Antonio Madeo

• Associate Professor
• Associate Professor at University of Calabria

Shakedown analyses require a precise evaluation of pointwise elastic stresses and, at the same time, an accurate representation of the elastoplastic solution for capturing the ratcheting mechanisms effectively. However, existing discretization methods often face a trade-off: techniques that optimize plasticity performance may compromise elastic acc...

In this paper, a hybrid variational framework for the Virtual Element Method (VEM) is proposed and a family of polygonal elements for plane elasticity is developed. Under specific assumptions, it is proved that the minimization of Total Potential Energy and the projection operation typical of enhanced VEM can be deduced from the stationary conditio...

This work presents a Virtual Element formulation (VE) for shear-deformable elastic plates. In particular, the Hybrid Virtual Element Method (HVEM) is adopted, which assumes a self equilibrated stress interpolation and an energy-based projection, eliminating the need for stabilization terms. This choice, together with a cubic linked interpolation fo...

Mixed Finite Elements (FEs) with assumed stresses and displacements provide many advantages in analysing shell structures. They ensure good results for coarse meshes and provide an accurate representation of the stress field. The shell FEs within the family designated by the acronym Mixed Isostatic Self‐equilibrated Stresses (MISS) have demonstrate...

A plasticity formulation for the Hybrid Virtual Element Method (HVEM) is presented. The main features include the use of an energy norm for the VE projection, a high-order divergence-free interpolation for stresses and a piecewise constant interpolation for plastic multipliers within element subdomains. The HVEM does not require any stabilization t...

A novel 8-node hybrid stress finite element (FE) is proposed for the efficient nonlinear analysis of in-plane loaded masonry walls. To provide a robust, easy-to-characterize mechanically, and computationally efficient practice-oriented numerical framework, masonry is idealized as an elasto-plastic homogeneous continuum. Elasto-plasticity is conside...

The seismic vulnerability represents a statistical measure of the susceptibility of structures to be damaged by seismic events of different intensities and requires an appropriate model of the uncertainties affecting geometry, materials and actions. Slender structures can exhibit a high seismic vulnerability, due to geometrically nonlinear phenomen...

Due to the inherent material nonlinearities, the analysis of masonry structures is generally performed by means of numerical simulations. Given their suitability for finite element approaches, continuum models are usually adopted. Clearly, within such approaches, nonlinear constitutive laws are needed, and often one relies on elasto-plastic models....

The Virtual Element Method (VEM) has been successfully adopted in many areas of solid mechanics, from linear elasticity to fracture [1]. It features the possibility of recovering fields inside the element domain through an interpolation of the displacement only along the element boundary. This aspect thereby facilitates the development of polygonal...

The development of reliable methods for assessing the seismic vulnerability at the urban scale of masonry aggregates could provide helpful guidance for reducing the expected damage and losses. However, the lack of structural data and the presence of many sources of uncertainty complicate the vulnerability analyses and reduce the effectiveness of nu...

Geometrically nonlinear phenomena and stability issues can significantly affect the seismic behaviour of a wide range of structures. Pallet rack systems, for instance, are prone to buckle when the material is still within the elastic range, undergoing sudden and catastrophic collapse mechanisms, as documented after several earthquakes. This work pr...

In this work, a stabilisation-free elastoplastic hybrid Virtual Element Method (HVEM) formulation is proposed [1]. Assumed stresses that a-priori satisfy equi- librium equations are selected. Meanwhile, the plastic multiplier is interpolated following an approach previously proposed for mixed Finite Elements [2]. The in- tegration of the constituti...

Mixed finite elements with self-equilibrated assumed stresses have proven to provide several advantages for analysing shell structures [1]. They guarantee high performance when using coarse meshes and accurately represent the stress field. This work aims to exploit those advantages to develop a solid-shell finite element for the geometrically nonli...

Hybrid finite elements with self-equilibrated assumed stresses have proven to provide several advantages for analysing shell structures [1]. They guarantee high performance when using coarse meshes and accurately represent the stress field. Additionally, they do not require assumptions about the displacement field within the element domain, and the...

