International Journal of Computational Methods

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for simulating violent water impinging jet flow problems. The presented SPH method involves three major modifications on the traditional SPH method, (1) The kernel gradient correction (KGC) and density correction are used to improve the computational accuracy and obtain smoothed pressure field, (2) a coupled dynamic solid boundary treatment (SBT) is used to remove the numerical oscillation near the solid boundary and ensure no penetration condition, (3) a free surface condition, which is obtained from the summation of kernel function and volume, is used to describe the water jet accurately. Different cases about violent impinging jet flows are simulated. The influences of impact velocity and angles are investigated. It is demonstrated that the presented SPH method has very good performance with accurate impinging jet patterns and pressure field distribution. It is also found that the pressure time histories of observation points are greatly influenced by the rarefaction wave from surrounding air. Closer distance from free surface can lead to quicker decay of the pressure time history.

A finite element model is developed in this paper for numerical modeling of the structural responses of FRP-strengthened reinforced concrete panels under blast loading. Strain rate effects for concrete in tension and compression, steel reinforcements and FRP sheets are taken into account in the finite element model. The commercial explicit hydrocode LS-DYNA is employed to carry out the numerical analysis. The proposed finite element model is validated by comparing the computed results of a conventional reinforced concrete panel and FRP-strengthened reinforced concrete panels under blast loading with the test data from the literature. In addition, the effects of FRP thickness, retrofitted surface, standoff distance and the charge mass on the blast resistance of FRP-strengthened reinforced concrete panels are investigated in this paper.

This paper presents a dissipative particle dynamics (DPDs) method for investigating the movement and deformation of biconcave shape red blood cells (RBCs) with the worm-like chain (WLC) bead spring. First, the stretching of a RBC is modeled and the obtained shape evolution of the cell agrees well with experimental results. Second, the movement and deformation of a RBC in shear flows are investigated and three typical modes (tumbling, intermittent and tank-treading) are observed. Lastly, an illustrating example of multi-RBCs in Poiseuille flow in a tube is simulated. We conclude that the presented DPD method with WLC spring can effectively model the movement and deformation of bioconcave cells.

We examine the recently-proposed density-scaled balanced continuum surface force (CSF) model with a level set-based curvature interpolation technique. The density-scaled balanced CSF model is combined with a numerical framework which is based on the coupled level set and volume-of-fluid (CLSVOF) method, the tangent of hyperbola for interface capturing/weighted line interface calculation (THINC/WLIC) scheme, the constrained interpolation profile conservative semi-Langrangian with rational function (CIP-CSLR) and the volume/surface integrated average-based multi-moment method (VSIAM3). The present CSF model is examined for various bench mark problems such as drop–drop collisions and drop splashing. Comparisons of the present model results with experimental observations and those from the other CSF models show that the present CSF model can minimize spurious current and capture complicated fluid phenomena with minimizing floatsam.

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters of model inputs are changed. Then, based on the failure probability ratio function, a global sensitivity analysis technique, called R-index, is proposed for measuring the average contribution of the distribution parameters to the failure probability while they vary in intervals. The proposed failure probability ratio function and R-index can be especially useful for failure probability reduction, reliability-based optimization and reduction of the epistemic uncertainty of parameters. The Monte Carlo simulation (MCS), Importance Sampling (IS) and Truncated Importance Sampling (TIS) procedures, which need only a set of samples for implementing them, are introduced for efficiently computing the proposed sensitivity indices. A numerical example is introduced for illustrating the engineering significance of the proposed sensitivity indices and verifying the efficiency and accuracy of the MCS, IS and TIS procedures. At last, the proposed sensitivity techniques are applied to a planar 10-bar structure for achieving a targeted 80% reduction of the failure probability.

