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Immersed particle method for fluid-structure interaction
... This simplifies greatly the mesh generation. Another computational method for the treatment of fluid-solid interactions is the Immersed Particle Method, where both the fluid and the structure are described using Lagrangian mesh free particles [Rabczuk, Gracie, Hsong, and Belytschko (2000)]. However, due to the lagrangian treatment of interfaces, these methods becomes cumbersome when extreme deformations and subsequently severe distortions of the finite element mesh or the particle distribution are observed. ...
Many colloidal-sized particles encountered in biological and membranebased separation applications can be characterized as soft vesicles such as cells, yeast, viruses and surfactant micelles. The deformation of these vesicles is expected to critically affect permeation by accommodating pore shapes and sizes or enhancing the adhesion with a pore surface. Numerical and theoretical modelings will be critical to fully understand these processes and thus design novel filtration membranes that target, not only size, but deformability as a selection criterion. The present paper therefore introduces a multiscale strategy that enables the determination of the permeability of a fibrous network with respect to complex fluids loaded with vesicles. The contributions are two-fold. First, we introduce a particle-based moving interface method that can be used to characterized the severe deformation of vesicles interacting with an immersed fibrous network. Second, we present a homogenization strategy that permits the determination of a network permeability, based on the micromechanisms of vesicle deformation and permeation. As a proof of concept, we then investigate the role of vesicle-solvent surface tension on the permeation of both solvent and vesicle through a simple fiber network. We find that vesicles are always retarded relative to the continuum (or solvent) flow, and that the relative selectivity for the continuum versus the vesicle is inversely proportional to the capillary number.
Cylindrical shell structures have excellent structural properties and load-bearing capacities in fields such as aerospace, marine engineering, and nuclear power. However, under high-pressure conditions, cylindrical shells are prone to cracking due to impact, corrosion, and fatigue, leading to a reduction in structural strength or failure. This paper proposes a static modeling method for damaged liquid-filled cylindrical shells based on the extended finite element method (XFEM). It investigated the impact of different initial crack angles on the crack propagation path and failure process of liquid-filled cylindrical shells, overcoming the difficulties of accurately simulating stress concentration at crack tips and discontinuities in the propagation path encountered in traditional finite element methods. Additionally, based on fluid‒structure interaction theory, a dynamic model for damaged liquid-filled cylindrical shells was established, analyzing the changes in pressure and flow state of the fluid during crack propagation. Experimental results showed that although the initial crack angle had a slight effect on the crack propagation path, the crack ultimately extended along both sides of the main axis of the cylindrical shell. When the initial crack angle was 0°, the crack propagation path was more likely to form a through-crack, with the highest penetration rate, whereas when the initial crack angle was 75°, the crack propagation speed was slower. After fluid entered the cylindrical shell, it spurted along the crack propagation path, forming a wave crest at the initial ejection position.
PurposeThe free vibration problem of a thin nanoplate with surface energy immersed in a viscous fluid medium is investigated in this article to assess the influence of different fluids on the vibration behavior of small-scale plates.Methods
Fluid–solid interaction is modeled based on Navier-Stokes equations, and surface energy is considered to apply small-scale effects. Finally, the solution of the equation of motion of nanoplate coupled with fluid is realized using the Galerkin weighted residual method.Results and Conclusion
According to the findings of this study, fluid density has a considerable impact on the reduction of the natural frequencies of plates at small scales, whereas viscosity has a negligible effect on the system's vibrational response. Moreover, the thickness of a nanoplate is inversely proportional to the influence of surface parameters on the nanoplate vibration as well as the effect of fluid on natural frequencies.
A new computational approach that combines the extended finite element method associated with variable-node elements and cohesive zone model is developed. By using a new enriched technique based on sign function, the proposed model using 4-node quadrilateral elements can eliminate the blending element problem. It also allows modeling the equal stresses at both sides of the crack in the crack-tip as assumed in the cohesive model, and is able to simulate the arbitrary crack-tip location. The multiscale mesh technique associated with variable-node elements and the arc-length method further improve the efficiency of the developed approach. The performance and accuracy of the present approach are illustrated through numerical experiments considering both mode-I and mixed-mode fracture in concrete.