The current demand for lightweight structures in a wide range of engineering applications leads to using thin-walled composite laminated structures whose behaviour is governed by buckling and postbuckling phenomena. Such a demand is pushing the borders of computational mechanics to enhance methods and algorithms for studying those structures’ geome...

This work proposes a numerical approach for the efficient analysis of in-plane loaded masonry walls. The nonlinear behaviour of the material is described using a multi-failure strength domain. This describes different failure mechanisms through a micro-mechanical model. By intersecting the limit surfaces related to each mechanism, a homogenised mul...

The enhanced Virtual Element Method (VEM) formulation, recently proposed by D’Altri et al.[1] for plane elasticity, provides numerous advantages over the classic VEM. The two main results are the absence of stabilisation terms and a considerable accuracy improvement. Upon this premise, this work shows how the enhanced VEM formulation can be obtaine...

Variable stiffness (VS) composite laminates provide larger freedom to design thin- walled structures than constant stifness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed s...

Fibre reinforced polymers are increasingly used in bridge structures for reducing their environmental impact, extending the service life and saving costs. In this work, we propose the use of composite laminates called Variable Angle Tow (VAT) to realise bridge structures. In VAT composite laminates, the fibre orientation changes pointwise over the...

Debris-flow represents a severe source of damage for buildings [1]. Procedures based on simplified approaches can provide great help to identify the most vulnerable buildings on areas at risk, in order to undertake retrofit and mitigation actions. In this work we propose a simplified vulnerability assessment method for structures exposed to fast mo...

Recent earthquakes have highlighted the high vulnerability of the industrial structures that are not specifically designed for accounting seismic forces. Among them, a widespread typology is characterised by steel structures without bracing or other antiseismic details and with masonry infills. With the aim of increasing the knowledge on the seismi...

The paper presents an automated procedure for deriving fragility curves for typological masonry aggregates, named META-FORMA-XL (MEchanical-Typological Approach FOR Masonry Aggregates – X Local). The topic deals with the urban-scale seismic vulnerability analysis, which can provide powerful information for developing risk mitigation plans and imple...

Buildings exposed to high-intensity flood actions can experience severe damage and collapse. Rapid procedures can significantly aid in identifying the most vulnerable buildings within large flood-risk areas, enabling the implementation of retrofitting and mitigation measures. Motivated by this need, in this work we propose a simplified vulnerabilit...

The paper presents a mechanical-based framework for the evaluation of local-scale seismic fragility curves. The approach is oriented to a seismic vulnerability assessment of unreinforced masonry buildings and makes use of basic exposure data easily obtained from survey or available in existing database. An efficient finite element model and static...

The use of mixed Finite Elements (FE) ensures better performance than more traditional displacement based formulations in different contexts. Some of the most significant advantages provided by the mixed FE technique are the elimination of many locking phenomena, the accuracy increasing and the robustness improvement of geometrically nonlinear anal...

All over the world, there has been growing interest in using fibre reinforce plastic (FRP) materials to realise new bridges and maintain the existing ones. Composite materials allow faster installation times and superior performance compared to concrete and steel, which have largely been used to construct bridges in the last century. In particular,...

A mixed shell finite element for the analysis of Variable Angle Tow (VAT) laminated composite structures undergoing geometrical nonlinearities is presented. Following the Hybrid-Trefftz method, the stress interpolation is derived from the linear elastic solution for symmetric composite materials. Displacement and rotation fields are only assumed al...

The increasing use of composite materials in civil structures has led to a demand for designs that reduce environmental impact, extend service life and save costs. This study proposes the use of Variable Angle Tow (VAT) composite laminates to further improve the structural efficiency of civil structures, particularly bridge girders. VAT composite l...

This work presents a numerical procedure for constructing mechanical-based fragility curves for industrial steel structures. In particular, the structures under considerations are characterised by the absence of anti-seismic details and by the presence of masonry infills. This structural typology has been identified in southern Italy and represents...

