Simulation of single mode Rayleigh–Taylor instability by SPH method

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh–Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace’s law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.     

Numerical modelling of the hydrodynamic ram phenomenon

Hydrodynamic ram (HRAM) is a phenomenon that occurs when a high-kinetic energy object penetrates a fluid-filled container. The projectile transfers its momentum and kinetic energy through the fluid to the surrounding structure, increasing the risk of catastrophic failure and excessive structural damage. This is of particular concern in the design of wing fuel tanks for aircraft since it has been identified as one of the important factors in aircraft vulnerability. In the present paper, the commercial finite-element code LS-DYNA has been used to simulate an HRAM event created by a steel spherical projectile impacting a water-filled aluminium square tube. Two different formulations (ALE and SPH) are employed to reproduce the event. Experimental tests which indicate the pressure at different points of the fluid, displacement of the walls and cavity evolution for different impact velocities are compared with the numerical results in order to assess the validity and accuracy of both ALE and SPH techniques in reproducing such a complex phenomenon.     

Solution of viscoelastic scattering problems in linear acoustics using hp Boundary/Finite Element Method

The interaction of acoustic waves with submerged structures remains one of the most difficult and challenging problems in underwater acoustics. Many techniques such as coupled Boundary Element (BE)/Finite Element (FE) or coupled Infinite Element (IE)/Finite Element approximations have evolved. In the present work, we focus on the steady‐state formulation only, and study a general coupled hp‐adaptive BE/FE method. A particular emphasis is placed on an a posteriori error estimation for the viscoelastic scattering problems. The highlights of the proposed methodology are as follows: (1) The exterior Helmholtz equation and the Sommerfeld radiation condition are replaced with an equivalent Burton–Miller (BM) boundary integral equation on the surface of the scatterer. (2) The BM equation is coupled to the steady‐state form of viscoelasticity equations modelling the behaviour of the structure. (3) The viscoelasticity equations are approximated using hp‐adaptive FE isoparametric discretizations with order of approximation p⩾5 in order to avoid the ‘locking’ phenomenon. (4) A compatible hp superparametric discretization is used to approximate the BM integral equation. (5) Both the FE and BE approximations are based on a weak form of the equations, and the Galerkin method, allowing for a full convergence analysis. (6) An a posteriori error estimate for the coupled problem of a residual type is derived, allowing for estimating the error in pressure on the wet surface of the scatterer. (7) An adaptive scheme, an extension of the Texas Three Step Adaptive Strategy is used to manipulate the mesh size h and the order of approximation p so as to approximately minimize the number of degrees of freedom required to produce a solution with a specified accuracy. The use of this hp‐scheme may exhibit exponential convergence rates. Several numerical experiments illustrate the methodology. These include detailed convergence studies for the problem of scattering of a plane acoustic wave on a viscoelastic sphere, and adaptive solutions of viscoelastic scattering problems for a series of MOCK0 models. Copyright © 1999 John Wiley & Sons, Ltd.     

流固耦合问题的PD-SPH建模与分析

针对涉及结构变形破坏的流固耦合(Fluid-structure interaction, FSI)问题,提出一种基于虚粒子和排斥力的近场动力学(Peridynamics, PD)-光滑粒子动力学(Smoothed particle hydrodynamics, SPH)耦合方法。结合PD方法求解不连续问题以及SPH方法在流体模拟方面的优势,分别采用PD方法与SPH方法求解固体域和流体域,并通过流体粒子-虚粒子接触算法处理流-固界面,既能利用粒子间排斥力有效防止粒子穿透现象发生,又能利用虚粒子修正流体粒子的边界缺陷,提高计算精度。采用PD-SPH耦合方法模拟静水压力作用下的铝板变形问题以及溃坝水流冲击弹性板问题,所得结果与解析解或其它数值结果吻合良好,验证了耦合方法的可行性和有效性。进一步应用耦合方法模拟了流体作用下的结构变形、破坏以及破坏后部分结构运动全过程,验证了PD-SPH耦合方法在流固耦合-结构破坏问题模拟方面的适用性。     

A new acoustic interface element for fluid-structure interaction problems

A new comprehensive acoustic 2-D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.     

A robust weakly compressible SPH method and its comparison with an incompressible SPH

This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering‐induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd.     

