International Journal of Computational Methods

Due to the increased use of composite materials in industrial applications, reliable and consistent finite element methods are required for the simulation and optimization of composite structures. In this paper, we presented the effect of finite element meshing in the modeling of degradation in composite structures under tensile stress; we have used an elastoplastic model to simulate the damage and plasticity behavior occurring in laminated composite structures carbon/epoxy: T300/914. This model works with different elements and the results obtained are not sensitive to mesh size. Thus, we have showed that two different meshes give the same results. Our findings are in good agreement compared to the experimental data.

The aim of the paper is to use Arbitrary Lagrangian Eulerian (ALE) formulation for fluid–structure interaction for modeling blood flow in artery. Predicting blood flow and its effects on arteries requires simulation of fluid–structure coupling with deformable mesh. For fluid simulation velocity–pressure formulation is used, we present the algorithm which allows to compute fluid velocity and pressure using explicit time integration. This method has been applied successfully for several applications including sloshing tank analysis. For the structure shell type elements with five points integration through the thickness to accurately represent bending effects, are modeled. Since the structure is deformable, to prevent high mesh distortion an elasticity material model for the mesh is used for mesh deformation. For fluid–structure coupling, explicit contact algorithm based on penalty method. Such a model can be used to study the profile of the flow and pressure waves as they propagate along the arteries. In the paper, the onset of a pressure pulse was simulated at the entrance of a three dimension straight artery blood vessel and the resulting dynamic response in the form of a propagating pulse wave through the wall was analyzed and compared. Good agreement was found between the numerical results and the theoretical description of an idealized artery. Work has also been done on implementing the material constitutive models specific for vascular applications.

Two-dimensional simulations of channel flow past an array of cylinders are carried out at high Reynolds numbers. Considering the thickness fluctuating effect on the equation of motion, a modified lattice Boltzmann method (LBM) is proposed. Special attention is paid to investigate the thickness fluctuations and vortex shedding mechanisms between 11 cylinders. Results for the velocity and vorticity differences are provided, as well as for the energy density and enstrophy spectra. The numerical results coincide very well with some published experimental data that was obtained by turbulent soap films. The spectra extracted from the velocity and vorticity fields are displayed from simulations, along with the thickness fluctuation spectrum H(k). Our results show that the statistics of thickness fluctuations resemble closely those of a passive scalar in turbulent flows.

In this study, a multi-scale finite element method was proposed to solve two linear scale-coupling stochastic elliptic PDE problems, a tightly stretched wire and flow through porous media. At microscopic level, the main idea was to form coarse-scale equations with a prescribed analytic form that may differ from the underlying fine-scale equations. The relevant stochastic homogenization theory was proposed to model the effective global material coefficient matrix. At the macroscopic level, the Karhunen–Loeve decomposition was coupled with a Polynomial Chaos expansion in conjunction with a Galerkin projection to achieve an efficient implementation of the randomness into the solution procedure. Various stochastic methods were used to plug the microscopic cell to the global system. Strategy and relevant algorithms were developed to boost computational efficiency and to break the curse of dimension. The results of numerical examples were shown consistent with ones from literature. It indicates that the proposed numerical method can act as a paradigm for general stochastic partial differential equations involving multi-scale stochastic data. After some modification, the proposed numerical method could be extended to diverse scientific disciplines such as geophysics, material science, biological systems, chemical physics, oceanography, and astrophysics, etc.

The present work investigates the fatigue life of a functionally graded material (FGM) made of aluminum alloy and alumina (ceramic) under cyclic mixed mode loading. Both element free Galerkin method (EFGM) and extended finite element method (XFEM) are employed to simulate and compare the fatigue crack growth. Partition of unity is used to track the crack path in XFEM while a new enrichment criterion is proposed to track the crack path in EFGM. The fatigue lives of aluminum alloy, FGM and an equivalent composite (having the same composition as of FGM) are compared for a major edge crack and center crack in a rectangular domain. The proposed enrichment criterion not only simulates the crack propagation but it also extends the applicability and robustness of EFGM for accurate estimation of fatigue life of component.

