International Journal of Computational Methods

This short article introduces first a Carbon-dioxide Balance Theory for sustainability of creatures living in the Earth atmosphere. A brief discussion then is presented on the importance of such a theory in policy making. An appeal is issued to all IJCM readers and author for making more efforts in creating computational methods and models to deal with sustainability issues.

The physics of fluid–fluid–solid contact line dynamics and wetting behaviors are closely related to the inter-particle and intra-molecular hydrodynamic interactions of the concerned multiple phase system. Investigation of surface tension, contact angle, and wetting behavior using molecular dynamics (MD) is practical only on extremely small time scales (nanoseconds) and length scales (nanometers) even if the most advanced high-performance computers are used. In this article we introduce two particle methods, which are smoothed particle hydrodynamics (SPH) and dissipative particle dynamics (DPD), for multiphase fluid motion on continuum scale and meso-scale (between the molecular and continuum scales). In both methods, the interaction of fluid particles and solid particles can be used to study fluid–fluid–solid contact line dynamics with different wetting behaviors. The interaction strengths between fluid particles and between fluid and wall particles are closely related to the wetting behavior and the contact angles. The effectiveness of SPH and DPD in modeling contact line dynamics and wetting behavior has been demonstrated by a number of numerical examples that show the complexity of different multiphase flow behaviors.

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modeling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is finite difference method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of FPDEs.

In this paper, an inverse method that combines the interval analysis with regularization is presented to stably identify the bounds of dynamic load acting on the uncertain structures. The uncertain parameters of the structure are treated as intervals and hence only their bounds are needed. Using the first-order Taylor expansion, the identified load can be approximated as a linear function of the uncertain parameters. In this function, it is assumed that the load at the midpoint of the uncertain parameters can be expressed as a series of impulse kernels. The finite element method (FEM) is used to obtain the response function of the impulse kernel and the response to the midpoint load is expressed in a form of convolution. In order to deal with the ill-posedness arising from the deconvolution, two regularization methods are adopted to provide the numerically efficient and stable solution of the desired unknown midpoint load. Then, a sensitivity analysis is suggested to calculate the first derivative of the identified load with respect to each uncertain parameter. Applying the interval extension in interval mathematics, the lower and upper bounds of identified load caused by the uncertainty can be finally determined. Numerical simulation demonstrates that the present method is effective and robust to stably determine the range of the load on the uncertain structures from the noisy measured response in time domain.

A Galerkin meshfree approach formulated within the framework of stabilized conforming nodal integration (SCNI) is presented for geometrically nonlinear analysis of large deflection shear deformable plates. This method is based upon a Lagrangian curvature smoothing in which the smoothed curvature is constructed within a nodal representative domain on the initial configuration. It is shown that the Lagrangian smoothed nodal gradients of the meshfree shape function is capable of exactly representing arbitrary constant curvature fields in the discrete sense of nodal integration. The consistent linearization is performed on the weak form of large deflection plate in the context of the total Lagrangian description. Subsequently, the discrete incremental equations are obtained by the method of SCNI in which to relieve the locking as well as ensure the stability of the present scheme, the bending contribution is evaluated using the smoothed nodal gradients, while the membrane and shear contributions are computed with the direct nodal gradients. The effectiveness of the present method is thoroughly demonstrated through several numerical examples.

This paper presents two novel and effective cell-based smoothed point interpolation methods (CS-PIM) using isoparametric PIM (PIM-Iso) shape functions and condensed radial PIM (RPIM-Cd) shape functions respectively. These two types of PIM shape functions can successfully overcome the singularity problem occurred in the process of creating PIM shape functions and make the constructed CS-PIM models work well with the three-node triangular meshes. Smoothed strains are obtained by performing the generalized gradient smoothing operation over each triangular background cells, because the nodal PIM shape functions can be discontinuous. The generalized smoothed Galerkin (GS-Galerkin) weakform is used to create the discretized system equations. Some numerical examples are studied to examine various properties of the present methods in terms of accuracy, convergence, and computational efficiency.

