174 research outputs found
On the use of the theory of dynamical systems for transient problems
This paper is a preliminary work to address the problem of dynamical systems
with parameters varying in time. An idea to predict their behaviour is
proposed. These systems are called \emph{transient systems}, and are
distinguished from \emph{steady systems}, in which parameters are constant. In
particular, in steady systems the excitation is either constant (e.g. nought)
or periodic with amplitude, frequency and phase angle which do not vary in
time. We apply our method to systems which are subjected to a transient
excitation, which is neither constant nor periodic. The effect of switching-off
and full-transient forces is investigated. The former can be representative of
switching-off procedures in machines; the latter can represent earthquake
vibrations, wind gusts, etc. acting on a mechanical system. This class of
transient systems can be seen as the evolution of an ordinary steady system
into another ordinary steady system, for both of which the classical theory of
dynamical systems holds. The evolution from a steady system to the other is
driven by a transient force, which is regarded as a map between the two steady
systems.Comment: 7 pages, 9 figure
A novel and effective way to impose boundary conditions and to mitigate the surface effect in state‑based Peridynamics
AbstractPeridynamics is a nonlocal continuum theory capable of modeling effectively crack initiation and propagation in solid bodies. However, the nonlocal nature of this theory is the cause of two main problems near the boundary of the body: an undesired stiffness fluctuation, the so‐called surface effect, and the difficulty of defining a rational method to properly impose the boundary conditions. The surface effect is analyzed analytically and numerically in the present paper in a state‐based peridynamic model. The authors propose a modified fictitious node method based on an extrapolation with a truncated Taylor series expansion. Furthermore, a rational procedure to impose the boundary conditions is defined with the aid of the fictitious nodes. In particular, Neumann boundary conditions are implemented via the peridynamic concept of force flux. The accuracy of the proposed method is assessed by means of several numerical examples for a state‐based peridynamic model: with respect to the peridynamic model adopting no corrections, the results are significantly improved even if low values of the truncation order for the Taylor expansion are chosen
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Use of the theory of dynamical systems for transient problems: application to the switching-on problem
This paper addresses the problem of dynamical systems with parameters varying in
time (transient systems). A method to predict their behaviour is proposed. This class of transient
systems can be seen as the evolution of an ordinary steady system into another ordinary steady
system, for both of which the classical theory of dynamical systems holds. The evolution from a
steady system to the other is driven by a transient force, which is regarded as a map between the two
steady systems. We apply our method to a system which is subjected to a transient excitation, that is
neither constant nor periodic, to simulate the effect of switching-on procedures
Matrix-based implementation and GPU acceleration of linearized ordinary state-based peridynamic models in MATLAB
Ordinary state-based peridynamic (OSB-PD) models have an unparalleled
capability to simulate crack propagation phenomena in solids with arbitrary
Poisson's ratio. However, their non-locality also leads to prohibitively high
computational cost. In this paper, a fast solution scheme for OSB-PD models
based on matrix operation is introduced, with which, the graphics processing
units (GPUs) are used to accelerate the computation. For the purpose of
comparison and verification, a commonly used solution scheme based on loop
operation is also presented. An in-house software is developed in MATLAB.
Firstly, the vibration of a cantilever beam is solved for validating the loop-
and matrix-based schemes by comparing the numerical solutions to those produced
by a FEM software. Subsequently, two typical dynamic crack propagation problems
are simulated to illustrate the effectiveness of the proposed schemes in
solving dynamic fracture problems. Finally, the simulation of the Brokenshire
torsion experiment is carried out by using the matrix-based scheme, and the
similarity in the shapes of the experimental and numerical broken specimens
further demonstrates the ability of the proposed approach to deal with 3D
non-planar fracture problems. In addition, the speed-up of the matrix-based
scheme with respect to the loop-based scheme and the performance of the GPU
acceleration are investigated. The results emphasize the high computational
efficiency of the matrix-based implementation scheme.Comment: 32 pages, 16 figure
impact force reconstruction in composite panels
Abstract Passive sensing is a branch of structural health monitoring which aims at detecting positions and intensities of impacts occurring on aeronautical structures. Impacts are one of the main causes of damage in composite panels, limiting the application of these modern components on aircraft. In particular, impacts can cause the so called barely visible impact damage which, if not detected rapidly, can grow and lead to catastrophic failure. The determination of the impact location and the reconstruction of impact force is necessary to evaluate the health of the structure. These data may be measured indirectly from the measurements of responses of sensors located on the system subjected to the impact. The impact force reconstruction is a complex inverse problem, where the cause is to be inferred from its consequences. Inverse problems are in general ill-posed and ill-conditioned. Therefore, several techniques have been employed in the last four decades and have proven to be effective within certain limitations. Among these methods, transfer function based methods have been mainly validated for low-energy impact where the linear assumption should be valid. Nonlinearities may affect the accuracy in the reconstruction process and thus in the evaluation of damage other techniques have been adopted, such as artificial neural networks (ANN) or genetic algorithms (GA). In this study, a stiffened panel model developed in Abaqus/CAE is first validated, then numerical simulations are used to obtain data for several impacts, characterized by different impact locations and different energy (by changing the impactor mass and/or velocity). Geometrical nonlinearities of the dynamic system are considered in order to represent accurately the mechanics of the composite panel. Then the complex nonlinear behavior will be modeled through a nonlinear system identification approach, such as ANN, and an intelligent algorithm with global search capabilities, such as GA, will be used in sequence to accurately recovery the impact force peak and, therefore, properly evaluate the health status of the structure
Numerical simulation of forerunning fracture in saturated porous solids with hybrid FEM/Peridynamic model
In this paper, a novel hybrid FEM and Peridynamic modeling approach proposed
in Ni et al. (2020) is used to predict the dynamic solution of hydro-mechanical
coupled problems. A modified staggered solution algorithm is adopted to solve
the coupled system. A one-dimensional dynamic consolidation problem is solved
first to validate the hybrid modeling approach, and both -convergence and
-convergence studies are carried out to determine appropriate discretization
parameters for the hybrid model. Thereafter, dynamic fracturing in a
rectangular dry/fully saturated structure with a central initial crack is
simulated both under mechanical loading and fluid-driven conditions. In the
mechanical loading fracture case, fixed surface pressure is applied on the
upper and lower surfaces of the initial crack near the central position to
force its opening. In the fluid-driven fracture case, the fluid injection is
operated at the centre of the initial crack with a fixed rate. Under the action
of the applied external force and fluid injection, forerunning fracture
behavior is observed both in the dry and saturated conditions.Comment: arXiv admin note: text overlap with arXiv:2307.1092
Hybrid FEM and peridynamic simulation of hydraulic fracture propagation in saturated porous media
This paper presents a hybrid modeling approach for simulating hydraulic
fracture propagation in saturated porous media: ordinary state-based
peridynamics is used to describe the behavior of the solid phase, including the
deformation and crack propagation, while FEM is used to describe the fluid flow
and to evaluate the pore pressure. Classical Biot poroelasticity theory is
adopted. The proposed approach is first verified by comparing its results with
the exact solutions of two examples. Subsequently, a series of pressure- and
fluid-driven crack propagation examples are solved and presented. The
phenomenon of fluid pressure oscillation is observed in the fluid-driven crack
propagation examples, which is consistent with previous experimental and
numerical evidences. All the presented examples demonstrate the capability of
the proposed approach in solving problems of hydraulic fracture propagation in
saturated porous media
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