Leonardo Leonetti - Academia.edu (original) (raw)

Papers by Leonardo Leonetti

Applied Sciences

This study investigates a system for monitoring displacements of underground pipelines in landsli... more 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 numerical processing tool coupled with a data acquisition system is proposed. The starting point is the measurement of axial strain at three points of discrete sections of the pipeline by Fiber Bragg grating sensors, used to approximate the trend of mean axial strain and bending curvatures along the pipe axis. A finite element analysis based on a 3D geometrically exact beam model is developed for computing the deformed configuration corresponding to the input strain field. After assigning the boundary conditions, a mixed iterative scheme is used for a quick solution to the nonlinear problem. Firstly, the tool is validated theoretically with be...

Lecture Notes in Mechanical Engineering, 2020

Direct Methods, 2020

The starting point of this work is the definition of an automatic procedure for evaluating the ax... more The starting point of this work is the definition of an automatic procedure for evaluating the axial force-biaxial bending yield surface of steel and reinforced concrete sections in fire. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is then formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. An incremental-iterative strategy is proposed for tracing this curve evaluating a sequence of safe states at increasing fire durations up to the limit fire duration, that is the time of exposure which leads to structural collapse. The procedure represents a global fire analysis able to take account of the stress redistribution over the frame. Numerical examples are given to illustrate the proposal.

Materials, 2021

Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufa... more 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 advantage of these tunable materials requires the development of computational design methods. The failure of such structures is often dominated by buckling and can be very sensitive to material configuration and geometrical imperfections. This work is a review of the recent computational developments concerning the optimisation of the response of composite thin-walled structures prone to buckling, showing how baseline products with unstable behaviour can be transformed in stable ones operating safely in the post-buckling range. Four main aspects are discussed: mechanical and discrete models for composite shells, material parametrization an...

The paper treats the formulation of the shakedown problem and, as special case, of the limit anal... more The paper treats the formulation of the shakedown problem and, as special case, of the limit analysis problem, using solid shell models and ES-FEM discratization technology. In this proposal the Discrete shear gap method is applied to alleviate the shear locking phenomenon.

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonli... more Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of thin walled structures. They make it possible to meet the C 1 requirement in the interior of surface patches, to avoid the use of finite rotations and to reduce the number of unknowns compared to shear flexible models. Locking elimination, patch coupling and iterative solution are crucial points for a robust and efficient nonlinear analysis and represent the main focus of this work. Patch-wise reduced integrations are investigated to deal with locking in large deformation problems discretized via a standard displacement-based formulation. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified, allowing to avoid locking without resorting to a mixed formulation. The Newton method with mixed integration points (MIP) is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden and a superior robustness with respect to the standard Newton scheme. A simple penalty approach for coupling adjacent patches, applicable to either smooth or non-smooth interfaces, is proposed. An accurate coupling, also for a nonmatching discretization, is obtained using an interface-wise reduced integration while the MIP iterative scheme allows for a robust and efficient solution also with very high values of the penalty parameter.

MatSciRN: Process & Device Modeling (Topic), 2021

The paper shows how to make the incremental-iterative solution significantly more efficient and r... more The paper shows how to make the incremental-iterative solution significantly more efficient and robust in geometrically non-linear structural problems discretized via displacement-based finite element formulations. The main idea is to relax the constitutive equations at each integration point (IP) during the iterations. The converged solution remains unchanged while the iteration matrix is computed using independent IP stresses. This reduces the number of iterations to obtain convergence and allows very large steps in incremental analyses. The computational cost of each iteration is the same as the original Newton method. Importantly, the robustness of the iterative process is unaffected by high membraneto-flexural stiffness ratios as opposite to the standard Newton method.

The paper proposes a strategy for the treatment of load combinations making the shakedown analysi... more The paper proposes a strategy for the treatment of load combinations making the shakedown analysis an affordable design tool for practical applications. The paper refers to 3D frames subjected to complex combinations of statical and dynamical loads defined according to Eurocode rules. The yield surface of the sections is defined by its support function values associated to presso-flexural mechanisms and it is approximated as Minkowski sum of ellipsoids. The detection of the significant vertexes of the elastic envelope is made possible by an efficient algorithm suitable for use in the case of response spectrum analyses.