A meshless method for axi‐symmetric poroelastic simulations: numerical study

A meshless model, based on the meshless local Petrov–Galerkin (MLPG) approach, is developed and implemented for the solution of axi‐symmetric poroelastic problems. The solution accuracy and the code performance are investigated on a realistic application concerning the prediction of land subsidence above a deep compacting reservoir. The analysis addresses several numerical issues, including the parametric selection of the optimal size of the local sub‐domains for the weak form and the nodal supports, the appropriate integration rule, and the linear system solver. The results show that MLPG can be more accurate than the standard finite element (FE) method on coarse discretizations, with its superiority decreasing as the nodal resolution increases. This is due to both a slower convergence rate and a progressively higher computational cost compared to FE. These drawbacks can be partially mitigated by improving the efficiency of the numerical integration and the system solver with the aid of projection techniques based on Krylov subspace methods. The outcome of the present analysis supports the development of coupled methods where a limited number of MLPG nodes are used to locally improve a FE solution. Copyright © 2006 John Wiley & Sons, Ltd.     

A general framework for fatigue reliability analysis of a high temperature component

Fatigue reliability analysis for a high temperature component is a complex task due to the difficulties of doing experiments and uncertainties occurring in practical engineering. Researchers usually focus on the fatigue life scatter of standard specimens since the life data are easily available from fatigue tests. An alternative method is proposed in this paper which can replace the real tests of high temperature components with finite element (FE) simulation. A constitutive model coupled damage rule is utilized in this work to describe the cyclic stress‐strain response. Then, the FE simulations is incorporated into the general framework for reliability assessment. An adaptive least squares support vector machines with Latin hypercube sampling and learning function is employed to construct limit state function. To verify the accuracy and robustness of proposed method, a numerical example is utilized. In the end of this paper, a three‐layer structure extrusion container is applied for whole flowchart of fatigue reliability analysis.     

A coupled SDPH–FVM method for gas‐particle multiphase flow: Methodology

This paper describes a novel methodology that combines smoothed discrete particle hydrodynamics (SDPH) and finite volume method (FVM) to enhance the effective performance in solving the problems of gas‐particle multiphase flow. To describe the collision and fluctuation of particles, this method also increases a new parameter, namely, granular temperature, according to the kinetic theory of granular flow. The coupled framework of SDPH–FVM has been established, in which the drag force and pressure gradient act on the SDPH particles and the momentum sources of drag force are added back onto the FVM mesh. The proposed technique is a coupled discrete‐continuum method based on the two‐fluid model. To compute for the discrete phase, its SDPH is developed from smoothed particle hydrodynamics (SPH), in which the properties of SPH are redefined with some new physical quantities added into the traditional SPH parameters, so that it is more beneficial for SDPH in representing the particle characteristics. For the continuum phase, FVM is employed to discretize the continuum flow field on a stationary grid by capturing fluid characteristics. The coupled method exhibits strong efficiency and accuracy in several two‐dimensional numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermomechanical finite element simulations of ultrasonically assisted turning

Ultrasonically assisted turning (UAT) is studied with finite element (FE) simulations and compared with conventional turning (CT) using both computational results and infrared thermography experiments. The two-dimensional thermomechanically coupled FE model of both UAT and CT utilizes MSC MARC general FE code and incorporates temperature dependent material properties, strain rate effects, heat generated due to plastic flow, contact interaction and friction at the cutter/workpiece interface. Material separation in front of a cutting edge and automatic remeshing of distorted elements are implemented in the developed computational scheme. Influence of friction on resultant temperatures and chip shapes in turning for both UAT and CT is discussed. Temperature fields in the cutting region and in the cutting tool for CT and UAT are studied and compared with the experimental data. A role of various heat transfer parameters on thermal processes in UAT and CT is investigated.     

Simulation of high velocity concrete fragmentation using SPH/MLSPH

The simulation of concrete fragmentation under explosive loading by a meshfree Lagrangian method, the smooth particle hydrodynamics method (SPH) is described. Two improvements regarding the completeness of the SPH‐method are examined, first a normalization developed by Johnson and Beissel (NSPH) and second a moving least square (MLS) approach as modified by Scheffer (MLSPH). The SPH‐Code is implemented in FORTRAN 90 and parallelized with MPI. A macroscopic constitutive law with isotropic damage for fracture and fragmentation for concrete is implemented in the SPH‐Code. It is shown that the SPH‐method is able to simulate the fracture and fragmentation of concrete slabs under contact detonation. The numerical results from the different SPH‐methods are compared with the data from tests. The good agreement between calculation and experiment suggests that the SPH‐program can predict the correct maximum pressure as well as the damage of the concrete slabs. Finally the fragment distributions of the tests and the numerical calculations are compared. Copyright © 2003 John Wiley & Sons, Ltd.     