In dealing with shot-peening simulation, existing literatures adopt finite element method (FEM), which establishes models of a single shot or several shots only, thus the effect of a large number of shots repeat impacting and the influence among adjacent shots are ignored. To overcome these disadvantages of FEM models, smoothed particle hydrodynamics (SPH)-coupled FEM modeling is presented, in which the shots are modeled by SPH particles and the target material is modeled by finite elements. The two parts interact through contact algorithm to simulate a number of shots impinging the target. Utilizing this model, a material model for shots is established, the relationships between compressive residual stress and peening frequencies, coverage, and velocities are analyzed. Steady compressive residual stress can be obtained by multiple peening; higher coverage can improve the compressive residual stress; faster velocities can induce greater and deeper maximum residual stress in target subsurface. The simulation results agree well with the existing experimental data. The study would not only provide a new powerful tool for the simulation of shot-peening process, but also be benefit to optimize the operating parameters.

A novel procedure, immersed smoothed finite element method (immersed S-FEM) is proposed for solving fluid–structure interaction (FSI) problems with moving nonlinear solids, using triangular type of mesh. The method consists of well-combined three ingredients: two-step Taylor-characteristic-based-Galerkin (TCBG) method for incompressible viscous Navier–Stokes flows, the S-FEM for explicit dynamics analysis of nonlinear solids and structures, and FSI conditions using immersed technique with a modified direct force evaluation technique. Such a combination is designed for ensuring stability, best possible efficiency, and simplicity and convenient to use. The proposed method is verified by numerical examples using triangular meshes, which demonstrate the validity, accuracy, and the second-order convergence properties of the present method in both space and time.

This paper proposes a novel design of an asymmetric gear that applies a larger pressure angle in the drive side and a standard pressure angle in the coast side via accurate stress analysis using the edge-based smoothed point interpolation method with triangular mesh (ES-PIM-(T3)). An asymmetric rack cutter is first developed. Then, the governing equations of the tooth profiles cut by the rack cutter are derived. Finally, five sets of asymmetric gears with the pressure angles of 20° /20°, 25°/20°, 30°/20°, 35°/20°, and 40°/20° are established to quantitatively check the stress distributions at the fillet of the drive side of these teeth. The best point for applying force in a static bending stress analysis and the best pressure angle in the drive side for a gear design are suggested.

This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.

Corrosion is a common phenomenon and critical aspects of steel structural application. It affects the daily design, inspection, and maintenance in structural engineering, especially for the heavy and complex industrial applications, where the steel structures are subjected to hash corrosive environments in combination of high working stress condition and often in open field and/or under high temperature production environments. In the paper, it presents the actual engineering application of advanced finite element methods in the predication of the structural integrity and robustness at a designed service life for the furnaces of alumina production, which was operated in the high temperature, corrosive environments, and rotating with high working stress condition.

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher-order CPIM shape functions have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch tests; (2) provides an upper bound of strain energy; (3) avoids the volumetric locking; and (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

This paper presents a thin plate formulation with nodal integration for bending analysis using three-node triangular cells and linear interpolation functions. The formulation was based on the classic thin plate theory, in which only deflection field was required and dealt with as the field variables. They were assumed to be piecewisely linear and expressed using a set of three-node triangular cells. Based on each node, the integration domain has been further derived, where the curvature in the domain was computed using a gradient smoothing technique (GST). As a result, the curvature in each integration domain is a constant whereby the deflection is compatible in the whole problem domain. The generalized smoothed Galerkin weak form is then used to create the discretized system equations where the system stiffness is obtained using simple summation operation. The essential rotational boundary conditions are imposed in the process of constructing the curvature field in conjunction with imposing the translational boundary conditions in the same way as undertaken in the standard FEM. A number of numerical examples were studied using the present formulation, including both static and free vibration analyses. The numerical results were compared with the reference ones together with those shown in the state-of-art literatures published. Very good accuracy has been achieved using the present method.

