Nicola Rizzi - Profile on Academia.edu (original) (raw)
Papers by Nicola Rizzi
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016
The aim of this paper is to find a computationally efficient and predictive model for the class o... more The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographi...
Masonry Panels As Second Gradient Microstructured Continua
Materials Science Forum, 2009
Influenza del modello di trave sul comportamento post-critico dei telai piani
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a co... more A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of the 2D body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions. The expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2D continuum. To account for the modelling abilities of the 2D continuum in the linear range, the eigenmode and eigenfrequencies of a given specimen are determined. The buckling and post-buckling behaviour of the same specimen, subjected to two different loading conditions are analysed as tests in the nonlinear range. The problems have been solved numerically by means of the C...
Coupled Instabilities in a Two-Bar Frame: A Qualitative Approach
Stability, Bifurcation and Postcritical Behaviour of Elastic Structures, 1991
The paper presents a study dedicated to analyzing the sensitivity of structures with open contour... more The paper presents a study dedicated to analyzing the sensitivity of structures with open contours to cracks. For this purpose, we analyze the particular case of the I-beam made by welding, for which we want to see how the frequencies of different modes of vibration change when a crack occurs in the weld joint between the web and the flange. The research is done using numerical simulations performed with the ANSYS program, from which the natural frequencies are obtained depending on the depth and extent of the crack. A large number of vibration modes and two types of boundary conditions are taken into account. We found that the frequency changes are small but still detectable and depend on the beam fixation mode. This makes it possible to detect cracks in the weld joint if the vibration modes where the decrease in frequency is significant are analyzed.
La poutre élastique en plusieurs pièces
Presses Polytechniques et Universitaires Romandes, 2012
Symbolic manipulations in buckling and postbuckling anal- ysis
Tecniche di omogeneizzazione per l’analisi delle murature
Continuum models with microstructure for periodic brickwork arches and vaults
Masonry Modeled as Nonlinear Structured Continuum
Flexural-torsional behaviour of thin-walled frames
Applicazioni di un modello monodimensionale per lo studio della biforcazione di travi di spessore sottile
Continuum Models for out of Plane Behaviour of Masonry Panels
Un modello modnodimansionale per l'analisi della biforcazione flesso-torsionale di travi di spessore sottile
We investigate the buckling of a ‘Roorda’ frame by means of a direct one-dimensional beam model. ... more We investigate the buckling of a ‘Roorda’ frame by means of a direct one-dimensional beam model. The frame is acted upon by a ‘dead’ load at the joint and is constrained there by an out-of-plane linear elastic spring. The possibility of warping constraints at the beam ends is also considered; the spring simulates the presence of braces in actual 3D frames. The numerical results are compared with those already obtained by the authors for an infinitely stiff spring.
One-dimensional continuum model of a modular lattice: identification of the constitutive functions for the contact and inertial actions
Modelli 2D con microstruttura per pannelli di muratura in 3D
Symmetric Bifurcation of Plane Frames through a Modified Potential Energy Approach
Journal of Structural Mechanics, 1980
The modified potential energy approach to the nonlinear analysis of slender elastic beams is empl... more The modified potential energy approach to the nonlinear analysis of slender elastic beams is employed to investigate the buckling and postbuckling behavior of two symmetric plane frames, namely a hinged portal frame and a hinged two-bar frame, The beams are assumed to be inextensible and shear undeformable. The “hybrid” functional on which the present analysis is based according to a
International Journal of Solids and Structures, 2016
In this paper a procedure for constructing a 1D continuum equivalent to a Koiter plate, is presen... more In this paper a procedure for constructing a 1D continuum equivalent to a Koiter plate, is presented. The result is used to build-up a coarse model of a Thin Walled Beam. The model results to be a nonlinear hyperelastic 1D second gradient continuum, endowed with an internal microstructure described by seven scalar kinematic parameters. The kinematic parameters are able to describe, although in a rough way, the deformation of the TWB in the plane of its cross-section. The nonlinear behaviour of a simply supported strut has been analyzed and the results compared with those given by the commercial finite element code ABAQUS.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016
The aim of this paper is to find a computationally efficient and predictive model for the class o... more The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographi...