Computer Methods in Applied Mechanics and Engineering, 2020

Isogeometric Kirchhoff-Love elements have been receiving increasing attention in geometrically no... more Isogeometric Kirchhoff-Love elements have been receiving increasing attention in geometrically nonlinear analysis of thin shells because they make it possible to meet the C 1 requirement in the interior of surface patches and to avoid the use of finite rotations. However, engineering structures of appreciable complexity are typically modeled using multiple patches and, often, neither rotational continuity nor conforming discretization can be practically obtained at patch interfaces. Simple penalty approaches for coupling adjacent patches, applicable to either smooth or non-smooth interfaces and either matching or non-matching discretizations, have been proposed. Although the problem dependence of the penalty coefficient can be reduced by scaling factors which take into account geometrical and material parameters, only high values of the penalty coefficient can guarantee a negligible coupling error in all possible cases. However, this can lead to an ill conditioned problem and to an increasing iterative effort for solving the nonlinear discrete equations. In this work, we show how to avoid this drawback by rewriting the penalty terms in an Hellinger-Reissner form, introducing independent fields work-conjugated to the coupling equations. This technique avoids convergence problems, making the analysis robust also for very high values of the penalty coefficient, which can be then employed to avert coupling errors. Moreover, a proper choice of the basis functions for the new fields provides an accurate coupling also for general non-matching cases, preventing overconstrained solutions. The additional variables are condensed out and then not involved in the global system of equations to be solved. A highly efficient approach based on a mixed integration point strategy and an interface-wise reduced integration rule makes the condensation inexpensive preserving the sparsity of the condensed stiffness matrix and the coupling accuracy. c

International Journal of Solids and Structures, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Nanomaterials, 2020

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generatio... more Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to...

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

The reasons of the better performances of mixed, stress-displacements, 3D solid

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

The paper improved S-FEMs formulations with an enriched displacement field, making use of modifie... more The paper improved S-FEMs formulations with an enriched displacement field, making use of modified Allman's shape functions. This mixed interpolation is the natural context in performing lower bound strategy for shakedown, limit analysis and elastoplastic analysis. The model takes advantages from the simplicity and few addressed requirements for good performances in nonlinear analysis. The simple assumption made for the stress field regards the convenience of using self-equilibrated stress interpolations in Cartesian coordinates. In the proposed composite elements the stress is discontinuous on the element and across their sides and the mesh of the elements is coincident with the discretization of the geometry. This stress interpolation is able to address the discontinuities in the plastic strain and, in such a way, to define in their description a finer mesh with respect the basic grid.

Computer Methods in Applied Mechanics and Engineering, 2020

Abstract Different strategies based on rotation vector and exact strain measure have been propose... more Abstract Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing flexible 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 to path dependence and numerical instability, i.e. error accumulation. It is also non objective, although both objectivity and path independence are recovered with h and p refinement. Corotational approaches do not have these drawbacks, even though the geometrically exact model is achieved by mesh refinement. In this work, we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations, which are then interpolated for the evaluation of the nonlinear strains. This choice makes the approach singularity-free, allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation: rotational variables, objectivity, exact strain measure, path independence and symmetric stiffness matrix for conservative loads. This last property is a consequence of the direct differentiation of the relation between local and global rotations, whose compact form also makes a simple and general definition of the internal forces and the tangent stiffness for any order of interpolation possible. In addition, we show how the common approach of interpolating incremental vectors can be made stable by a simple updating procedure based on local rotations carried out at the end of each increment in order to avoid cumulative errors. Geometrically exact 3D beams are considered as a demonstrative example. An iterative strategy based on mixed integration points is used to solve the nonlinear discrete equations efficiently.

Computer Methods in Applied Mechanics and Engineering, 2018

Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced mod... more Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced model, of the behavior of shell structures when failure is dominated by buckling. In this work, we propose an isogeometric version of the method based on a solid-shell model. A NURBS interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the CAD model to the structural one. A linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix, which allows us to easily eliminate thickness locking and model multi-layered composites. Reduced integration schemes, which take into account the continuity of the shape functions, are used to avoid interpolation locking and make the integration faster. A Mixed Integration Point strategy makes it possible to transform the displacement model into a mixed (stress-displacement) one, required by the Koiter method to obtain accurate predictions, without introducing stress interpolation functions. The result is an efficient numerical tool for buckling and initial post-buckling analysis of composite shells, characterized by a low number of DOFs and integration points and by a simple and quick construction of the reduced model.