This study contributes to the development of a ‘fundamental, atomistic basis’ to inform macro-scale models that can provide significant insights about the effect of dislocation microstructure evolution during plastic deformation. Within a mesoscale model, multi-dislocation interactions can be studied which are capable of driving high-stress effects such as dislocation nucleation under low applied stresses, due to stress-concentration in dislocation pile-ups at interfaces. This study establishes a methodology to evaluate a phenomenological model for atomic-scale crystal defect interactions from molecular dynamics simulations, which is a critical step for mesoscale studies of plastic deformation in metals. Dislocations are affected by thermally activated processes that become energetically favorable as the stress approaches a threshold value. The nudged elastic band technique is ideal for evaluating the energetic activation parameters from atomic simulations. With this method, the activation energy and volume were obtained for the process of homogeneous nucleation of a full dislocation loop in pure FCC aluminum. Using the (atomistic) activation parameters, a constitutive mathematical model is developed for simulations at the mesoscale, to evaluate the critical (local) shear stress threshold. The constitutive model is effective for extrapolating from an atomistic timeframe of femtoseconds to experimentally accessible timespans of seconds.

This paper represents some basic mathematic theories for G${}^s$ spaces of functions that can be used for weakened weak (W²) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G${}^s$ spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H¹ spaces. We then prove the equivalence of the G^s norms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and $\alpha$S-FEM to examine the properties of a smoothed method based on G^s spaces, in comparison with the standard FEM with weak formulation.

In this paper, a standard numerical method with piecewise linear interpolation on Shishkin mesh is suggested to solve a weakly coupled system of singularly perturbed boundary value problem for second-order ordinary differential difference equations with discontinuous convection coefficients and source terms. An error estimate is derived by using the supremum norm and it is of almost first-order convergence. Numerical results are provided to illustrate the theoretical results.

The low accuracy near the boundary or the interface in SPH method has been paid extensive attention. The Finite Particle Method (FPM) is a significant improvement to the traditional SPH method, which can greatly improve the computational accuracy for boundary particles. However, there are still some inherent defects for FPM, such as the long computing time and the potential numerical instability. By conducting matrix decomposition on the basic equations of FPM, an improved FPM method (IFPM) is proposed, which can not only maintain the high accuracy of FPM for boundary particles, but also keep the invertibility of the coefficient matrix in FPM. The numerical results show that the IFPM is really an effective improvement to traditional FPM, which could greatly reduce the computing time. Finally, the modified method is applied to two transient problems.

In this paper, an unsteady preconditioning formulation for multi-phase flows with arbitrary equation of state based on the approximated Riemann solver is developed for multi-phase flows at all speed. This paper considers a homogeneous two-phase multi-equation mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature-dependent hybrid equation of state. Benchmark test cases, including one-dimensional (1D) condensation shock in the cavitated nozzle and two-dimensional (2D) cavitated blunt body problem, demonstrate accurate capturing of interfaces, shock waves and cavitation zones.

Soil liquefaction induced by earthquakes poses a great threat to urban areas, not only by causing direct damages to infrastructures but also by delaying rescue and relief actions. Established engineering assessment methods using indices such as factor of safety against liquefaction (FL) tend to overestimate liquefaction hazards. While the standard usage of soil dynamic analysis for liquefaction assessment is limited to a single site with detailed site information. In this paper, we propose a framework based on soil dynamics for assessing liquefaction hazard for urban areas which contain numerous sites with borehole logs only. The framework is featured by generating analysis models and by estimating material parameters automatically from available borehole information. The governing equations for soil dynamics are solved by a finite element code. Liquefaction hazard is assessed according to the solutions of excess pore water pressure for given seismic waves. As demonstrations, we show simulation results of simple shear tests and of seismic response for a target site under loadings of artificial and of actual seismic waves. The automatic model construction and parameter estimation enable this framework being applied effectively for urban-area-wide liquefaction assessment, as an alternative for the current practices based on engineering indices.

The unsteady viscous flow around a 12000TEU ship model entering the Third Set of Panama Locks with different eccentricity is simulated by solving the unsteady Reynolds averaged Navier–Stokes (RANS) equations in combination with the $k-\omega$SST turbulence model. Overset grid technology is utilized to maintain grid orthogonality and the effects of the free surface are taken into account. The hydrodynamic forces, vertical displacement as well as surface pressure distribution are predicted and analyzed. First, a benchmark test case is designed to validate the capability of the present methods in the prediction of the viscous flow around the ship when maneuvering into the lock. The accumulation of water in front of the ship during entry into a lock is noticed. A set of systematic computations with different eccentricity are then carried out to examine the effect of eccentricity on the ship–lock hydrodynamic interaction.

