Cheng-Yu Ku, Chein-Shan Liu, Weichung Yeih, Chia-Ming Fan

The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.2, pp. 33-34, 2011, DOI:10.3970/icces.2011.019.033

Abstract In this paper, a novel method, named the perturbed dynamical method, is proposed to solve nonlinear systems whose Jacobian matrix is singular. The concept of the proposed method roots from the conventional homotopy method but it takes the advantages of converting a vector function to a scalar function by using the square norm of the vector function to conduct a scalar-based homotopy method. Then, a small parameter, which is similar to the perturbation theory, is introduced to the singular systems of nonlinear equations such that the modified singular systems of nonlinear equations become nonsingular and the asymptotic solutions may be… More >

Cheng-Yu Ku^1,2,3,Weichung Yeih^1,2, Chein-Shan Liu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.076.083

Abstract In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of Non-Linear Algebraic Equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM), and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventional Newton method using a certain fictitious time-like function. The formulation presented… More >

Anil Misra¹, Shiping Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.2, pp. 197-216, 2009, DOI:10.3970/cmes.2009.052.197

Abstract The behavior of contact between solid bodies with rough surfaces under combined normal and shear loading remains a problem of interest in many areas of engineering. In this paper, we have utilized a micromechanical methodology to derive an expression of stress-displacement relationship applicable to combined normal and shear loading conditions. The micromechanical methodology considers the mechanics of asperity contacts and the interface roughness in terms of asperity height and asperity contact orientation distribution. A numerical procedure is implemented to evaluate the derived expressions under complex and mixed loading conditions using an incremental approach. We find that the proposed numerical procedure… More >