The paper presents a study on the seismic fragility of masonry aggregates by considering both global and local collapse mechanisms. Within the framework of urban-scale vulnerability analyses, studying the seismic behavior of the building stock of historical centers represents an intricate challenge, in which the complexity of the urban fabric and t...

The analysis of reinforced concrete shell structures accounting for material nonlinearity is addressed. The structural response is numerically evaluated using a mixed shell finite element and a plasticity-based material behaviour. The finite element is a quadrilateral with four nodes and is based on self-equilibrated assumed stresses. The kinematic...

This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin‐walled structures. The structure is discretized by an isogeometric solid‐shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal stra...

Shell structures made of Reinforced Concrete (RC) are used in many civil engineering applications. However, their analysis can frequently require a high computational cost, since fine mesh discretisations are needed for accurate solutions. In this work, a Finite Element (FE) for the analysis of RC shells is presented. It has four nodes and 24 degre...

This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue...

A 4-nodes flat shell Finite Element (FE) is formulated on the basis of an assumed interpolation of the stress and displacement fields in order to perform the elastoplastic analysis of reinforced concrete structures. The nonlinear material behavior of the concrete is described through a confinement-sensitive plasticity constitutive model not requiri...

This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin-walled structures. The structure is discretized by an isogeometric solid-shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal stra...

Mixed assumed stress finite elements for elastic-perfectly plastic materials require the solution of a Closest Point Projection (CPP) involving all the element stress parameters for the integration of the constitutive equation. Here, a dual decomposition strategy is adopted to split the CPP at the element level into a series of CPPs at the integrat...

Mixed assumed stress finite elements (FEs) have shown good advantages over traditional displacement‐based formulations in various contexts. However, their use in incremental elasto‐plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic‐perfectly plastic materials and small deformati...

This study investigates a system for monitoring displacements of underground pipelines in landslide-prone regions. This information is an important alarm indicator, not only to prevent the failure of the line itself but also to mitigate the direct consequences of landslides on buildings and infrastructures in the affected area. Specifically, a nume...

A reduced order model for the nonlinear dynamic seismic analysis of elasto‐plastic 3D frame structures is presented. It is based on an approximated solution space for the displacement field that is assumed as the sum of two subspaces. The first subspace is generated by the relevant linear elastic modes of the generalized stiffness/mass linear eigen...

The multi‐modal Koiter method is a reduction technique for estimating quickly the nonlinear buckling response of structures under mechanical loads requiring a fine discretization. The reduced model is based on a quadratic approximation of the full model using a few linear buckling modes and their second order corrections, followed by the projection...

A corotational flat shell element for the geometrically nonlinear analysis of laminated composite structures is presented. The element is obtained from the Hellinger–Reissner variational principle with assumed stress and displacement fields. The stress interpolation is derived from the linear elastic solution for symmetric composite materials. The...

Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufacturing methods are enabling the realization of composite materials with spatially varying material properties. Variable angle tow fibre composites are a representative example, but also nanocomposites are opening new interesting possibilities. Taking a...

The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions t...

A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of...

The optimisation of the structural behaviour of the wing is one of the key aspects in the design of future aircraft. Enhanced freedom to designers has been offered by the stiffness-tailoring capability of Variable Angle Tow (VAT) laminates. Efficient and robust optimisation strategies are, consequently, of great importance to fully explore such an...

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing beams undergoing large rotations. The interpolation of the total rotation vector is path independent but also singular at the full angle and non objective. The interpolation of the incremental rotation vector avoids the singularity...

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing exible bodies undergoing arbitrary large rotations. To avoid the singularity of the vector-like parametrization, the interpolation of the incremental rotation vector is the most popular approach in this context, even if this leads...

