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Purpose The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve... more
Purpose The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems. Design/methodology/approach The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place. Findings The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points. Originality/value The current study paves the road for future studies on dynamic and static crack propagation p...
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Ls-Prepost was used to generate the model. Ls-Dyna was used to simulate the behaviour of this material under compressive loads. The objective was to reproduce deformation mechanisms and to compare the numerical load-displacement curves... more
Ls-Prepost was used to generate the model. Ls-Dyna was used to simulate the behaviour of this material under compressive loads. The objective was to reproduce deformation mechanisms and to compare the numerical load-displacement curves with those obtained from ...
Therefore, the present work proposes a numerical approach to modify the chin bar of a helmet with the aim of reducing the risk of BSF and of satisfying the requirements of the current standards. Two types of FE simulations were carried... more
Therefore, the present work proposes a numerical approach to modify the chin bar of a helmet with the aim of reducing the risk of BSF and of satisfying the requirements of the current standards. Two types of FE simulations were carried out in the present work by means of LS‐Dyna software. The first one involved a helmeted HYBRID III head and neck which was hit by a cylindrical impactor on the chin bar of the helmet at a velocity of 3.5 m/s. This simulation was adopted from the test method in for the chin bar in order to measure the induced neck force due to the impact on the chin bar. The second type of FE simulation was the virtual impact test for the chin bar of the full‐face helmet according to ECE 22.05. The proposed approach was developed to optimize the composite chin bar of a full‐face helmet to reduce the risk of BSF, which is one of the most common types of injury among motorcycle accidents but is not clearly addressed in standards. The results show that the developed appro...
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Cracks are present in almost all structural components. It is of the highest importance to be able to describe fatigue crack propagation in engineering structures for a safe use and to define a proper repair and maintenance program. Even... more
Cracks are present in almost all structural components. It is of the highest importance to be able to describe fatigue crack propagation in engineering structures for a safe use and to define a proper repair and maintenance program. Even though a large amount of analytical work has been performed, the description of the behaviour of actual component geometries under realistic loading conditions require the use of numerical methods. The modeling of damage propagation phenomena is usually a difficult task because it is necessary to have the capability of describing generation and growth of material discontinuities. In the last thirty years, several approaches have been developed to model and simulate fatigue crack growth in structural components such as the boundary element method [1], the finite element method [2], mesh free methods [3], the extended finite element method [4] and the free Galerkin method [5]. In these approaches, it is necessary to define a criterium to predict the ...
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This paper aims to define a homogenised constitutive relation for the global behaviour of periodic composite structures in the case of non-linear material components. Special emphasis is put on the description of the generality of the... more
This paper aims to define a homogenised constitutive relation for the global behaviour of periodic composite structures in the case of non-linear material components. Special emphasis is put on the description of the generality of the algorithm which, in principle, can be applied to any kind of nonlinear material behaviour affecting the representative volume element. The method is currently restricted to plane situations with monotonic proportional loading.
Publisher Summary The advent of energy-momentum conserving time integration schemes has introduced a class of robust and accurate algorithms to solve geometrically nonlinear structural dynamic problems. The time-discretization of an... more
Publisher Summary The advent of energy-momentum conserving time integration schemes has introduced a class of robust and accurate algorithms to solve geometrically nonlinear structural dynamic problems. The time-discretization of an external force has to be studied carefully to obtain an advantage of the energy conserving based method. This differs from the autonomous dissipative case, where a straightforward application proved useful. An accurate discretized description of the change of energy because of the external force might not be simple to find. This chapter discusses the different discretizations of the external force term in a simple Duffing's oscillator. A comparison of the resulting algorithm is based on the investigations of stable and unstable manifold of a periodic saddle cycle.
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Homogenization theory is applied to the elastic analysis of beams composed of many fibers parallel to the beam axis. We first analyze the microstructure of the beam to define the local perturbation of a global mean behavior, due to... more
Homogenization theory is applied to the elastic analysis of beams composed of many fibers parallel to the beam axis. We first analyze the microstructure of the beam to define the local perturbation of a global mean behavior, due to nonhomogeneity. We describe this perturbation using first- and second-order terms in the asymptotic expansion of displacements in the power series of
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This work describes two newly developed computational tools that greatly improve the efficiency and the applicability of peridynamics-based software to computational mechanics. The first contribution is concerned with a new, flexible and... more
This work describes two newly developed computational tools that greatly improve the efficiency and the applicability of peridynamics-based software to computational mechanics. The first contribution is concerned with a new, flexible and accurate way to couple peridynamic grids to FEM meshes. The coupling produces a new computational method that applies FEM or PD discretisations where required and couples them in a way that keeps the advantages of both approaches and avoids their pitfalls. The second contribution is about a simple and accurate implicit solution of static problems in which the usual prototype microelastic brittle material (elasto-brittle) model is adopted. Finally a computational example is presented to show the potentialities of the new computational techniques.