Masonry Panels As Second Gradient Microstructured Continua
Materials Science Forum, 2009
Influenza del modello di trave sul comportamento post-critico dei telai piani
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017
A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a co... more A nonlinear two-dimensional (2D) continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which, in turn, is assumed as a model of a pantographic structure made up by two families of equispaced beams, superimposed and connected by pivots. The deformation measures of the beams of the network and that of the 2D body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions. The expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2D continuum. To account for the modelling abilities of the 2D continuum in the linear range, the eigenmode and eigenfrequencies of a given specimen are determined. The buckling and post-buckling behaviour of the same specimen, subjected to two different loading conditions are analysed as tests in the nonlinear range. The problems have been solved numerically by means of the C...
Coupled Instabilities in a Two-Bar Frame: A Qualitative Approach
Stability, Bifurcation and Postcritical Behaviour of Elastic Structures, 1991
The paper presents a study dedicated to analyzing the sensitivity of structures with open contour... more The paper presents a study dedicated to analyzing the sensitivity of structures with open contours to cracks. For this purpose, we analyze the particular case of the I-beam made by welding, for which we want to see how the frequencies of different modes of vibration change when a crack occurs in the weld joint between the web and the flange. The research is done using numerical simulations performed with the ANSYS program, from which the natural frequencies are obtained depending on the depth and extent of the crack. A large number of vibration modes and two types of boundary conditions are taken into account. We found that the frequency changes are small but still detectable and depend on the beam fixation mode. This makes it possible to detect cracks in the weld joint if the vibration modes where the decrease in frequency is significant are analyzed.
La poutre élastique en plusieurs pièces
Presses Polytechniques et Universitaires Romandes, 2012
Symbolic manipulations in buckling and postbuckling anal- ysis
Tecniche di omogeneizzazione per l’analisi delle murature
Continuum models with microstructure for periodic brickwork arches and vaults
Masonry Modeled as Nonlinear Structured Continuum
Flexural-torsional behaviour of thin-walled frames
Applicazioni di un modello monodimensionale per lo studio della biforcazione di travi di spessore sottile
Continuum Models for out of Plane Behaviour of Masonry Panels
Un modello modnodimansionale per l'analisi della biforcazione flesso-torsionale di travi di spessore sottile
We investigate the buckling of a ‘Roorda’ frame by means of a direct one-dimensional beam model. ... more We investigate the buckling of a ‘Roorda’ frame by means of a direct one-dimensional beam model. The frame is acted upon by a ‘dead’ load at the joint and is constrained there by an out-of-plane linear elastic spring. The possibility of warping constraints at the beam ends is also considered; the spring simulates the presence of braces in actual 3D frames. The numerical results are compared with those already obtained by the authors for an infinitely stiff spring.
One-dimensional continuum model of a modular lattice: identification of the constitutive functions for the contact and inertial actions
Modelli 2D con microstruttura per pannelli di muratura in 3D
Symmetric Bifurcation of Plane Frames through a Modified Potential Energy Approach
Journal of Structural Mechanics, 1980
The modified potential energy approach to the nonlinear analysis of slender elastic beams is empl... more The modified potential energy approach to the nonlinear analysis of slender elastic beams is employed to investigate the buckling and postbuckling behavior of two symmetric plane frames, namely a hinged portal frame and a hinged two-bar frame, The beams are assumed to be inextensible and shear undeformable. The “hybrid” functional on which the present analysis is based according to a
International Journal of Solids and Structures, 2016
In this paper a procedure for constructing a 1D continuum equivalent to a Koiter plate, is presen... more In this paper a procedure for constructing a 1D continuum equivalent to a Koiter plate, is presented. The result is used to build-up a coarse model of a Thin Walled Beam. The model results to be a nonlinear hyperelastic 1D second gradient continuum, endowed with an internal microstructure described by seven scalar kinematic parameters. The kinematic parameters are able to describe, although in a rough way, the deformation of the TWB in the plane of its cross-section. The nonlinear behaviour of a simply supported strut has been analyzed and the results compared with those given by the commercial finite element code ABAQUS.