International Journal of Computational Methods

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for numerical simulation of free-surface flow problems. The presented SPH method involves two major modifications on the traditional SPH method: (1) kernel gradient correction (KGC) and density correction to improve the computational accuracy in particle approximation and (2) RANS turbulence model to capture the inherent physics of flow turbulence. In the simulation, artificial compressibility for modeling incompressible fluid and ghost particles for treating solid boundaries are both applied. The presented SPH has been applied to two dam-breaking problems. We demonstrated that the presented SPH method has very good performance with more accurate flow patterns and pressure field distribution.

Ballast water has frequently been used in ships to provide stability and adjust trim, stress, and torsion for optimal steering and propulsion. Numerical simulation of the movement of ballast water and its interaction with the solid walls of operating ships are very difficult for traditional grid-based numerical models. In this paper, the smoothed particle hydrodynamics (SPH) method is applied to simulate water tank sloshing and the movement of ships carrying ballast water in three cases. Numerical results of water tank sloshing are compared with experimental ones. Numerical results of ships indicate that carrying ballast water in several separated small tanks generally makes a ship more stable, but keeping ballast water in one big tank generally makes a ship more unstable.

Based on the molecular dynamics (MD) method, the single-crystalline copper nanowire with different surface defects is investigated through tension simulation. For comparison, the MD tension simulations of perfect nanowire are first carried out under different temperatures, strain rates, and sizes. It has concluded that the surface–volume ratio significantly affects the mechanical properties of nanowire. The surface defects on nanowires are then systematically studied in considering different defect orientation and distribution. It is found that the Young's modulus is the insensitive of surface defects. However, the yield strength and yield point show a significant decrease due to the different defects. Different defects are observed to serve as a dislocation source.

This paper presents a fast multipole boundary element approach to the 3D acoustic shape sensitivity analysis based on the discrete adjoint variable method. The Burton–Miller formula is used to conquer the fictitious eigenfrequency problem of the original boundary integral equation method in solving exterior acoustic problems. Constant elements are used to discretize the boundary, so that the hypersingular integrals contained in the formulae can be evaluated explicitly and directly. Numerical examples are presented to demonstrate the accuracy and efficiency of the present approach.

The modal topology optimization method of continuum structure based on element-free Galerkin (EFG) method is presented by integrating solid isotropic material with penalization (SIMP) method with the optimality criteria method, and the penalty method is used to impose essential boundary conditions. The density of Gauss point and nodal density are selected as the design variables respectively, and the maximum of the first-order natural frequency is specified as the objective function. The sensitivity analysis algorithm is derived by using direct differential method. The examples are finished by selecting the two types of design variables respectively. The results obtained show that the checkerboard phenomenon does not appear when nodal density is selected as the design variable, and also verify that topology optimization method presented is feasible.

A unified scaled boundary finite element method (SBFEM) in the frequency domain was proposed for a semi-infinite reservoir with uniform cross section subjected to horizontal and vertical ground excitations, and a methodology was presented to solve the unified SBFEM through decomposing the unified SBFEM into two parts; one part modeling the reservoir subjected to horizontal excitations and the other part modeling the whole reservoir subjected to vertical excitations. The accuracy of the unified SBFEM and its solving methodology was validated through analyzing numerical examples. The SBFEM solutions were in good agreement with analytical or other numerical method's solutions.

This study develops an adaptive time-stepping procedure of Newmark integration scheme for transient elastodynamic problems, based on the semi-analytical scaled boundary finite element method (SBFEM). In each time step, a posteriori local error estimator based on the linear distributed acceleration is employed to estimate the error caused by the time discretization. The total energy of the domain, consisting of the kinetic energy and the strain energy, is calculated semi-analytically. The time increment is automatically adjusted according to a simple criterion. Three examples with stress wave propagation were modeled. The numerical results show that the developed method is capable of limiting the local error estimator within specified targets by using an optimal time increment in each time step.

The scaled boundary finite element method (SBFEM) is used to solve the seepage problems with multi-material regions. Two models of dam base with waterproof screen and dam body with the regions of two materials are established. The numerical solutions are obtained and then compared with the analytical results or numerical solutions in the references. The conclusion shows that the SBFEM has more satisfactory accuracy and less data preparation amount.

