Weichung Yeih^1,2, I-Yao Chan¹, Chia-Ming Fan¹, Jiang-Jhy Chang¹, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 169-194, 2014, DOI:10.3970/cmes.2014.099.169

Abstract In this paper, the Cauchy inverse problem of the nonlinear steady-state heat equation is studied. The double iteration process is used to tackle this problem in which the outer loop is developed based on the residual norm based algorithm (RNBA) while the inner loop determines the evolution direction and the modified Tikhonov's regularization method (MTRM) developed by Liu (Liu, 2012) is adopted. For the conventional iteration processes, a fixed evolution direction such as F, B⁻¹F, B^TF or αF+(1-α)B^TF is used where F is the residual vector, B is the Jacobian matrix, the superscript '-1' denotes the inverse, the… More >

Taha Sochi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 151-168, 2014, DOI:10.3970/cmes.2014.099.151

Abstract In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the More >

Weichung Yeih^1,2, I-Yao Chan¹, Cheng-Yu Ku¹, Chia-Ming Fan¹, Pai-Chen Guan³

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 123-149, 2014, DOI:10.3970/cmes.2014.099.123

Abstract In this paper, a novel double iteration process for solving the nonlinear algebraic equations is developed. In this process, the outer iteration controls the evolution path of the unknown vector x in the selected direction u which is determined from the inner iteration process. For the inner iteration, the direction of evolution u is determined by solving a linear algebraic equation: B^TBu = B^TF where B is the Jacobian matrix, F is the residual vector and the superscript ''T'' denotes the matrix transpose. For an ill-posed system, this linear algebraic equation is very difficult to solve since the resulting… More >

Baofeng Li ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 105-122, 2014, DOI:10.3970/cmes.2014.099.105

Abstract In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach. More >

Yasunori Yusa¹, Shinobu Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.1, pp. 87-104, 2014, DOI:10.3970/cmes.2014.099.087

Abstract To speed up the elastic–plastic analysis of a large-scale model with a crack in which plasticity is observed near the crack, the partitioned coupling method is applied. In this method, the entire analysis model is decomposed into two non-overlapped domains (i.e., global and local domains), and the two domains are analyzed with an iterative method. The cracked local domain is modeled as an elastic–plastic body, whereas the large-scale global domain is modeled as an elastic body. A subcycling technique is utilized for incremental analysis to reduce the number of global elastic analyses. For a benchmark More >

L. Dong¹, A. Alotaibi², S.A. Mohiuddine², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.1, pp. 1-85, 2014, DOI:10.3970/cmes.2014.099.001

Abstract In this expository article, a variety of computational methods, such as Collocation, Finite Volume, Finite Element, Boundary Element, MLPG (Meshless Local Petrov Galerkin), Trefftz methods, and Method of Fundamental Solutions, etc., which are often used in isolated ways in contemporary literature are presented in a unified way, and are illustrated to solve a 4^th order ordinary differential equation (beam on an elastic foundation). Both the primal formulation, which considers the 4^th order ODE with displacement as the primitive variable, as well as two types of mixed formulations (one resulting in a set of 2 second-order ODEs,… More >

Xiaomin An¹, Min Xu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.6, pp. 601-629, 2014, DOI:10.3970/cmes.2014.098.601

Abstract Nonlinear aeroelasticity, caused by the interaction between nonlinear fluid and geometrically nonlinear structure, is studied by an improved CFD and CSD coupled program. An AUSMpw+ flux splitting scheme, combined with an implicit time marching technology and geometric conservation law, is utilized to solve unsteady aerodynamic pressure; The finite element co-rotational theory is applied to model geometrically nonlinear two-dimensional and three-dimensional panels, and a predictor-corrector program with an approximately energy conservation is developed to obtain nonlinear structure response. The two solvers are connected by Farhat’s second order loosely coupled method and the aerodynamic loads and structural More >

X. X. Cui¹, X. Zhang^1,2, X. Zhou³, Y. Liu¹, F. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.6, pp. 565-599, 2014, DOI:10.3970/cmes.2014.098.565

Abstract The material point method (MPM) discretizes the material domain by a set of particles, and has showed advantages over the mesh-based methods for many challenging problems associated with large deformation. However, at the same time, it requires more computational resource and has difficulties to construct high order scheme when simulating the fluid in high explosive (HE) explosion problems. A coupled finite difference material point (CFDMP) method is proposed through a bridge region to combine the advantages of the finite difference method (FDM) and MPM. It solves a 3D HE explosion and its interaction with the… 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 >