International Journal of Computational Methods

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N_c, N_q and N_γ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Parabolic partial differential equations possessing nonlocal initial and boundary specifications are used to model some real-life applications. This paper focuses on constructing fast and accurate analytic approximations via an easy, elegant and powerful algorithm based on a double power series representation of the solution via ordinary polynomials. Consequently, a parabolic partial differential equation is reduced to a system involving algebraic equations. Exact solutions are obtained when the solutions are themselves polynomials. Some parabolic partial differential equations are treated by the technique to judge its validity and also to measure its accuracy as compared to the existing methods.

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

We construct an efficient quadrature method for the integration of the Galerkin weak form over general 3D polyhedral elements based on the radial integration method (RIM). The basic idea of the proposed method is to convert the polyhedral domain integrals to contour plane integrals of the element by utilizing the RIM which can be used for accurate evaluation of various complicated domain integrals. The quadrature construction scheme for irregular polyhedral elements involves the treatment of the nonpolynomial shape functions as well as the arbitrary geometry shape of the elements. In this approach, the volume integrals for polyhedral elements with triangular or quadrilateral faces are evaluated by transforming them into face integrals using RIM. For those polyhedral elements with irregular polygons, RIM is again used to convert the face integrals into line integrals. As a result, the volume integration of Galerkin weak form over the polyhedral elements can be easily carried out by a number of line integrals along the edges of the polyhedron. Some benchmark numerical examples including the patch tests are utilized to demonstrate the accuracy and convenience of the proposed method.

In this paper, a method for construction of the time-dependent approximate Green's function for the initial boundary value problem in a radially multilayered cylinder is suggested. This method is based on determination of the eigenvalues and the orthogonal set of the eigenfunctions; regularization of the Dirac delta function in the form of the Fourier series with a finite number of terms; expansion of the unknown Green's function in the form of Fourier series with unknown coefficients and computation of a finite number of unknown Fourier coefficients. Computational experiment confirms the robustness of the method for the approximate computation of the Dirac delta function and Green's function.

An edge-based smoothed finite element method (ESFEM) using two-step Taylor Galerkin (TS-TG) algorithm is formulated for two-dimensional solid dynamics problems using linear elements. Although explicit method with classical displacement formulations is the traditional way to simulate fast impact, errors accumulate rapidly resulted from mass, momentum or energy nonconservation. The proposed method is momentum conservative so that energy fluctuations can be minimal and stay bounded for long time. In the present method, the problem areas are firstly discretized into a series of triangular cells, and edge-based smoothing domains are further formed associated with the cell edges. The strain field using the gradient smoothing technique over each smoothing domain is smoothed, which is used for performing the numerical integration. The triangular elements using ESFEM can work for extremely distorted meshes. The newly proposed method can present a good property of accuracy and conservation for a long time.

A boundary condition (BC) related mixed element method is presented to address the corner problem in boundary element method (BEM) for 3D elastostatic problems. In this method, noncontinuous elements (NCEs) are only used at the displacement-prescribed corners/edges and continuous elements (CEs) in other places, which can decrease the degrees of freedom (DOFs) compared to the approach using NCEs at all corners/edges. Moreover, an automatic generation algorithm of BC related mixed linear triangular elements is implemented with the help of 3D modeling engine ACIS, and the boundary element analysis (BEA) is integrated into CAD systems. In order to solve large scale problems, the fast multipole BEM (FMBEM) with mixed elements is proposed and utilized in the BEA. The examples show that the node shift scheme adopting 1/4 is optimal and the BEM/FMBEM using mixed elements can produce more accurate results by only increasing a small number of DOFs.

Object Oriented Finite Element Analysis (OOF2) is used to predict the thermal and mechanical properties of Al–MgO composites. In this work, three compositions of composites containing 5%, 10% and 15% MgO (by volume) are studied. The influence of MgO volume fraction is examined in terms of effective Young's modulus and coefficient of thermal expansion of the composites. In addition, the stress and strain contours are plotted, which are helpful to understand the mechanical behavior of these composites. It is noted that the properties of composites are improved because of the presence of MgO. However, local stresses increase with filler content.

In order to model nonlinear breaking waves with moving boundary and coastal sandbar migration; we presented a morphodynamic model, where hydrodynamic equations (free surface flows) and sediment transport equation are solved in a coupled manner. The originality lies in the development of an innovative approach, in which, we project the horizontal velocity onto a basis functions depending only on the variable z and we calculate analytically the vertical velocity and the nonhydrostatic pressure. The choice of basis depends on the problem under consideration. This model is numerically stable because there is no mesh in the vertical direction. This model is accurate because we can directly introduce functions that best fits the physical nature of the flow. Our model is validated through laboratory measurements carried out by Dingemans [1994, J. Comput. Phys. 231, 328–344], Cox and Kobayashi [2000, J. Geophys. Res. 105(c6), 223–236. and Dette et al. [2002, Coast. Eng. 47, 137–177].

In this paper, we have studied the fractional order model of tumor cells growth and their interactions with general immune effector cells, by using multi-step generalized differential transform method (MSGDTM). We discussed this nonlinear model because it differs from most others in the literature. It takes into account (i) the infiltration of the tumor by CTLs (cytotoxic T lymphocytes) and (ii) the possible effects of effector cell inactivation. The approximate solutions obtained by MSGDTM are highly accurate and valid for a longer period of time.