B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.

Event-driven method (EDM) and the time-driven method (TDM) are two main branches of discrete element methods (DEM) for the simulations of granular materials. A new algorithm is introduced in this paper where different models are used for different local volume fractions. TDM time step is used for the cases with high volume fractions and EDM time step is used for the cases with low volume fractions. Whether the local volume fraction is low or high is determined by the number of neighbors in the Verlet table. While the time step updating the Verlet table is the same as the time step for those particles without neighbors in the Verlet table.

In this paper, a novel linear equation solution method is proposed based on a row elimination back-substitution method (REBSM). The elimination and back-substitution procedures are carried out on individual row levels. The advantage of the proposed method is that it is much faster and requires less storage than the Gaussian elimination algorithm and, therefore, is capable of solving larger systems of equations. The method is particularly efficient for solving band diagonal sparse systems with symmetric or nonsymmetric coefficient matrices, and can be easily applied to popular numerical methods, such as the finite element method and the boundary element method. Detailed Fortran codes and examples are given to demonstrate the robustness and efficiency of the proposed method.

This study analyzed thin-plate bending problems with a geometrical nonlinearity using the Hermite reproducing kernel approximation and sub-domain-stabilized conforming integration. In thin-plate bending analyses, the deflections and rotations satisfy so-called Kirchhoff mode reproducing conditions. It is then possible to solve large deflection analyses of thin plates, such as elastic bucking problems, with high accuracy and efficiency. Total Lagrangian method is applied to solve the geometrical nonlinearity of the thin plates' deflections and rotations. The Green–Lagrange strain and second Piola–Kirchhoff stress forms are adopted to represent the strains and stresses in the thin plates. Mathematical formulation and some numerical examples are also demonstrated.

A structured overset grid approach coupled with Reynolds-Averaged Navier-Stokes (overset-RANS) method is presented to provide an accurate resolution of two surface ships moving with opposite velocity in viscous fluids. The RANS equations with shear stress transport (SST) k - ω model are employed to treat the viscous turbulent flows. The fully nonlinear boundary condition at the free surface is satisfied at each time step and the evolution of the free surface is achieved by using the level set method. A structured overset grid approach is used to allow flexibility in grid generation, local mesh refinement, as well as the simulation of moving objects while maintaining good grid quality. The presented overset-RANS method is demonstrated by two surface Wigley ship hulls moving with opposite velocity in still water. The simulating results illustrate the feasibility of the presented method to compute the complex viscous free surface flows interacting with many moving ships in still water or in waves.

Extreme elevation of temperature principally threatens tunnel linings and may cause fatal disaster; the recovery of it may take a long time and significant traffic troubles. System of equations is to be described and solution in terms of boundary element method (BEM) is suggested. Moreover, a technique of time-dependent eigenparameters enables one to apply parallel computations and converts the strongly nonlinear system to pseudo-linear one using the influence and polarization tensors. Consequently, instead of repeated solution of large systems of equations, the multiplication of pre-calculated influence matrices has to be carried out instead. In order to properly create the above-outlined procedure, internal cells are selected in the regions primarily connected by the change of temperature. Some examples follow the theory.

Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.

This study reviews our recent efforts in the development and application of crack propagation modeling approaches based on the scaled boundary finite element method (SBFEM). These include models for linear and nonlinear, static and dynamic, and single and multiple crack propagation problems, and application to efficient prediction of deterministic size effect laws and complicated fracture behavior of reinforced concrete structures. The advantages and disadvantages of these approaches are compared with the FEM.

In this paper, the probabilistic solutions of the multi-degree-of-freedom (MDOF) or large-scale stochastic dynamic systems with polynomial type of nonlinearity and excited by Gaussian white noise excitations are obtained and investigated with the subspace method proposed recently by the authors. The space of the state variables of large-scale nonlinear stochastic dynamic (NSD) system excited by white noises is separated into two subspaces. Both sides of the Fokker–Planck–Kolmogorov (FPK) equation corresponding to the NSD system is then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in another subspace is formulated. Therefore, the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale NSD systems solvable with the exponential polynomial closure (EPC) method. A simple flexural beam on nonlinear elastic springs is analyzed with the subspace method to show the effectiveness of the subspace-EPC method in this case.

