Bohou Xu¹, Yibing Yang¹, Zhong-Ping Jiang², Daniel W. Repperger³

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 159-174, 2010, DOI:10.3970/cmes.2010.057.159

Abstract A modified two-dimensional parameter-induced stochastic resonance (2D-PSR) system is proposed. Both theoretical and simulation results indicate that the 2D-PSR system performs a resonant-like behavior when system parameters are properly adjusted. When applied to degraded image processing, 2D-PSR technique is proved to be able to attain higher SNR gain than traditional linear filters. Due to its strong robustness to environmental changes, adaptability, and complementarities with other methods, the proposed 2D-PSR technique turns out to be promising in the field of image processing. More >

Chia-Cheng Tsai¹, Chein-Shan Liu², Wei-Chung Yeih³

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.2, pp. 131-152, 2010, DOI:10.3970/cmes.2010.056.131

Abstract The fictitious time integration method (FTIM) previously developed by Liu and Atluri (2008a) is combined with the method of fundamental solutions and the Chebyshev polynomials to solve Poisson-type nonlinear PDEs. The method of fundamental solutions with Chebyshev polynomials (MFS-CP) is an exponentially-convergent meshless numerical method which is able to solving nonhomogeneous partial differential equations if the fundamental solution and the analytical particular solutions of the considered operator are known. In this study, the MFS-CP is extended to solve Poisson-type nonlinear PDEs by using the FTIM. In the solution procedure, the FTIM is introduced to convert a Poisson-type nonlinear PDE into… More >

David Stevens¹, Henry Power^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111

Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations. The Kirchhoff transformation… More >

Yongchang Cai^1,2, J.K. Paik³, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.3, pp. 335-368, 2009, DOI:10.3970/cmes.2009.054.335

Abstract This paper presents a simple finite element method, based on assumed moments and rotations, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A von Karman type nonlinear theory of deformation is employed in the updated Lagrangian co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. The Reissner variational principle is used in the updated Lagrangian co-rotational reference frame, to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix of the beam element in the co-rotational reference frame. The explicit expression for the finite rotation of… More >

Yongchang Cai^1,2, J.K. Paik³, Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 123-152, 2009, DOI:10.3970/cmes.2009.053.123

Abstract This paper presents a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A co-rotational reference frame, involving the axes of each finitely rotated beam finite-element, is used as the Updated Lagrangian reference frame for the respective element. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. An assumed displacement approach is used to derive an explicit expression for the (12x12)symmetrictangent stiffness matrix… More >

Chein-Shan Liu¹, Weichung Yeih², Chung-Lun Kuo³, Satya N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 47-72, 2009, DOI:10.3970/cmes.2009.053.047

Abstract Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): F_i(x_j) = 0, i, j = 1,... ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one to solve the NAEs, due to the ease of its numerical implementation. However, this type of algorithm is sensitive to the initial guess of solution, and is expensive in terms of the computations of the Jacobian matrix ∂F_i/∂x_j and its inverse at each iterative step. In addition, the Newton-like methods restrict one to construct an iteration procedure for n-variables by using n-equations,… More >

Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 43-82, 2009, DOI:10.3970/cmes.2009.048.043

Abstract Differential Quadrature (DQ) is one of the efficient derivative approximation techniques but it requires a regular domain with all the points distributed only along straight lines. This severely restricts the DQ while solving the irregular domain problems discretized by the random field nodes. This limitation of the DQ method is overcome in a proposed novel strong-form meshless method, called the random differential quadrature (RDQ) method. The RDQ method extends the applicability of the DQ technique over the irregular or regular domains discretized using the random field nodes by approximating a function value with the fixed reproducing kernel particle method (fixed… More >

J. Noorzaei¹, K.H. Bayagoob², A.A. Abdulrazeg¹, M.S. Jaafar^1,1, T.A. Mohammed¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 43-60, 2009, DOI:10.3970/cmes.2009.047.043

Abstract This paper focuses on the development, verification and application of a three-dimensional finite element code for coupled thermal and structural analysis of roller compacted concrete dams. The Kinta RCC gravity dam, which is the first roller compacted concrete dam in Malaysia, has been taken for the purpose of verification of the finite element code. The actual climatic conditions and thermal properties of the materials were considered in the analysis. The structural stress analysis was performed using the elasto-plastic stress analysis. The Mohr yield criterion which is widely used for concrete plasticity modeling was adopted in this study. The results have… More >

F. Yan^1,2, Y. Miao^2,3, Q. N. Yang²

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.1, pp. 21-50, 2009, DOI:10.3970/cmes.2009.046.021

Abstract A novel boundary type meshless method called Quasilinear Hybrid Boundary Node Method (QHBNM), which combines quasilinearization method, dual reciprocity method (DRM) and hybrid boundary node method (HBNM), is developed to solving a class of nonlinear problems. The nonlinear term of the governing equation is linearized by the generated quasilinearization method, in which the solution of the linearized equation can exactly converge to the solution of original equation at a very wide range initial value, and the convergence rate is quadratic. Then dual hybrid boundary node method is applied to solving the linearized equation, in which DRM is introduced into HBNM… More >

Sirajul Haq^1,2, Siraj-Ul-Islam³, Marjan Uddin^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 115-136, 2009, DOI:10.3970/cmes.2009.044.115

Abstract A mesh free method for the numerical solution of the nonlinear Schrodinger (NLS) and coupled nonlinear Schrodinger (CNLS) equation is implemented. The presented method uses a set of scattered nodes within the problem domain as well as on the boundaries of the domain along with approximating functions known as radial basis functions (RBFs). The set of scattered nodes do not form a mesh, means that no information of relationship between the nodes is needed. Error norms L₂, L_∞ are used to estimate accuracy of the method. Stability analysis of the method is given to demonstrate its practical applicability. More >