In numerical simulation of gaseous detonation, due to the complexity of the computational domain, negative density and pressure often emerge in high resolution numerical computing, which leads to blow-ups. The paper provides high order discontinuous Galerkin (DG) positivity-preserving scheme for two-dimensional (2D) Euler equations with two-step chemical reaction which preserve positivity of density, pressure and chemical reaction process. A positivity-preserving limiter is added in high order DG scheme without influencing conservation, accuracy and stability. The method is verified by parallel numerical simulations and is approved to be well applied to numerical simulation of gaseous detonation propagation with complicated geometry boundary.

In the present paper, a comparative study is presented between three-dimensional (3D) graded finite element and boundary integral equation methods capable of modeling quasi-static behaviors of heterogeneous plates with circular holes made of functionally graded materials (FGMs). The formulations are derived based on the 3D theory of elasticity. The volume fractions of the constituent materials of the FGM plates are assumed to vary through the thickness direction according to an exponential law. The graded finite element formulations are developed based on the Rayleigh–Ritz energy method. Somigliana stress identity is implemented numerically for 3D elasticity analysis of the heterogeneous isotropic plates, employing graded elements. Based on the resulting governing equations and the weighted residual technique, an effective boundary element formulation is implemented for the elastic FGM plates. To verify numerical results of the present work, several examples are provided. The comparison made for a homogenous plate shows an excellent concordance between the results.

Considering the methods with future points technique from second derivative general linear methods (SGLMs) point of view, makes it possible to improve their stability properties. In this paper, we extend the stability regions of a modified version of E2BD formulas to optimal one and show its effectiveness by numerical verifications. Also, implementation issues, with numerical experiments, of these methods are investigated in a variable step-size mode.

In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We start from the 2D case sketched in Cavoretto et al. [2011] and the approximation scheme presented in [Cavoretto et al. (2011); Cavoretto et al. (2015)], and then we extend the reconstruction scheme of separatrices in the cases of three-dimensional models with two and three stable equilibria. For this purpose we construct computational algorithms and procedures for the detection and the refinement of points located on the separatrix manifolds that partition the phase space. The use of the so-called Radial Basis Function (RBF) Partition of Unity (PU) method is used to reconstruct the separatrices.

It is shown that many materials in practical engineering have different moduli in tension and compression. Especially, graphene, a magical material with the highest strength, is a kind of bi-modulus material. In this paper, mechanical response of bi-modulus Winkler foundation beam under nonlinear temperature distribution along height of the beam is studied. A new and convenient method, “intersecting line criterion”, is proposed to certify number of neutral axis in foundation beam and governing equation (set) of position of neutral axis is established, which is solved by iteration procedure of Newton’s method in Matlab. Semi-analytical solutions of stress, deflection and bending moment are subsequently obtained. Meanwhile, a finite element calculation procedure for calculating the temperature stress in bi-modulus structures is developed. Return the analytical solution to the result of the same modulus theory, and compare the analytical solution with finite element procedure solution and common finite element software Abaqus simulation solution. It shows that both of semi-analytical solution and calculation procedure proposed are reliable to use. Finally, discrepancies between nonlinear temperature effect and linear temperature and external force effect are discussed, which may supply some suggestions for calculation and optimization of such structures and members.

Generalized integral representation method (GIRM) is designed to numerically solve initial and boundary value problems for differential equations. In this work, we develop numerical schemes based on 1- and 2-step GIRMs for evaluation of the two-dimensional problem of advective diffusion in an infinite domain. Accurate approximate solutions are obtained in both cases of GIRM and compared to the exact ones. The derivation of GIRM is straightforward and implementation is simple.

This paper suggests a new method of computing interior forces and deformations of the base-slab of a dock settling basin. The base element is considered as a finite beam under the action of bending supported by subgrade soil. The deformation of the subgrade is determined through the Fuss–Winkler model. The basic parameter (i.e., coefficient of subgrade reaction) of this model is a nonlinear parabolic equation along the length of the beam. The solution of this model leads to an ordinary differential equation that can be solved by using boundary conditions and Picard limit of a sequence method. After the solution of the equation, the deformations and interior forces are computed at any arbitrary cross section of the beam and the results of this study are compared with the other methods offered in the literature and compatible outcomes are achieved.