analytical procedure presented moves stems from the limit analysis of local mechanisms prescribed by the current Italian code. An analytical model is developed, which provides a simple tool for quick seismic evaluations of existing arches and for the design of...

Dynamic characteristics of linear structural systems are governed by natural frequencies and mode-shapes. In this work we focus on linear discrete structures dependent by a random parameter, assumed to be Gaussian. A perturbation approach is adopted in order to perform a computationally advantageous solution strategy. We at first study the random e...

The free dynamics of a parabolic arch is studied in order to identify a localized damage. The identification technique is based on the combined use of time-frequency vibration signals processing and modal-based properties referred to finite element models of the arch. By relying on the information gathered for the undamaged and damaged states, the...

Literature often studies stability of trivial equilibrium paths, relying on suitable constraints; however, here we study stability of non-trivial, non-linear solutions of the equilibrium field equations for thin-walled cantilevers under end shearing forces, either dead or follower, using a direct one-dimensional model coarsely describing warping. W...

We investigate inner shearing constraints for a direct one-dimensional beam model coarsely describing warping. In particular, we study how they affect the field equations for the elastic buckling of open thin-walled beams. We show that the distinction between the axes of the shear centres and of the centroids is crucial for the kinematics of the be...

Si studia la stabilità alla Ljapounov di forme d’equilibrio non banali di travi in parete sottile asimmetriche. Il modello, monodimensionale diretto, ha cinematica finita e un descrittore sommario d’ingobbamento. La dinamica deriva dal bilancio di potenza, le relazioni costitutive sono iperelastiche non lineari. Si descrivono così forme d’equilibri...

La procedura di analisi limite contemplata dalla NTC-08 e relativa Circolare esplicativa n. 617/2009 per la valutazione del livello di sicurezza di strutture murarie nei confronti di possibili meccanismi locali è applicata in questo lavoro agli archi a profilo circolare. Le equazioni ottenute consentono di eseguire valutazioni rapide del livello di...

A finite differences procedure is used to study the buckling of non-trivial equilibrium solutions for open thin-walled beams in a dynamic setting. A direct one-dimensional model with a coarse descriptor of warping is adopted. The algorithm describes non-trivial equilibrium paths by integrating discretized field equations, suitably written in terms...

This paper discusses the computational problems that arise in the application of higher-order multiple scale methods to general multiresonant multiparameter systems. Complex amplitude equations are first analytically derived and their structure analyzed solely in the light of existing resonance conditions. A qualitative study of the complex amplitu...

We consider a cantilever beam partially resting on a linear visco-elastic foundation of generalized Winkler type. The length and placement of the partial foundation are variable. The beam is subjected to a sub-tangential force at its unconstrained end. The stability of some of its non-trivial equilibrium configurations is investigated by a numerica...

This paper is concerned with the identification of the dynamic moduli of viscoelastic constitutive models on the basis of a nonlinear optimization method by fitting data on carbon black-filled rubber. The models considered can be categorized in two different classes according to the definition of the relaxation function: models whose kernel decays...

Si considera una mensola parzialmente appoggiata su fondazione viscoelastica sollecitata all’estremo libero da una forza sub-tangenziale. Si studia la stabilità di sue configurazioni d’equilibrio non banali tramite una procedura alle differenze finite. Le condizioni critiche di buckling e flutter sono assai sensibili ad alcuni parametri; compaiono...

Fading memory is a distinguishing characteristic of viscoelastic solids. Its assessment is often achieved by measuring the stress due to harmonic strain histories at different frequencies: from the experimental point of view, the storage and loss moduli are, hence, introduced. On the other side, the mathematical modeling of viscoelastic materials i...

In this contribution we implement a suitably adapted version of the finite differences technique to solve the field equations for a thin-walled beam, as obtained by means of a direct one-dimensional model. This technique lets us find non trivial equilibrium paths and study their stability under both conservative and non conservative actions. Some r...

Carbon black-filled rubber and soft biological tissues are only two examples of materials which undergo large deformation processes and exhibit relevant dissipation and hysteresis losses. Nonlinear viscoelasticity encompass a wide class of constitutive models aimed at describing the behavior of such materials. The main goal of the present paper is...

The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is...

The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The masonry is considered as a composite material obtained as a regular distribution of blocks connected by horizontal and vertical mortar joints. The macromechanical equivalent Cosserat medium is derived by a rational homogenization procedu...

A multi-scale nonlinear homogenization procedure is presented for the analysis of the in-plane structural response of masonry panels characterized by a regular texture. A Cosserat continuum model is adopted at the macroscopic level, while a classical Cauchy model is employed at the microscopic scale; proper bridging conditions are stated to connect...

A technique for finding the stiffnesses and shear flows in multi-cell thin-walled girders subjected to linear elastic torsion is proposed. The girder is thought as the superposition of elementary closed tracks, just like open girders are the juxtaposition of thin strips. For each track there is a uniform value of the stress flow function, found by...

A Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial fu...

A generalized damped Becks column under pulsating actions is considered. The nonlinear partial integrodifferential equations of motion and the associated boundary conditions, expanded up to cubic terms, are tackled through a perturbation approach. The multiple scales method is applied to the continuous model in order to obtain the bifurcation equat...

The classical Lindstedt–Poincaré method is adapted to analyze the nonlinear normal modes of a piecewise linear system. A simple two degrees-of-freedom, representing a beam with a breathing crack is considered. The fundamental branches of the two modes and their stability are drawn by varying the severity of the crack, i.e., the level of nonlinearit...

Different solution strategies to the relaxed Saint-Venant problem are presented and comparatively discussed from a mechanical and computational point of view. Three approaches are considered; namely, the displacement approach, the mixed approach, and the modified potential stress approach. The different solution strategies lead to the formulation o...

A mechanical model describing finite motions of nonshallow cables around the initial catenary configurations is proposed. An exact kinematic formulation accounting for finite displacements is adopted, whereas the material is assumed to be linearly elastic. The nondimensional mechanical parameters governing the motions of nonshallow cables are obtai...

The critical and post-critical behavior of a non-conservative non-linear structure, undergoing statical and dynamical bifurcations, is analyzed. The system consists of a purely flexible planar beam, equipped with a lumped visco-elastic device, loaded by a follower force. A unique integro-differential equation of motion in the transversal displaceme...

A non-linear mechanical model of non-shallow linearly elastic suspended cables is employed to investigate the non-linear modal characteristics of the free planar motions. An asymptotic analysis of the equations of motion is carried out directly on the partial-differential equations overcoming the drawbacks of a discretization process. The direct as...

Free wave propagation patterns for general three-coupled periodic structures are investigated by means of the transfer matrix approach. It is shown that an exhaustive description of the propagation domains requires spaces that are stratified in homogeneous regions, whose dimension is given by the number of invariants of the transfer matrix characte...

A geometrically exact mechanical model describing large motions of nonshallow elastic cables is employed to investigate the linear and nonlinear properties of the cable planar modes. Considering the potential and kinetic linear modal energy content, it is shown that the elasto-static and elastodynamic modes are located around the various crossover...

The post-critical behavior of a cantilever beam with rectangular cross-section, under simultaneous action of conservative and non-conservative loads, is analyzed. An internally constrained Cosserat rod model is adopted to describe the dynamics of the beam in finite displacement regime. The bifurcation equations for simple buckling (divergence), sim...

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in...

Free undamped in-plane vibrations of shear undeformable beams around their highly buckled configurations are investigated neglecting rotary inertia effects. The beams are inertially nonuniform since a lumped mass is rigidly clamped along the span. Two mechanical models are considered depending on the boundary conditions in the post-buckling phases....

The natural frequencies and mode shapes of planar shear undeformable beams around their curved pre-stressed post-buckling configurations are investigated neglecting rotary inertia effects. Two mechanical models are considered depending on the assumed boundary conditions in the buckling and post-buckling phases. With the first model, the beam is con...

A general multiresonant system is considered, in which the linear frequency and, possibly, a forcing frequency are involved in a set of linear conditions. The nature of the resonances is first discussed, by distinguishing independent and dependent equations, and both the analysis and design problems of the system are addressed. Rules are then given...

A geometrically exact mechanical model of nonshallow elastic cables subjected to aerodynamic forces generated by the mean wind velocity field is discussed. The linearization around the catenary configuration leads to the prediction of the critical galloping velocities and the critical modes accomplished employing the Routh-Hurwitz theorem. Then, th...

General three-coupled periodic systems are dealt with by means of transfer matrices of single units. The solutions of the associated characteristic equation are discussed in terms of invariant quantities by exploiting the well-known reversibility of its coefficients. An exhaustive description of the free wave propagation patterns is given on the in...

An adapted version of the Multiple Scale Method is formulated to analyze 1:1 resonant multiple Hopf bifurcations of discrete autonomous dynamical systems, in which, for quasi-static variations of the parameters, an arbitrary number m of critical eigenvalues simultaneously crosses the imaginary axis. The algorithm therefore requires discretizing con...

Employing the geometrically exact approach, the governing equations of nonlinear planar motions around nonshallow prestressed equilibrium states of slender beams are derived. Internal kinematic constraints and approximations are introduced considering unshearable extensible and inextensible beams. The obtained approximate models, incorporating quad...

The natural frequencies and mode shapes of planar shear undeformable beams around their curved prestressed post-buckling configurations are investigated. Two mechanical models are considered depending on the assumed boundary conditions in the buckling and post-buckling phases. Namely, with the first model, the beam is considered inextensible becaus...