In this paper, interaction between regular waves and free roll motion of a two-dimensional (2D) floating body is investigated by our in-house meshless particle solver MLParticle-SJTU based on modified moving particle semi-implicit (MPS) method. Numerical wave tank (NWT) is developed to calculate the interaction between waves and floating body, including wave-maker module and free roll motion module. The comparison between the numerical wave elevation and analytical solution shows that the MLParticle-SJTU solver can provide acceptable accuracy of wave making. Roll motion and force acting on the floating body in waves are in good agreement with experimental results. Profiles of the wave surface surrounding floating body are presented.

High axial force in central columns induced by strong vertical earthquake component is one of the most important factors in failure of subway stations. In this paper, the pushover method is adopted to simulate nonlinear behaviors of a multi-story subway station in Shanghai with different axial compression ratios through the general purpose finite element code ABAQUS. To simulate concrete material degradation during an earthquake accurately, the concrete damaged plasticity model was selected to trace damage characteristics of central columns. The softening index was used to describe the damage of the overall structure. Numerical results showed that in the structure level, the increase of axial compression ratio leads to the remarkable decrease of the structure ductility. The value of the softening index become less, which implies that the range and magnitude of damage to the structure become less either. However it should be noted that damages may be concentrated on certain members of the structure, such as central columns which are commonly considered to be the weakest but most critical part of an underground structure. In the member level, numerical results also showed that the increase of axial compression ratio led to small eccentric compression failure of central columns and accelerated the development of their compression damage.

An unsteady double-diffusive natural convection flow in an inclined rectangular enclosure subject to an applied magnetic field and heat generation parameter is studied. The enclosure is heated and concentrated from one side and cooled from the adjacent side. The other two sides are adiabatic. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamline, isotherm and iso-concentration contours. We have further obtained the average Nusselt numbers and average Sherwood numbers for various values of buoyancy ratio and different angles of the magnetic field by considering three different inclination angles of the enclosure while keeping the aspect ratio fixed. The results indicate that the flow pattern, temperature and concentration fields are significantly dependent on the buoyancy ratio and the magnetic field angles. It is found that different angles of the magnetic field suppress the convection flow and its direction influences the flow patterns. This leads to the appearance of inner loop and multiple eddies.

In this paper, we proposed a new highly efficient two-point sixth-order family of Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. In terms of computational cost, each member of the family requires two-function and two first-order derivative evaluations per iteration. On the account of the results obtained, it is found that our proposed methods are efficient and show better performance than existing sixth-order methods available in the literature. Further, it is also noted that larger basins of attraction belong to our methods as compared to the existing ones. On the other hand, the existing methods are slower and have darker basins while some of them are too sensitive upon the choice of the initial value.

Current contact force models are expected to be used under different environments, where the dynamical parameter estimation becomes an important issue in accurately analyzing the overall behavior of mechanical system especially for complex contact situations. In recent years, a significant amount of research has been carried out in relation to the nonlinear inverse problems, which can be generally divided into two categories: one is the linear method and the other can be called the nonlinear one. In this paper, both methods are described and compared. The linear method is based on the Taylor series and Exponentially Weighted Recursive Least Squares (EWRLS) estimation method. Whereas, the core of the nonlinear one is the Unscented Kalman Filter (UKF). The Lankarani–Nikravesh (L–N) contact force model is employed to quantify the contact effect in this paper, since it is proven to be more consistent with the physics of contact. Some simulation examples are employed to evaluate the convergence sensitivity of these two methods to parameter initial conditions. And the comparisons under the same simulation condition between both methods indicate that the nonlinear one is more robust and can converge faster than the linear one.

A multi-resolution moving particle semi-implicit (MPS) method is applied into two-dimensional (2D) free surface flows based on our in-house particle solver MLParticle-SJTU in the present work. Considering the effect of different size particles, both the influence radiuses of two adjacent particles are replaced by the arithmetic mean of their interaction radiuses. Then the modifications for kernel function of differential operator models are derived, respectively. In order to validate the present multi-resolution MPS method, two cases are carried out. Firstly, a hydrostatic case is performed. The results show that the contour of pressure field by multi-resolution MPS is quite in agreement with that by single resolution MPS. Especially, the multi-resolution MPS can still provide a relative smooth pressure together with the single resolution MPS in the vicinity of the interface between the high resolution and low resolution particles. For a long time simulation, the kinetic energy of particles by multi-resolution MPS can decrease quickly to the same level as that of single resolution MPS. In addition, a 2D dam breaking flow is simulated and the multi-resolution case can run stably during the whole simulation. The pressure by the multi-resolution MPS is in agreement with experimental data together with single resolution MPS. The contour of pressure field by the former is also similar to that by the later. Finally, the simulation by multi-resolution MPS is as accurate as the traditional MPS with fine particles distributed in the whole domain and the corresponding CPU time can be reduced.