In this study, a hydromechanical model for fluid flow in fractured porous media is presented. We assume viscous fluids and the coupling equations are derived from the mass and momentum balance equations for saturated porous media. The fluid flow through discrete cracks will be modelled by the extended finite element method and an implicit time integration scheme. We also present a consistent linearization of the underlying non-linear discrete equations. They are solved by the Newton-Raphson iteration procedure in combination with a line search. Furthermore, the model is extended to includes crack propagation. Finally, examples are presented to demonstrate the versatility and efficiency of this two-scale hydromechanical model. The results suggest that the presence of the fracture in a deforming, porous media has great impact on the fluid flow and deformation patterns.
We present a novel method to model large deformation fluid-structure-fracture interaction, which is characterized by the fact that the fluid induced loads lead to fracture of the structure, and the fluid medium fills the resulting crack opening; the mutual interaction between the crack faces and the surrounding fluid contributes substantially to the overall dynamics. A mesh refitting approach is utilized to model the quasi-static fracture of the structure, and a robust embedded interface formulation is used to solve the fluid flow equations. The proposed method employs a strongly coupled partitioned scheme with Aitken's Δ² method as convergence accelerator. Selected numerical examples of increasing complexity are presented to evaluate the performance of the proposed fluid-structure-fracture coupling algorithm. The most difficult simulation of the reported examples involves a number of complex phenomena: mixed-mode crack propagation through the structure, fluid starts to fill the crack opening, complete fracture of the structure into two pieces of which one is carried away by the flow.
A Thermomechanical Extended Layerwise Method (TELM) is developed for the laminated composite plates with multiple delaminations and transverse cracks. The discontinuity of displacements and temperature induced by multiple delaminations is simulated by strong discontinuous function while the discontinuity of strain and temperature gradient between dissimilar layers is modeled by a weak discontinuous function. Transverse cracks are modeled using classical Extended Finite Element Method (XFEM). The coupled thermomechanical variational principle is employed to derive the Euler equations and the discrete forms. Since the displacement and temperature fields are solved simultaneously, a fully coupled time integration method is developed based on the Newmark integration algorithm and Crank-Nicolson scheme. The strain energy release rate for multiple delamination fronts and stress intensity factors for transverse cracks are calculated by the Virtual Crack Closure Technique and the Interaction Integral Method, respectively. The proposed method is applied to the steady-state thermomechanical problems, elastic and thermomechanical dynamic problems for isotropic and composite plates with transverse cracks and multiple delaminations.
Peridynamics (PD) is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome of the simulation. However, capturing of complex mixed-mode crack patterns has been proven to be difficult with PD. On the other hand, the extended finite element method (XFEM) is one of the most popular methods for fracture which allows crack propagation with minimal remeshing. It requires a fracture criterion which is independent of the underlying discretization though a certain refinement is needed in order to obtain suitable results. This article presents a comparative study between XFEM and PD. Therefore, two examples are studied. The first example is crack propagation in a double notched specimen under uniaxial tension with different crack spacings in loading direction. The second example is the specimens with two center cracks. The results show that PD as well as XFEM are well suited to capture this type of behaviour.
In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two-phase and three-phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three-phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well-known element free Galerkin mesh-free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh-free methods. Different problems of multimaterial poro-elasticity including fully saturated, partially saturated one, and two-phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.
The meshless Shepard and least squares (MSLS) method and the meshless
Shepard method are partition of unity based meshless interpolations
which eliminate the problems by other meshless methods such as the
difficulty in direct imposition of the essential boundary conditions.
However, singular weight functions have to be used in both methods to
enforce the approximation interpolatory, which leads to the loss of
smoothness in approximation and locally oscillatory results. In this
paper, an improved MSLS interpolation is developed by using dually
defined nodal supports such that no singular weight function is
required. The proposed interpolation satisfies the delta property at
boundary nodes and the compatibility condition throughout the domain,
and is capable of exactly reproducing the basis function. The
computational cost of the present interpolation is much lower than the
moving least-squares approximation which is probably the most widely
used meshless interpolation at present.
