M. G. He¹, C.L. Tan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 317-349, 2013, DOI:10.3970/cmes.2013.095.315

Abstract The self-regularization technique in the Boundary Element Method (BEM) originally proposed by Cruse and Richardson (1996, 1999) in their work for two-dimensional (2-D) stress analysis is extended to three-dimensional (3-D) elastostatics in this paper. The regularization scheme addresses the issue of accurate numerical evaluation of the integrals due to the singularity of the kernel functions of the integral equations. It is first implemented for the determination of displacements and stresses at interior points of the solution domain, and very accurate results are obtained even when these points are very close to the surface of the More >

H.T. Liu^1,2, Z. Chen², S. Jiang², Y. Gan³, M.B. Liu⁴, J.Z. Chang¹, Z.H. Tong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 303-315, 2013, DOI:10.3970/cmes.2013.095.303

Abstract Dissipative particle dynamics (DPD) and molecular dynamics (MD) are both Lagrangian particle-based methods with similar equations except that the DPD specification for the force definition on the particles is the result of coarsegraining, and these two methods usually get the similar results in some specific cases. However, there are still some unknown differences between them. Considering the water response to external force, a comparative study of DPD and MD is conducted in this paper, which provides a better understanding on their relation, and a potential way to effectively bridge nanoscale and mesoscale simulation procedures. It More >

Ashraf Balabel¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 283-302, 2013, DOI:10.3970/cmes.2013.095.283

Abstract This paper presents the numerical results obtained from the numerical simulation of turbulent liquid jet atomization due to three distinctly different types of liquid jets/air orientations; namely, coflow jet, coaxial jet and the combined coflow-coaxial jet. The applied numerical method, developed by the present authors, is based on the solution of the Reynolds-Averaged Navier Stokes (RANS) equations for time-dependent, axisymmetric and incompressible two-phase flow in both phases separately and on regular and structured cell-centered collocated grids using the control volume approach. The transition from one phase to another is performed through a consistent balance of… More >

Ahmad Shirzadi¹, Vladimir Sladek², Jan Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 259-282, 2013, DOI:10.3970/cmes.2013.095.259

Abstract This paper is concerned with the development of a numerical approach based on the Meshless Local Petrov-Galerkin (MLPG) method for the approximate solutions of the two dimensional nonlinear reaction-diffusion Brusselator systems. The method uses finite differences for discretizing the time variable and the moving least squares (MLS) approximation for field variables. The application of the weak formulation with the Heaviside type test functions supported on local subdomains (around the nodes used in MLS approximation) to semi-discretized partial differential equations yields the finite-volume local weak formulation. A predictor-corrector scheme is used to handle the nonlinearity of More >

L. Sun¹, G. Yang², Q. Zhang³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 235-258, 2013, DOI:10.3970/cmes.2013.095.234

Abstract We propose numerical integration rules for meshless local Petrov- Galerkin methods (MLPG) employed to solve elliptic partial different equations (PDE) with Neumann boundary conditions. The integration rules are required to satisfy an integration constraint condition of Green’s formula type (GIC). GIC was first developed in [Babuska, Banerjee, Osborn, and Zhang (2009)] for Galerkin meshless method, and we will show in this paper that it has better features for MLPG due to flexibility of MLPG in choosing different trial and test function spaces. A general constructive algorithm is presented to design the integration rules satisfying GIC. More >

Haitao Liao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 207-234, 2013, DOI:10.3970/cmes.2013.095.207

Abstract The constrained optimization multi-dimensional harmonic balance method for calculating the quasi-periodic solutions of nonlinear systems is presented. The problem of determining the worst quasi-periodic response is transformed into a nonlinear optimization problem with nonlinear equality constraints. The general nonlinear equality constraints are built using a set of nonlinear algebraic equations which is derived using the multi-dimensional harmonic balance method. The Multi- Start algorithm is adopted to solve the resulting constrained maximization problem. Finally, the validity of the proposed method is demonstrated with a Duffing oscillator and numerical case studies for problems with uncertainties are performed More >

S.D. Akbarov^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 173-205, 2013, DOI:10.3970/cmes.2013.095.173

Abstract By employing the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies (TLTEWISB) the time-harmonic Lamb’s problem for a system comprising a finite pre-strained half-space and finite pre-strained covering layer made of incompressible materials is examined for the case where the material of the covering layer is stiffer than that of the half-space material. It is assumed that on the upper free face plane of the covering layer the point-located time-harmonic force acts. The elasticity relations of the materials are described through Treloar’s potential. The corresponding boundary-value problem is solved by employing the Hankel… More >

Zichun Yang^1,2,3, Kunfeng Li^1,4, Qi Cai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 143-171, 2013, DOI:10.3970/cmes.2013.095.143

Abstract The conventional probabilistic reliability model for structures is based on the “probability assumption” and “binary-state assumption”. These assumptions are often offset the reality of practical engineering and lead to a wrong conclusion. In fact, besides randomness, fuzziness which is different from randomness in nature is also a prevalent uncertainty factor and plays an important role in structural reliability assessment. In this paper, a novel structural reliability model with random variables and fuzzy variables is established by using the fuzzy set theory, possibility theory and probability measure for fuzzy events, based on the “mixed probability and More >

Sanderson L. Gonzaga de Oliveira¹, Mauricio Kischinhevsky², João Manuel R. S. Tavares³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 119-141, 2013, DOI:10.3970/cmes.2013.095.119

Abstract A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve timedependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical More >

R.A. Amaro Junior¹, L.Y. Cheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.2, pp. 87-118, 2013, DOI:10.3970/cmes.2013.095.087

Abstract In this paper simulations of brittle fracture and hydroelastic problems are carried out by using a numerical approach based on the Moving Particle Simulation (MPS) method. It is a meshless method used to model both fluid and elastic solid, and all the computational domain is discretized in Lagrangian particles. A higher order accuracy gradient operator is used herein by adopting a correction matrix. Also, in order to correctly simulate the collision of the fragments, a contact detection algorithm that takes into account the presence of the solid surfaces generated by brittle fracture is proposed. In… More >