I metamateriali sono impiegati in molti campi dell'ingegneria e delle scienze applicate. Esibiscono peculiari proprietà fisico-meccanico, acustiche ed elettromagnetiche grazie a specifiche configurazioni tridimensionali dei materiali di cui sono costituiti. L’idea è quella di poter progettare metamateriali con proprietà di filtraggio delle onde sis...

Variable Angle Tow (VAT) laminates have notably enhanced the possibilities of tailoring the stiffness properties of thin-walled structures. This increased freedom meets the need for designing lighter-weight structures. Consequently, buckling and postbuckling phenomena often lead the structural response and have to be considered from the preliminary...

Composite foundation is proposed as seismic isolation strategy of new building. This is based on filtering capacity of metamaterial which can be design for filtering the most dangerous frequencies for building. Following an accurate seismic local response analysis of soil the resonancy frequency can be identified and internal resonance frequency of...

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analysing flexible bodies undergoing arbitrary large rotations. To avoid the singularity of the vector-like parametrisation, the interpolation of the incremental rotation vector [1] is the standard approach in this context, even if this lead...

The stiffness-tailoring capability of Variable Angle Tow (VAT) laminates gives enhanced freedom to design thin-walled structures. One key advantage of tow steering is the ability to redistribute stresses improving buckling performance, leading to reduction in material weight and costs. The aim of this work is to optimise the initial postbuckling be...

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of l...

The optimisation of the structural behaviour of the wing is one of the key as- pects in the design of future aircraft. Enhanced freedom to designers has been offered by the stiffness-tailoring capability of Variable Angle Tow (VAT) laminates. Efficient and robust optimisation strategies are, consequently, of great importance to fully ex- plore such...

The stiffness-tailoring capability of Variable Angle Tow (VAT) laminates gives enhanced freedom to designthin-walled structures. One key advantage of tow steering is the ability to redistribute stresses improving buckling performance, leading to reduction in material weight and costs. The aim of this work is to optimise the initial postbuckling beh...

In this work, the post-buckling analysis of thin-walled beams by using the Generalized Beam Theory (GBT) is presented. To this purpose, a geometrically nonlinear GBT finite element is developed by exploiting the features of mixed-stress GBT finite element formulation in the framework of the Implicit Corotational Method (ICM). The application of the...

A numerical stochastic strategy for the optimisation of composite elastic shells undergoing buckling is presented. Its scope is to search for the best stacking sequence that maximises the collapse load optimising the post-buckling behaviour. Its feasibility is due to a reduced order model built for each material setup starting from a hybrid solid-s...

Thin-walled beams with open cross-section, as those tipically obtained in cold-working manufacturing processes, exhibit a significant geometrically nonlinear behaviour due to cross-section distortion phenomena. The Generalized Beam Theory (GBT), as originally proposed by Schardt [1], is an effective tool to account for cross-section distortion phen...

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a-posteriori the effects of the imperfections in the reduced non-linear equa...

An Imperfection Sensitivity Analysis (ISA) of Variable Angle Tow (VAT) curved panels subject to different load/boundary conditions is presented. The ISA described in [1] is performed using a fast-running software that employs a Koiter asymptotic approach in FEM context [2] and a Monte Carlo simulation to test a large number geometrical imperfection...

A geometrically nonlinear Generalized Beam Theory is formulated and the results in the framework of buckling analyses are discussed. The geometrically nonlinear model is recovered reusing the model available in the linear context. This generalization to the nonlinear context is obtained exploiting the corotational based method called Implicit Corot...

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a-posteriori the effects of the imperfections in the reduced non-linear equa...

In the paper the post-buckling behaviour of thin-walled channel cross-section columns made of Fiber Metal Laminate subjected to an axial compressions is considered. The main interest is focused on the initial imperfection influence on the post-buckling response and thus the sensitivity analysis with application of Monte Carlo simulations is perform...

The novel methodology for imperfection sensitivity analysis, presented in Barbero et al.1 is here applied for the evaluation of limit load of composite cylindrical shells. Koiter’s perturbation method is used to calculate the imperfection paths emanating from mode interaction bifurcations and the Monte Carlo method is used to test a large number of...

