Y. T. Wu¹, Y. F. Nie², Z. H. Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 297-325, 2014, DOI:10.3970/cmes.2014.099.297

Abstract Four representative multiscale methods, namely asymptotic homogenization method (AHM), heterogeneous multiscale method (HMM), variational multiscale (VMS) method and multiscale finite element method (MsFEM), for elliptic problems with multiscale coefficients are surveyed. According to the features they possess, these methods are divided into two categories. AHM and HMM belong to the up–down framework. The feature of the framework is that the macroscopic solution is solved first with the help of effective information computed in local domains, and then the multiscale solution is resolved in local domains using the macroscopic solution when necessary. VMS method andMsFEM fall More >

F.L.S. Bussamra¹, E.Lucena Neto¹, W.M. Ponciano¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 255-272, 2014, DOI:10.3970/cmes.2014.099.255

Abstract Hybrid-Trefftz stress finite elements have been applied with success to the analysis of linear and non-linear problems in structural mechanics. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The stress field satisfies the Trefftz constraint a priori, i.e., it is extracted from the Navier equation solution. This type of element has provided remarkable improvement in stress predictions compared to the standard displacement-based finite elements. In this work, solution of stress concentration problems is carried out by hexahedral hybrid-Trefftz stress element models. Stress concentration factors and stress intensity factors are then More >

T.A. Elgohary¹, L. Dong², J.L. Junkins³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.6, pp. 543-563, 2014, DOI:10.3970/cmes.2014.098.543

Abstract In this study, the Scalar Homotopy Methods are applied to the solution of post-buckling and limit load problems of solids and structures, as exemplified by simple plane elastic frames, considering only geometrical nonlinearities. Explicitly derived tangent stiffness matrices and nodal forces of large-deformation planar beam elements, with two translational and one rotational degrees of freedom at each node, are adopted following the work of [Kondoh and Atluri (1986)]. By using the Scalar Homotopy Methods, the displacements of the equilibrium state are iteratively solved for, without inverting the Jacobian (tangent stiffness) matrix. It is well-known that,… More >

Cheng-Yu Ku ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.5, pp. 509-541, 2014, DOI:10.3970/cmes.2014.098.509

Abstract This paper proposes the numerical solution of three-dimensional Laplacian problems in a multiply connected domain using the collocation Trefftz method with multiple source points. A numerical solution for three-dimensional Laplacian problems was approximated by superpositioning T-complete functions formulated from 36 independent functions satisfying the governing equation in the cylindrical coordinate system. To deal with complicated problems for multiply connected domain, we adopted the generalized multiple source point boundary collocation Trefftz method which allows many source points in the Trefftz formulation without using the decomposition of the problem domain. In addition, to mitigate a severely ill-conditioned More >

Tao Zhang^1,2, Yiqian He³, Leiting Dong⁴, Shu Li¹, Abdullah Alotaibi⁵, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 509-533, 2014, DOI:10.3970/cmes.2014.097.509

Abstract In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the… More >

A.E. Kampitsis¹, E.J. Sapountzakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 367-409, 2014, DOI:10.3970/cmes.2014.103.367

Abstract In this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution More >

A. Roychowdhury^1,2, A. Nandy¹, C.S. Jog¹, R. Pratap^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.2, pp. 91-110, 2014, DOI:10.3970/cmes.2014.103.091

Abstract We present a hybrid finite element based methodology to solve the coupled fluid structure problem of squeeze film effects in vibratory MEMS devices, such as gyroscopes, RF switches, and 2D resonators. The aforementioned devices often have a thin plate like structure vibrating normally to a fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping. For accurate modelling of such devices the squeeze film effects must be incorporated.… More >

P.A. Trapper¹, P.Z. Bar-Yoseph²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 19-47, 2014, DOI:10.3970/cmes.2014.103.019

Abstract The space-time discontinuous Galerkin method for multi-dimensional nonlinear hyperbolic systems is enhanced with a generalized technique for splitting a flux vector that is not limited to the homogeneity property of the flux. This technique, based on the flux’s characteristic decomposition, extends the scope of the method’s applicability to a wider range of problems, including elastodynamics. The method is used for numerical solution of a number of representative problems based on models of vibrating string and vibrating rod that involve the propagation of a sharp front through the solution domain. More >

Annamaria Mazzia¹, Giorgio Pini¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 475-497, 2014, DOI:10.3970/cmes.2014.102.475

Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. One of pure meshless methods main applications is for implementing Adaptive Discretization Techniques. In this paper, we describe our fresh node–wise refinement technique, based upon estimations of the “local” Total Variation of the approximating function. We numerically analyze the accuracy and efficiency of our MLPG–based refinement. Solutions to test Poisson problems are approximated, which undergo large variations inside small portions of the domain. We show that 2D problems can be accurately solved. The gain in accuracy with respect to uniform More >

Akpofure E. Taigbenu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 271-289, 2014, DOI:10.3970/cmes.2014.102.271

Abstract The solutions to inverse heat conduction problems (IHCPs) are provided in this paper by the Green element method (GEM), incorporating the logarithmic fundamental solution of the Laplace operator (Formulation 1) and the timedependent fundamental solution of the diffusion differential operator (Formulation 2). The IHCPs addressed relate to transient problems of the recovery of the temperature, heat flux and heat source in 2-D homogeneous domains. For each formulation, the global coefficient matrix is over-determined and ill-conditioned, requiring a solution strategy that involves the least square method with matrix decomposition by the singular value decomposition (SVD) method, More >