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This chapter presents a strategy to couple the finite point method with peridynamic grids. The coupling is performed without introducing any additional blending function or arbitrary choice of tuning parameters with a completely meshless... more
This chapter presents a strategy to couple the finite point method with peridynamic grids. The coupling is performed without introducing any additional blending function or arbitrary choice of tuning parameters with a completely meshless approach. The method is used to study transient elastodynamic problems involving dynamic crack propagation.
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Recent challenges in structural health monitoring have been arising from new safety requirements and the increasing use of composite materials for aerospace structures. The behavior of composite materials is much more complex than that of... more
Recent challenges in structural health monitoring have been arising from new safety requirements and the increasing use of composite materials for aerospace structures. The behavior of composite materials is much more complex than that of metallic alloys [1], [2]. For composite materials, impacts are one of the main causes of damage and it becomes crucial to correctly determine if an impact has occurred, and therefore if damage is present, especially because composites are subjected to the so called barely visible impact damage which can eventually lead to the catastrophic failure of the system [3].
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Abstract In this paper a new collocation technique for constructing time-dependent absorbing boundary conditions (ABCs) applicable to elastic wave motion is devised. The approach makes use of plane waves which satisfy the governing... more
Abstract In this paper a new collocation technique for constructing time-dependent absorbing boundary conditions (ABCs) applicable to elastic wave motion is devised. The approach makes use of plane waves which satisfy the governing equations of motion to construct the absorbing boundary conditions. The plane waves are adjusted so that they can cope with the satisfaction of radiation boundary conditions. The proposed technique offers some advantages and exhibits the following features: it is easy to implement; its approximation scheme is local in space and time and thus it does not deal with any routine schemes such as Fourier and Laplace transform, making the method computationally less demanding; as the employed basis functions used to construct the absorbing boundary condition are residual-free, it requires neither any differential operator (to approximate the wave dispersion relation), nor any auxiliary variables; it constructs Dirichlet-type ABCs and hence no derivatives of the field variables are required for the imposition of radiation conditions. In this study, we apply the proposed technique to the solution procedure of a collocation approach based on the finite point method which proceeds in time by an explicit velocity-Verlet algorithm. It contributes to developing a consistent meshless framework for the solution of unbounded elastodynamic problems in time domain. We also apply the proposed method to a standard finite element solver. The performance of the method in solution of some 2D examples is examined. We shall show that the method exhibits appropriate results, conserves the energy almost exactly, and it performs stably in time even in the case of long-term computations.
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Abstract The motion of a windshield wiper blade is modelled by a mass-spring-damper system on a moving frictional surface. The system dynamics is time-varying, since three different regimes of motion, characterized by different degrees of... more
Abstract The motion of a windshield wiper blade is modelled by a mass-spring-damper system on a moving frictional surface. The system dynamics is time-varying, since three different regimes of motion, characterized by different degrees of freedom, are possible. Indeed the system, which schematizes a blade cross-section, can experience stick and slip motions when it is in contact with the glass surface, and free-flight motion when it is detached. The contact between the system and the surface is governed by Stribeck׳s friction law and Poisson׳s impact law, which make the dynamics non-smooth. The model is numerically implemented in an event-driven code, and simulations are performed which reproduce the three basic classes of undesired oscillations observed in the motion of real windscreen wipers, i.e., squeal, reversal and chattering noises. Attention is focused on the causes of these vibrations, and remedies for reducing or avoiding them are proposed.
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Abstract An example of dynamic crack propagation in a 2D plate is used to clearly describe a problem affecting regular peridynamic grids: the crack-path dependence on the grid orientation. The problem, potentially very damaging for a... more
Abstract An example of dynamic crack propagation in a 2D plate is used to clearly describe a problem affecting regular peridynamic grids: the crack-path dependence on the grid orientation. The problem, potentially very damaging for a computational method devised to simulate in particular crack propagation conditions, is investigated and better understood. In order to solve it the paper proposes a strategy which involves an increase of the computational cost when applied to the whole discretized domain. The use of adaptive refinement techniques allows to apply such a strategy only where crack propagation is taking place and, in this way, drastically increases the computational efficiency.