Bi-modulus materials exhibit the different modulus in tension and compression. The value of elastic modulus and Poisson ratio of every point in the bi-modulus elastic body not only depend on the material itself, but also the stress state and the strain state of the point. The uncertainty and nonlinearity of the elastic constitutive relation result in that the bi-modulus elastic problem is the complicated nonlinear problem This paper aims at studying the bi-modulus elastic constitutive equation employed in the bi-modulus finite element numerical method (FEM). The new elastic matrix model is proposed based on Ye’s principal strain criterion with the assumption that the Poisson ratio maintain constant whenever in tension or in compression, and the elastic matrix is symmetric by equivalent transmitting. The shear modulus expression of this elastic matrix model is derived to enable the elastic matrix completely and improve the convergence of the FEM calculation. The statically indeterminate bi-modulus beam is analyzed by means of FEM employing the proposed elastic matrix model. The effects of the tensile modulus to compressive modulus ratio and the boundary condition on the stress and deflection of the bi-modulus beam is studied.

The reliability optimization has achieved great concern in recent years. Nowadays, many researchers obtain allocation results which can maximize the system reliability subject to the system budget. In these researches, the effect of system’s functions is always neglected or only considering the single main function of system. In addition, there are also no obvious evidences in results to distinguish the importance level of different units. However, complex systems tend to perform multiple functions. What’s more, the use frequency of each function and the combinations of units to realize different functions are not the same. In addition, the use demand of different functions is decided by different task environments, the demand differentiation of functions has led to the usage of frequency of various functions having different levels about reliability. Therefore, the reliability optimization allocation only considering cost constraint conditions is not accurate and will results in disaccord between the obtained results with actual situation.

Focusing on the problem mentioned above, a reliability optimization allocation method that considers cost constraint and importance factor is proposed. In this paper, we consider systems consisting of units characterized by different reliability and importance factors. Such systems are multi-function because they must perform different tasks depending on the combination of units. Different functions may work simultaneously. Firstly, the concept of importance factor is defined to describe the importance of a unit and the required importance factor level of system functions in the task is also given. To deal with the differentiation of system functions, the corresponding bound about importance factor are executed when looking for the optimal solution. Similarly, the cost constraint is also forced. Finally, in order to reduce the randomness of intelligent algorithm, a number of optimization are conducted and a rule is proposed to select the most optimal solution from all the optimal solutions which are obtained in every iterative loop.

Example of an integrated transmission device is presented. To begin with, we establish the reliability function of system as the objective optimization function. Then, the restraint of budget and different demands of importance factor of system functions are posed. Furthermore, using a genetic algorithm as the optimization tool, the optimization result can be obtained. Finally, the most optimal solution is selected. The results show that, the method, we proposed is more correct and more approximate than the reality. To verify the advantages and engineering applicability of the new method, the results obtained by the new method are compared with the results obtained under different conditions using basic genetic algorithm, without considering functions and the differentiation of functions, to solve the allocation problem of integrated transmission device, respectively.

The reliability optimization allocation method presented in this paper can not only consider the constraint of cost but also can consider the diversities of functions, and thus the optimization results will be more approximate in actual situation. At the same time, this paper can also provide guidance for the similar reliability optimization problem.

In this paper, vibration control algorithms for a large space truss structure are investigated. First, a precise integration method is used to solve the differential equation such that the validity and efficiency of the algorithm are guaranteed. Second, on the basis of the discrete algebraic equation combined with the decentralized control theory, the solving method of the control force based on the linear quadratic (LQ) optimal control theory is improved. Third, a new control method, the eigenvalue control method, is proposed in this paper, and its relationship with the LQ optimal control method is discussed. Finally, these two control methods are applied to the structure to analyze the effectiveness of vibration suppression. The simulation results show that the proposed algorithms can quickly suppress the vibration of a large space truss structure.