Meccanica, 2017

The classical Eurocode-compliant ultimate limit state (ULS) analysis of reinforced concrete secti... more 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, computed via a ULS procedure and a limit analysis approach, is presented. To this end, a preliminary qualitative discussion outlines modeling assumptions aiming to reproduce the physical behavior of reinforced concrete cross sections with respect to ductility and confinement issues. Besides the theoretical importance of the proposed approach, numerical experiments prove that limit analysis yields not only very accurate results but also a computationally effective procedure that can be affordably used in common design practice.

Engineering with Computers, 2017

Limit State of Materials and Structures, 2013

A mathematical programming formulation of strain-driven path-following strategies to perform shak... more A mathematical programming formulation of strain-driven path-following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in a FEM context, is presented. From the optimization point of view, standard arc-length strain driven elastoplastic analysis, recently extended to shakedown, are identified as particular decomposition strategies used to solve a proximal point algorithm applied to the static shakedown theorem that is then solved by means of a convergent sequence of safe states. The mathematical programming approach allows: a direct comparison with other nonlinear programming methods, simpler convergence proofs and duality to be exploited. Due to the unified approach in terms of total stresses, the strain driven algorithms become more effective and less nonlinear with respect to a self equilibrated stress formulation and easier to implement in existing codes performing elastoplastic analysis.

Direct Methods for Limit and Shakedown Analysis of Structures, 2015

Direct Methods for Limit and Shakedown Analysis of Structures, 2015

Using the static theorem and an algorithm based on dual decomposition, an efficient formulation f... more Using the static theorem and an algorithm based on dual decomposition, an efficient formulation for the shakedown analysis of 3D frame is proposed. An efficient treatment of the load combinations and an accurate and simple definition of the yield function of cross-section are proposed to increase effectiveness and to make shakedown analysis an affordable design tools.

Applied Sciences

This study investigates a system for monitoring displacements of underground pipelines in landsli... more 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 numerical processing tool coupled with a data acquisition system is proposed. The starting point is the measurement of axial strain at three points of discrete sections of the pipeline by Fiber Bragg grating sensors, used to approximate the trend of mean axial strain and bending curvatures along the pipe axis. A finite element analysis based on a 3D geometrically exact beam model is developed for computing the deformed configuration corresponding to the input strain field. After assigning the boundary conditions, a mixed iterative scheme is used for a quick solution to the nonlinear problem. Firstly, the tool is validated theoretically with be...

Lecture Notes in Mechanical Engineering, 2020

Direct Methods, 2020

The starting point of this work is the definition of an automatic procedure for evaluating the ax... more The starting point of this work is the definition of an automatic procedure for evaluating the axial force-biaxial bending yield surface of steel and reinforced concrete sections in fire. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is then formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. An incremental-iterative strategy is proposed for tracing this curve evaluating a sequence of safe states at increasing fire durations up to the limit fire duration, that is the time of exposure which leads to structural collapse. The procedure represents a global fire analysis able to take account of the stress redistribution over the frame. Numerical examples are given to illustrate the proposal.

Materials, 2021

Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufa... more 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 advantage of these tunable materials requires the development of computational design methods. The failure of such structures is often dominated by buckling and can be very sensitive to material configuration and geometrical imperfections. This work is a review of the recent computational developments concerning the optimisation of the response of composite thin-walled structures prone to buckling, showing how baseline products with unstable behaviour can be transformed in stable ones operating safely in the post-buckling range. Four main aspects are discussed: mechanical and discrete models for composite shells, material parametrization an...

The paper treats the formulation of the shakedown problem and, as special case, of the limit anal... more The paper treats the formulation of the shakedown problem and, as special case, of the limit analysis problem, using solid shell models and ES-FEM discratization technology. In this proposal the Discrete shear gap method is applied to alleviate the shear locking phenomenon.