The apparent hoop tensile strength of glass fiber-reinforced polyester pipes plays an important role during their design procedure. In some cases, glass fiber-reinforced polyester pipes industry used hydraulic failure pressure to obtain this value. In addition to the expensive and time-consuming characteristics of this experiment, it underestimates the apparent hoop tensile strength. A sequential failure modelling is developed to predict apparent hoop tensile strength modelling integrating classical lamination theory and progressive damage modelling. Developed modelling takes into account influence of incorporated sand layer in glass fiber-reinforced polyester pipe wall construction. Experimental study is conducted to validate developed technique. A very good agreement is observed between experimentally measured apparent hoop tensile strength of glass fiber-reinforced polyester pipes and predicted values employing sequential failure modelling.
A simple multiscale analysis framework for heterogeneous solids based on a
computational homogenization technique is presented. The macroscopic strain is
linked kinematically to the boundary displacement of a circular or spherical
representative volume which contains the microscopic information of the
material. The macroscopic stress is obtained from the energy principle between
the macroscopic scale and the microscopic scale. This new method is applied to
several standard examples to show its accuracy and consistency of the method
proposed.
A coupled fluid–structure modeling methodology for running ductile fracture in pressurized pipelines has been developed. The pipe material and fracture propagation have been modeled using the finite-element method with a ductile fracture criterion. The finite-volume method has been employed to simulate the fluid flow inside the pipe, and the resulting pressure profile was applied as a load in the finite-element model. Choked-flow theory was used for calculating the flow through the pipe crack. A comparison to full-scale tests of running ductile fracture in steel pipelines pressurized with hydrogen and with methane has been done, and very promising results have been obtained.
A 2D coupled two-mesh interaction model for blast gas flow through fractured and fragmented solid media is presented. It is mainly designed to solve blast problems where a complicated set of wide difficult phenomena are involved: shock waves, progressive fracturing, gas–solid interactions, stability of dynamic solution, contact mechanics, etc. The present approach is based on a gas flow through an equivalent porous medium and allows for temporal and spatial variations of mass, density, pressure and internal energy of the gas throughout the explosion process. The solid domain is represented by a combined finite/discrete element technique which is capable of modeling progressive cracking and fragmentation and any potential normal and frictional contacts during the cracking and post cracking phases. The approach allows for accurate evaluation of variations of geometries of voids and crack openings in order to facilitate the coupling effects on gas flow computations.A set of simple benchmark tests are used to verify the coupling and gas flow algorithms, while a rather complex engineering problem of progressive fracture of a masonry box due to an internal explosion is simulated to assess the overall performance of the proposed approach and to discuss various aspects of gas and solid phases in detail.
The present work aims to make a further development of a novel meshfree method for free vibration analysis of classical Kirchhoff’s plates. The deflection of plates is approximated by the moving Kriging interpolation method which possesses the Kronecker’s delta property. This thus makes the proposed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. A standard weak form is adapted to discrete the governing partial differential equations of plates. Numerical examples with different geometric shapes are considered to demonstrate the applicability and the accuracy of the proposed method.
In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied.
In this paper, sloshing phenomenon in a rectangular tank under a sway excitation is studied numerically and experimentally.
Although considerable advances have occurred in the development of numerical and experimental techniques for studying liquid
sloshing, discrepancies exist between these techniques, particularly in predicting time history of impact pressure. The aim
of this paper is to study the sloshing phenomenon experimentally and numerically using the Smoothed Particle Hydrodynamics
method. The algorithm is enhanced for accurately calculating impact load in sloshing flow. Experiments were conducted on a
1:30 scaled two-dimensional tank, undergoing translational motion along its longitudinal axis. Two different sloshing flows
corresponding to the ratio of exciting frequency to natural frequency were studied. The numerical and experimental results
are compared for both global and local parameters and show very good agreement.
KeywordsSloshing–Lagrangian methods–Smoothed Particle Hydrodynamics (SPH)–Impact pressure
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