International Journal of Computational Methods

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.

Laminar mixed convection of an Al${}_{\mathrm{\text{2}}}$O${}_{\mathrm{\text{3}}}$/water nanofluid inside a vertical channel is investigated numerically. Single-phase and two-phase Eulerian models are employed to analyze flow and thermal fields of the nanofluid in conjunction with the suitable expressions for the particle viscosity and effective particle thermal conductivity. The results of two-phase Eulerian model are compared with the single-phase model and with the published experimental data. Effects of the solid volume fraction, Reynolds number and Grashof number on the heat transfer performance of the nanofluid are investigated and discussed in detail.

The moving Kriging interpolation (MKI) is an accurate approximation method that has the interpolating property. However, it is rarely used in meshless methods because of its low efficiency. In this paper, we proposed an efficient MKI method, the complex variable moving Kriging interpolation (CVMKI) method, for “domain” type meshless method. Further, we proposed the CVMKI-based element-free Galerkin (CVMKIEFG) method for 2D potential problems. CVMKIEFG is an efficient meshless method and can impose the essential boundary conditions directly and easily. We proposed two formulations for CVMKIEFG: the conventional formulation and the cell-based formulation. The latter formulation is proposed for higher efficiency. Three 2D example problems are presented to demonstrate the efficiency and accuracy of CVMKIEFG.

A new plane shape-free multi-node singular hybrid stress-function (HS-F) element with drilling degrees of freedom, which can accurately capture the stress intensity factors at the crack tips, is developed. Then, a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently. Only simple remeshing with an unstructured mesh is needed for each simulation step. Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.

In this paper, the geometrically nonlinear transverse bending behavior of the shear deformable laminated composite spherical shell panel under hygro-thermo-mechanical loading is investigated. The laminated composite panel model has been developed mathematically based on the higher-order shear deformation theory and Green–Lagrange nonlinear strain kinematics. The material model is introduced through the micromechanical approach explicitly in terms of the matrix properties, the fiber properties, and the fiber volume fractions. Theoretical formulation is developed based on the hygrothermal dependent composite material properties to evaluate the corrugated behavior of the laminated structure. In addition to that, all the nonlinear higher-order terms arising in the strain displacement relation are included in the present formulation for accurate prediction of the flexural behavior. The desired nonlinear governing equations are obtained using the variational method and discretized with the help of suitable finite element steps. The desired responses are computed by solving the nonlinear equations numerically using the direct iterative method. The convergence behavior of the developed nonlinear numerical model has been checked and validated by comparing the responses with those available published literature. Finally, the effect of hygrothermal environment, geometrical and material parameters and the support conditions on the transverse bending behavior of the laminated composite curved shell panel have been highlighted by solving different numerical examples.

Free vibration of laminated cross-ply plates of variable thickness including transverse problem is solved numerically to obtain eigenvalues as frequency parameter and associated eigenvectors which are spline coefficients. The variation of frequency parameters with respect to the aspect ratio, side-to-thickness ratio, ply-angle, number of layer and thickness variations for two different materials under simply supported boundary conditions are analyzed.

We present a computational method based on the spectral deferred corrections (SDC) time integration technique and the essentially nonoscillatory (ENO) finite volume method for hyperbolic problems. The SDC technique is used to advance the solutions in time with high-order of accuracy. The ENO method is used to define high-order cell edge quantities that are then used to evaluate numerical fluxes. The coupling of the SDC method with a high-order finite volume method (piece-wise parabolic method (PPM)) is first carried out by Layton et al. [J. Comput. Phys. 194(2) (2004) 697]. Issues about this approach have been addressed and some improvements have been added to it in Kadioglu et al. [J. Comput. Math. 1(4) (2012) 303]. Here, we investigate the implications when the PPM method is replaced with the well-known ENO method. We note that the SDC-PPM method is fourth-order accurate in time and space. Therefore, we kept the order of accuracy of the ENO procedure as fourth-order in order to be able to make a consistent comparison between the two approaches (SDC-ENO versus SDC-PPM). We have tested the new SDC-ENO technique by solving smooth and nonsmooth hyperbolic problems. Our numerical results indicate that the fourth-order of accuracy in both space and time has been achieved for smooth problems. On the other hand, the new method performs very well when it is applied to nonlinear problems that involve discontinuous solutions. In other words, we have obtained highly resolved discontinuous solutions with essentially no-oscillations at or around the discontinuities.

The aim of this paper is to present a novel method of data sample reduction that can be applied, in particular, to the classification of interval type imprecise information. Its concept is based on the sensitivity method, inspired by artificial neural networks, while the goal is to increase the number of apposite classifications, and, consequently, to increase calculation speed. As evident in this paper, the use of reduction algorithm eliminates the particular elements of all data sample patterns which have insignificant or negative influence on the correctness of classification. The methodology was tested on pseudo-random and real data, as well as by way of comparative analysis with similar task algorithms. The presented procedure was also tested for use in situations in which the data sample representing the individual classes had been obtained by the k-means clustering procedure.

This paper presents a new particle formulation for extreme material flow analyses in the bulk forming applications. The new formulation is first established by an introduction of a smoothed displacement field to the standard Galerkin formulation to eliminate zero-energy modes in conventional particle methods. The discretized system of linear equations is consistently derived and integrated using a direct nodal integration scheme. The linear formulation is next extended to the large deformation quasi-static analysis of inelastic materials. As quasi-static Lagrangian simulation proceeds in the severe deformation range, the analysis method is switched to explicit dynamics formulation and an adaptive Lagrangian kernel approach is preformed to reset the reference configuration and maintain the injective deformation mapping at the particles. Both nonconvex and convex meshfree approximations are investigated in this study. Several numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed method.

This series of two papers aim to improve the rotation-free (RF) triangle model previously developed by the authors and apply it for drape/cloth simulations. To avoid a previously un-observed drawback, the membrane strain obtained from the three-node displacement interpolation is replaced by the one obtained from the six-node interpolation. Dynamic simulations are made possible by explicit time integration. Instead of using dense structural meshes, the quality of draped patterns is improved by global adaptive remeshing. The works in this paper provide important and necessary techniques for practical applications of the RF triangle in the drape simulation. In part II, other techniques including collision handling and garment construction are further discussed and some practical applications of garments on still and moving human body model would be presented.

In this paper, a new tool for the solution of nonlinear differential equations is presented. It is named rational homotopy perturbation method (RHPM). It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. Furthermore, in order to deal with BVP problems, we propose a modification of RHPM method. The obtained results show that RHPM is a powerful tool capable to generate highly accurate rational solutions.