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonli... more Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of thin walled structures. They make it possible to meet the C 1 requirement in the interior of surface patches, to avoid the use of finite rotations and to reduce the number of unknowns compared to shear flexible models. Locking elimination, patch coupling and iterative solution are crucial points for a robust and efficient nonlinear analysis and represent the main focus of this work. Patch-wise reduced integrations are investigated to deal with locking in large deformation problems discretized via a standard displacement-based formulation. An optimal integration scheme for third order C 2 NURBS, in terms of accuracy and efficiency, is identified, allowing to avoid locking without resorting to a mixed formulation. The Newton method with mixed integration points (MIP) is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden and a superior robustness with respect to the standard Newton scheme. A simple penalty approach for coupling adjacent patches, applicable to either smooth or non-smooth interfaces, is proposed. An accurate coupling, also for a nonmatching discretization, is obtained using an interface-wise reduced integration while the MIP iterative scheme allows for a robust and efficient solution also with very high values of the penalty parameter.

MatSciRN: Process & Device Modeling (Topic), 2021

The paper shows how to make the incremental-iterative solution significantly more efficient and r... more The paper shows how to make the incremental-iterative solution significantly more efficient and robust in geometrically non-linear structural problems discretized via displacement-based finite element formulations. The main idea is to relax the constitutive equations at each integration point (IP) during the iterations. The converged solution remains unchanged while the iteration matrix is computed using independent IP stresses. This reduces the number of iterations to obtain convergence and allows very large steps in incremental analyses. The computational cost of each iteration is the same as the original Newton method. Importantly, the robustness of the iterative process is unaffected by high membraneto-flexural stiffness ratios as opposite to the standard Newton method.

The paper proposes a strategy for the treatment of load combinations making the shakedown analysi... more The paper proposes a strategy for the treatment of load combinations making the shakedown analysis an affordable design tool for practical applications. The paper refers to 3D frames subjected to complex combinations of statical and dynamical loads defined according to Eurocode rules. The yield surface of the sections is defined by its support function values associated to presso-flexural mechanisms and it is approximated as Minkowski sum of ellipsoids. The detection of the significant vertexes of the elastic envelope is made possible by an efficient algorithm suitable for use in the case of response spectrum analyses.

Computer Methods in Applied Mechanics and Engineering, 2020

Isogeometric Kirchhoff-Love elements have been receiving increasing attention in geometrically no... more Isogeometric Kirchhoff-Love elements have been receiving increasing attention in geometrically nonlinear analysis of thin shells because they make it possible to meet the C 1 requirement in the interior of surface patches and to avoid the use of finite rotations. However, engineering structures of appreciable complexity are typically modeled using multiple patches and, often, neither rotational continuity nor conforming discretization can be practically obtained at patch interfaces. Simple penalty approaches for coupling adjacent patches, applicable to either smooth or non-smooth interfaces and either matching or non-matching discretizations, have been proposed. Although the problem dependence of the penalty coefficient can be reduced by scaling factors which take into account geometrical and material parameters, only high values of the penalty coefficient can guarantee a negligible coupling error in all possible cases. However, this can lead to an ill conditioned problem and to an increasing iterative effort for solving the nonlinear discrete equations. In this work, we show how to avoid this drawback by rewriting the penalty terms in an Hellinger-Reissner form, introducing independent fields work-conjugated to the coupling equations. This technique avoids convergence problems, making the analysis robust also for very high values of the penalty coefficient, which can be then employed to avert coupling errors. Moreover, a proper choice of the basis functions for the new fields provides an accurate coupling also for general non-matching cases, preventing overconstrained solutions. The additional variables are condensed out and then not involved in the global system of equations to be solved. A highly efficient approach based on a mixed integration point strategy and an interface-wise reduced integration rule makes the condensation inexpensive preserving the sparsity of the condensed stiffness matrix and the coupling accuracy. c

International Journal of Solids and Structures, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Nanomaterials, 2020

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generatio... more Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element schemes so as to control the loss of stability and overall nonlinear response. Three types of optimizations are considered: variable through-the-thickness volume fraction of random carbon nanotubes (CNTs) distributions, variable volume fraction of randomly oriented CNTs within the mid-surface, aligned CNTs with variable orientation with respect to the mid-surface. The collapse load, which includes both limit points and deformation thresholds, is chosen as the objective/cost function. An efficient computation of the cost function is carried out using the Koiter reduced order model obtained starting from an isogeometric solid-shell model to...