The probability density function (PDF) solution of the response is formulated for nonlinear systems under discrete Poisson impulse excitation. The PDF solution is governed by the Kolmogorov–Feller (KF) equation, which is approximately solved by the exponential–polynomial closure (EPC) method. A Duffing oscillator is further investigated in the case of either Gaussian or non-Gaussian distributed amplitude of Poisson impulse to show the effectiveness of the EPC method in these cases. The numerical analysis shows that the EPC method with the polynomial order being 6 presents a good result compared with the simulated result, even in the tails of the PDF of the oscillator response.

Subdivision surface modeling, which is based on polygon mesh modeling, can generate a whole smooth geometry without limiting to the topology and connectivity. Meanwhile, the boundary element analysis (BEA), which is based on the boundary integral equation, requires only boundary discretization of the body in question. Thus, performing BEA directly on the subdivision surface models may be a promising way to realize the seamless integration. This work presents a unified framework for the BEA and CAD modeling based on the subdivision surface. Numerical examples for 3D potential problems have demonstrated that the implementation is successful.

The presentation is mainly devoted to the research on the regularized boundary integral equations (BIEs) with indirect unknowns for torsion problem of the anisotropic uniform bar. Based on a new view and idea, a novel regularization technique is pursued, in which the nonsingular indirect BIE (IBIE) excluding the CPV and HFP integrals is established. Such torsion problems can be solved directly by using the presented technique without transforming them into isotropic ones, for this reason, no inverse transform is required. Moreover, a unique feature of the shear stress BIEs expressed by density functions is that they are independent of the warp BIEs and, as such, can be collocated at the same locations as the warp BIEs. This provides additional and concurrently useable equations for various purposes. Besides, in the numerical implementation, the boundary geometric is depicted by exact elements, while the distribution of the boundary quantity on each element is approximated by a discontinuous quadratic element. Some numerical examples will be applied to validate the current scheme. It is shown that a better precision and high-computational efficiency can be achieved by the presentation.

This paper presents a curvature-constructed method (CCM) for bending analysis of thin plates using three-node triangular cells and assumed piecewisely linear deflection field. In the present CCM, the formulation is based on the classic thin plate theory, and only deflection field is treated as the field variable that is assumed piecewisely linear using a set of three-node triangular background cells. The slopes at nodes and/or the mid-edge points of the triangular cells are first obtained using the gradient smoothing techniques (GST) over different smoothing domains. Three schemes are devised to construct the curvature in each cell using these slopes at nodes and/or the mid-edge points. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential rotational boundary conditions are imposed in the process of constructing the curvature field, and the translational boundary conditions are imposed in the same way as in the standard FEM. A number of numerical examples, including both static and free vibration analyses, are studied using the present CCM and the numerical results are compared with the analytical ones and those in the published literatures. The results show that outstanding schemes can obtain very accurate solutions.

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.

A granule hydrodynamics method is proposed in studying complex dynamic behavior of wind-blown movement system. Fluid in the wind-blown movement system is discretized into elastic fluid granules in a certain scale of time and space. It is considered that fluid motion is caused by fluid granules collision and fluid density difference (or pressure difference). Based on the essential properties of fluid, the constitutive relations of fluid granules are well established in the proposed granule hydrodynamics method, fluid state equation, and fluid sound velocity derivative state equation are adopted to study motion law of fluid or fluid–solid coupling, rather than the Navier–Stokes equation in traditional fluid mechanics. Results on classical shear flow in a cavity based on the proposed granule hydrodynamics method agree well with those based on finite difference method and smoothed particle hydrodynamics method, which verifies the validity and feasibility of the granule hydrodynamics method. Two more numerical examples of solid–fluid coupling of a multiple moving solid system are also provided, which proves the feasibility, convenience, and uniqueness of the proposed method.