On the completeness of meshfree particle methods

The completeness of Smooth Particle Hydrodynamics (SPH) and its modifications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in finite-difference approximations. Several techniques which restore various levels of completeness by satisfying reproducing conditions on the approximation or the derivatives of the approximation are examined. A Petrov–Galerkin formulation for a particle method is developed using approximations with corrected derivatives. It is compared to a normalized SPH formulation based on kernel approximations and a Galerkin method based on moving least-square approximations. It is shown that the major difference is that in the SPH discretization, the function which plays the role of the test function is not integrable. Numerical results show that approximations which do not satisfy the completeness and integrability conditions fail to converge for linear elastostatics, so convergence is not expected in non-linear continuum mechanics. © 1998 John Wiley & Sons, Ltd.     

Hydroelasticity in water-entry problems: Comparison between experimental and SPH results

Hydroelastic impacts are of major interest in naval applications since, due to the mutual interaction between structural deformation and fluid motion, the impact-induced pressure and the impact dynamics can highly differ from a quasi-static solution. Hydroelastic effects are mostly important when the vessels are made with composite lightweight structures, due to the higher impact speed that can be reached. This work present an experimental and numerical study on the hydroelastic phenomena during the water-entry of elastic wedges. The numerical model is based on a coupled FEM and Smoothed Particle Hydrodynamics (SPH) formulation available in the commercial code Ls-Dyna. Results are compared with experiments about slamming of elastic wedges varying thickness, deadrise angle and impact velocity. Special attention is paid to the structural deformations. In particular, it is shown that more than one mode shape dominates the structural deformation in case of high hydroelastic impacts. Very high hydroelastic effects are observed, and the numerical solutions are found to be in good agreement with the measured data. The range of validity of the SPH technique to investigate hydroelastic effects during the water entry of elastic wedges is also outlined.     

A coupled two‐scale shell model with applications to layered structures

In this paper a coupled two‐scale shell model is presented. A variational formulation and associated linearization for the coupled global–local boundary value problem is derived. For small strain problems, various numerical solutions are computed within the so‐called FE ² method. The discretization of the shell is performed with quadrilaterals, whereas the local boundary value problems at the integration points of the shell are discretized using 8‐noded or 27‐noded brick elements or so‐called solid shell elements. At the bottom and top surface of the representative volume element stress boundary conditions are applied, whereas at the lateral surfaces the in‐plane displacements are prescribed. For the out‐of‐plane displacements link conditions are applied. The coupled nonlinear boundary value problems are simultaneously solved within a Newton iteration scheme. With an important test, the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified.Copyright © 2013 John Wiley & Sons, Ltd.     

ITERATIVE SOLUTION OF COUPLED FE/BE DISCRETIZATIONS FOR PLATE–FOUNDATION INTERACTION PROBLEMS

In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate–foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.     

Simulation of ductile crack propagation in dual-phase steel

The modified Mohr–Coulomb and the extended Cockcroft–Latham fracture criteria are used in explicit finite-element (FE) simulations of ductile crack propagation in a dual-phase steel sheet. The sheet is discretized using tri-linear solid elements and the element erosion technique is used to model the crack propagation. The numerical results are compared to quasi-static experiments conducted with five types of specimens (uniaxial tension, plane-strain tension, in-plane shear, 45° and 90° modified Arcan) made from a 2 mm thick sheet of the dual-phase steel Docol 600DL. The rate-dependent J ₂ flow theory with isotropic hardening was used in the simulations. The predicted crack paths and the force–displacement curves were quite similar in the simulations with the different fracture criteria. Except for the 45° modified Arcan test, the predicted crack paths were in good agreement with the experimental findings. The effect of using a high-exponent yield function in the prediction of the crack path was also investigated, and it was found that this improved the crack path prediction for the 45° modified Arcan test. In simulations carried out on FE models with a denser spatial discretization, the prediction of localized necking and crack propagation was in better accordance with the experimental observations. In four out of five specimen geometries, a through-thickness shear fracture was observed in the experiments. By introducing strain softening in the material model and applying a dense spatial discretization, the slant fracture mode was captured in the numerical models. This did not give a significant change in the global behaviour as represented by the force–displacement curves.     

Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches

The meshless local Petrov–Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/finite element (FE) method and a coupled MLPG/boundary element (BE) method are proposed in this paper to improve the solution efficiency. A procedure is developed for the coupled MLPG/FE method and the coupled MLPG/BE method so that the continuity and compatibility are preserved on the interface of the two domains where the MLPG and FE or BE methods are applied. The validity and efficiency of the MLPG/FE and MLPG/BE methods are demonstrated through a number of examples. Received 6 June 2000