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A new nonlocal theory of continuum, called Peridynamics, was introduced in 2000. While the classical theory of solid mechanics employs spatial derivatives in order to solve the motion equation and consequently requires the derivability of... more
A new nonlocal theory of continuum, called Peridynamics, was introduced in 2000. While the classical theory of solid mechanics employs spatial derivatives in order to solve the motion equation and consequently requires the derivability of the displacement field, Peridynamics employs an integral formulation of the equation of motion which leads to the possibility to analyze structures without specific techniques whenever discontinuities, such as cracks or inhomogeneities, are involved. Peridynamics has proven to be able to handle several phenomena concerning crack propagation. There are two variants of the theory, bond-based and state-based. The former is a particular case of the latter, which can also be found in two versions, the ordinary, in which the interaction force between two nodes is aligned with their current relative position, and the non-ordinary, in which interaction forces can have different directions and classical models can be directly introduced in the formulation, ...
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Stable manifolds of saddle points are important in defining the dynamics of smooth nonlinear dynamical systems [1]. The stable manifold theorem for a fixed point states that there are local stable and unstable manifolds tangent to the... more
Stable manifolds of saddle points are important in defining the dynamics of smooth nonlinear dynamical systems [1]. The stable manifold theorem for a fixed point states that there are local stable and unstable manifolds tangent to the eigenspaces of the linearised system at the fixed point. The global stable (and unstable) manifold is given by the union of backward (and forward) mappings in time of the local manifold. If we restrict our attention to two-dimensional Poincare maps of three-dimensional flows, at a saddle point of the map, which corresponds to a saddle-limit cycle of the flow, the linearised system will have one-dimensional stable and unstable eigenspaces. At the saddle the local manifolds are tangent to the eigenvectors and in a neighbourhood of the saddle the local manifolds are therefore approximated by these eigenvectors [2]. A numerical procedure to compute the global stable manifolds derives directly from what we just said: a fixed point of a Poincare map is located with standard numerical algorithms [2] and its eigenvectors are computed. If it is a saddle point then an eigenvector is larger than one in modulus and the other is smaller. The stable eigenspace corresponds to the eigenvalue smaller than one. A number of points approximately lying on the stable manifold are then generated by choosing them close to the saddle in the direction of the stable eigenvector. The global stable manifold can be traced by integrating backward in time such a set of points. Numerical issues can affect the computation of the stable manifold; in particular the ‘stretching’ of the manifolds may reduce the degree of accuracy with which the manifold is reconstructed, but most of these problems have been successfully overcome for smooth systems [2].
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ABSTRACT
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ABSTRACT This paper describes a new numerical method to compute the separatrix of the basins of attraction of coexisting attractors in a forced friction oscillator. Numerical results show that its intersection with a Poincaré section is a... more
ABSTRACT This paper describes a new numerical method to compute the separatrix of the basins of attraction of coexisting attractors in a forced friction oscillator. Numerical results show that its intersection with a Poincaré section is a non-smooth curve.
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The dynamics of mechanical systems with dry friction is affected by non-smooth bifurcations, which have been recently partially classified as ‘sliding bifurcations’. In applied science a bifurcation is usually seen as the point in which... more
The dynamics of mechanical systems with dry friction is affected by non-smooth bifurcations, which have been recently partially classified as ‘sliding bifurcations’. In applied science a bifurcation is usually seen as the point in which the number of fixed points and/or (quasi-)periodic solutions changes. The paper describes with several detailed examples that ‘sliding bifurcations’ do not always correspond to such definition.
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This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the... more
This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the stability of the orbit but does not affect the orbit itself.
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The present paper describes an unusual example of chaotic motion occurring in a nonsmooth mechanical system affected by dry friction. The mechanical system generates one-dimensional maps the orbits of which seem to exhibit sensitive... more
The present paper describes an unusual example of chaotic motion occurring in a nonsmooth mechanical system affected by dry friction. The mechanical system generates one-dimensional maps the orbits of which seem to exhibit sensitive dependence on initial conditions only in an extremely small set of their field of definition. The chaotic attractor is composed of zones characterized by very different rates of divergence of nearby orbits: in a large portion of the chaotic attractor the system motion follows a regular pattern whereas the more usual irregular motion affects only a small portion of the attractor. The irregular phase reintroduces the orbit in the regular zone and the sequence is repeated. The Lyapunov exponent of the map is computed to characterize the steady state motions and confirm their chaotic nature.
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ABSTRACT