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

The reasons of the better performances of mixed, stress-displacements, 3D solid

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016

The paper improved S-FEMs formulations with an enriched displacement field, making use of modifie... more The paper improved S-FEMs formulations with an enriched displacement field, making use of modified Allman's shape functions. This mixed interpolation is the natural context in performing lower bound strategy for shakedown, limit analysis and elastoplastic analysis. The model takes advantages from the simplicity and few addressed requirements for good performances in nonlinear analysis. The simple assumption made for the stress field regards the convenience of using self-equilibrated stress interpolations in Cartesian coordinates. In the proposed composite elements the stress is discontinuous on the element and across their sides and the mesh of the elements is coincident with the discretization of the geometry. This stress interpolation is able to address the discontinuities in the plastic strain and, in such a way, to define in their description a finer mesh with respect the basic grid.

Computer Methods in Applied Mechanics and Engineering, 2020

Abstract Different strategies based on rotation vector and exact strain measure have been propose... more Abstract Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing flexible 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 to path dependence and numerical instability, i.e. error accumulation. It is also non objective, although both objectivity and path independence are recovered with h and p refinement. Corotational approaches do not have these drawbacks, even though the geometrically exact model is achieved by mesh refinement. In this work, we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations, which are then interpolated for the evaluation of the nonlinear strains. This choice makes the approach singularity-free, allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation: rotational variables, objectivity, exact strain measure, path independence and symmetric stiffness matrix for conservative loads. This last property is a consequence of the direct differentiation of the relation between local and global rotations, whose compact form also makes a simple and general definition of the internal forces and the tangent stiffness for any order of interpolation possible. In addition, we show how the common approach of interpolating incremental vectors can be made stable by a simple updating procedure based on local rotations carried out at the end of each increment in order to avoid cumulative errors. Geometrically exact 3D beams are considered as a demonstrative example. An iterative strategy based on mixed integration points is used to solve the nonlinear discrete equations efficiently.

Computer Methods in Applied Mechanics and Engineering, 2018

Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced mod... more Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced model, of the behavior of shell structures when failure is dominated by buckling. In this work, we propose an isogeometric version of the method based on a solid-shell model. A NURBS interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the CAD model to the structural one. A linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix, which allows us to easily eliminate thickness locking and model multi-layered composites. Reduced integration schemes, which take into account the continuity of the shape functions, are used to avoid interpolation locking and make the integration faster. A Mixed Integration Point strategy makes it possible to transform the displacement model into a mixed (stress-displacement) one, required by the Koiter method to obtain accurate predictions, without introducing stress interpolation functions. The result is an efficient numerical tool for buckling and initial post-buckling analysis of composite shells, characterized by a low number of DOFs and integration points and by a simple and quick construction of the reduced model.

Meccanica, 2017

The classical Eurocode-compliant ultimate limit state (ULS) analysis of reinforced concrete secti... more 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, computed via a ULS procedure and a limit analysis approach, is presented. To this end, a preliminary qualitative discussion outlines modeling assumptions aiming to reproduce the physical behavior of reinforced concrete cross sections with respect to ductility and confinement issues. Besides the theoretical importance of the proposed approach, numerical experiments prove that limit analysis yields not only very accurate results but also a computationally effective procedure that can be affordably used in common design practice.

Engineering with Computers, 2017

Limit State of Materials and Structures, 2013

A mathematical programming formulation of strain-driven path-following strategies to perform shak... more A mathematical programming formulation of strain-driven path-following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in a FEM context, is presented. From the optimization point of view, standard arc-length strain driven elastoplastic analysis, recently extended to shakedown, are identified as particular decomposition strategies used to solve a proximal point algorithm applied to the static shakedown theorem that is then solved by means of a convergent sequence of safe states. The mathematical programming approach allows: a direct comparison with other nonlinear programming methods, simpler convergence proofs and duality to be exploited. Due to the unified approach in terms of total stresses, the strain driven algorithms become more effective and less nonlinear with respect to a self equilibrated stress formulation and easier to implement in existing codes performing elastoplastic analysis.

Direct Methods for Limit and Shakedown Analysis of Structures, 2015

Direct Methods for Limit and Shakedown Analysis of Structures, 2015

Using the static theorem and an algorithm based on dual decomposition, an efficient formulation f... more Using the static theorem and an algorithm based on dual decomposition, an efficient formulation for the shakedown analysis of 3D frame is proposed. An efficient treatment of the load combinations and an accurate and simple definition of the yield function of cross-section are proposed to increase effectiveness and to make shakedown analysis an affordable design tools.