Underwater acoustical imaging techniques and the inverse analysis of acoustic scattering problems have now found many important engineering applications. Based on the physical optics approximation, the ramp response signal can be proven that it is proportional to the profile function of the scatterer, which is defined as the area of cross section of the object perpendicular to the direction of wave propagation. The image synthesis technique named as the approximate limiting surface technique is applied to generated underwater objects by using the ramp responses of the objects. The modification should be made by an iterative procedure which will adjust the parameters of each surface and will yield a result until the profile functions of this generated image at all looking angles are consistent with the input ones. Several typical objects are presented to demonstrate the process of the 3D image generation and the results indicate that the qualities of the final images are quite acceptable. The further research work is to build an automatic iterative mechanism to generate the final image for a submerged object.

In this paper, an efficient optimization method named NIO-SLP is suggested for uncertain structures by using the non-probabilistic interval model to quantify the uncertainty. A general nonlinear interval optimization (NIO) problem is investigated, in which both of the objective function and constraints are nonlinear and uncertain. A sequence of approximate optimization sub-problems are created based on the first-order Taylor expansion and each one degenerates into a simple linear interval optimization (LIO) problem. An iterative mechanism is proposed to update the design space and whereby make the optimization sequence converge at the optimum. Two numerical examples are investigated to demonstrate the effectiveness of the present method.

This paper presents a direct numerical simulation of particle sedimentation in two-phase flow with thermal convection. The sedimentation processes of elliptical particles are investigated in three different scenarios with isotherm, hot, and cold Newtonian fluids. We demonstrate that different particle shapes and orientations can result in quite different flow behaviors. Some interesting results have been obtained, which are very helpful for better understanding of the particle sedimentation processes.

For a honeycomb structure used for absorbing crash energy and protecting the safety of human or instruments, the bigger the specific energy absorption (SEA) is, the more popular it would be when the peak crushing stress (σ_p) was retained small enough. In order to improve the energy absorption capacity, crashworthiness optimization for honeycomb structures with various cell specifications are studied in this paper. Detailed numerical models are established for those honeycomb structures by using an explicit finite element method code LS-DYNA. The numerical simulation results are then used as the design samples for constructing metamodels. The optimal Latin hypercube design (OLHD) method is employed for the selection of sampling design points in the design space, and the polynomial functions, radial basis functions (RBF), Kriging, multivariate adaptive regression splines (MARS), and support vector regression (SVR) are utilized to formulate the two optimal objectives SEA and σ_p. It is found that the polynomial function is the most efficient in constructing the crashworthiness metamodels of honeycombs among the above-mentioned methods. Then, the polynomial function models of SEA and σ_p are chosen as the surrogate models in the crashworthiness optimization. In order to further validate the polynomial function models, the polynomial function models of SEA and σ_p are compared with the analytical solutions based on Wierzbicki's theory and Kunimoto and Yamada's theory, respectively. An excellent correlation has been established. As such, the multi-objective particle swarm optimization algorithm (MOPSOA) is applied to obtain the Pareto front of SEA with σ_p of the honeycomb structures with various cell specifications, which has resulted in a range of optimal designs of honeycomb structures by the multi-objective optimization.

This paper studies the resonant frequencies and the associated vibration modes of an individual double-walled carbon nanotube, using gradient smoothing technique. The study uses a double-elastic beam based on the Euler beam theory with the consideration of the intertube van der Waals interactions. A gradient smoothed formulation is deployed to deal with the fourth-order differential equation of the Euler beam problems for dynamic analysis of the double-walled carbon nanotubes. In the double-thin beam problems, a set of linear shape functions are adopted to approximate the displacement field. Smoothing domains are then formed for computing the smoothed curvature and bending moment field. Compared with analysis results of multi-beam theory, numerical examples indicate that very accurate results could be yielded when a reasonable number of nodes were used. The results also showed that non-coaxial intertube resonance would be excited at the higher resonant frequencies of double-walled carbon nanotubes. In addition, free vibration of a double-walled carbon nanotube with inner wall simple supported and outer wall one end fixed and the other end free is studied.