The design of lightweight structures is often driven by buckling phenomena. Increasing demands for fuel efficient aircraft structures makes post-buckled designs attractive from a structural weight perspective. How-ever, the need for reliable and efficient design tools that accurately model the emerging nonlinear post-buckled landscape, potentially...

Both composite materials and stress concentration are common issues in modern structural engineering. In this paper, analytical integration of the singular kernels is performed for boundary element analysis (BEM) of elastic, plane orthotropic media with stress concentrations. Analytical integration leads to accuracy and efficiency improvements over...

An imperfection sensitivity analysis of thin-walled cold-formed steel members in compression is presented. The members under investigation are perforated steel pallet racks in compression of different lengths. The analysis is based on a finite element implementation of the Koiter method coupled with Monte Carlo simulation. It is based on an intensi...

In this work we propose an extension of the MISS-4 flat shell element [1] to the geometrically nonlinear analysis of variable-angle tow (VAT) composite plates using the Koiter asymptotic approach [2]. Variable-angle tows describe curvilinear fiber paths in a composite lamina and are a promising technology for tailoring the buckling and post-bucklin...

A mixed quadrilateral 3D finite element, obtained from the Hellinger-Reissner functional, is presented for linear static and buckling analyses of variable-angle tow (VAT) composite plates. Variable-angle tows describe curvilinear fiber paths within composite laminae and are a promising technology for tailoring the buckling and post-buckling capabil...

An imperfection sensitivity analysis of cold-formed steel pallet racks in compression is presented. The analysis is based on Koiter’s approach and Monte Carlo simulation on one hand, and the ECBL (Erosion of Critical Buckling Load) approach on the other one. Mode interaction is taken into account and, based on that, the limit load and erosion of cr...

This paper reports the results of a numerical investigation concerning the relevance and Direct Strength Method (DSM) prediction of the ultimate strength erosion caused by local-distortional-global (LDG) interaction in cold-formed steel fixed-ended lipped channel columns. The geometries of the columns analysed (cross-section dimensions and lengths)...

An imperfection sensitivity analysis of cold-formed steel members in compression is presented. The analysis is based on Koiter’s approach and Monte Carlo simulation. If the modes interaction is correctly accounted, than the limit load and the erosion of critical buckling load can be easily evaluated. Thousands of imperfection can be analysed with v...

A new 2-node finite element for the Generalized Beam Theory is developed based on the hybrid complementary energy functional, involving nodal displacements and equilibrating stresses within the element as independent variables. Assumed stresses are rationally derived basing on the stresses associated to analytical solutions of some particular cases...

An imperfection sensitivity analysis of cold-formed steel members in compression is presented. The analysis is based on Koiter’s approach and Monte Carlo simulation. Mode interaction is correctly accounted and limit load and erosion of critical buckling load evaluated. Thousand of imperfection can be analysed with very low computational cost and an...

The design of composite structures is most often dominated by buckling [1], complex-post buckling behaviour and sensitivity to imperfections. Imperfection sensitivity analysis requires the identification of a large number of buckling modes and their interaction. Because of the large number of possible modes and our a priori ignorance about which on...

The possibility to establish clear relationships between the results of the Generalized Beam Theory (GBT) and those of the classical beam theories is a crucial issue for a correct theoretical positioning of the GBT within the other existing beam theories as well as for the application of the GBT in the current engineering practice. With this in min...

A new mixed stress 4-node flat shell finite element, designed for the linear and nonlinear analysis of folded plate structures, is presented. The kinematics of the element is defined by 24 dofs with in- and out-of-plane displacements assumed to be quadratic, controlled by displacement and rotation parameters through an Allman like interpolation, an...

A mixed finite element for linear and nonlinear analysis of laminated folded plates is presented in this paper. The mixed formulation affords accurate prediction of stresses, which are needed for damage and failure analysis. Static condensation of the stress parameters results in a displacement-only element that is easy to integrate into commercial...