X.G. Yuan^1,2, H.W. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 175-184, 2008, DOI:10.3970/cmes.2008.032.175

Abstract In this paper, a dynamic problem that describes void formation and motion in an incompressible hyperelastic solid sphere composed of a transversely isotropic Valanis-Landel material is examined, where the sphere is subjected to a class of periodic step tensile loads on its surface. A motion equation of void is derived. On analyzing the dynamical properties of the motion equation and examining the effect of material anisotropy on void formation and motion in the sphere, we obtain some new and interesting results. Firstly, under a constant surface tensile load, it is proved that a void would More >

Hossein M. Shodja^1,2,3, Alireza Hashemian^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 17-34, 2008, DOI:10.3970/cmes.2008.032.017

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 71-84, 2008, DOI:10.3970/cmes.2008.031.071

Abstract Iterative algorithms for solving a nonlinear system of algebraic equations of the type: 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 due to its easy numerical implementation. However, this type of algorithm is sensitive to the initial guess of the solution and is expensive in the computations of the Jacobian matrix ∂ F_i/ ∂ x_j and its inverse at each iterative step. In a time-integration of a system of nonlinear Ordinary Differential Equations (ODEs) of the type B_ijx_j + F_i = 0… More >

Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 27-36, 2008, DOI:10.3970/cmes.2008.030.027

Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li¹, X. Zhao², T.T. Nguyen², G.Y. Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 109-126, 2008, DOI:10.3970/cmes.2008.028.109

Abstract A smoothed finite element method (SFEM) is presented to analyze linear and geometrically nonlinear problems of plates and shells using bilinear quadrilateral elements. The formulation is based on the first order shear deformation theory. In the present SFEM, the elements are further divided into smoothing cells to perform strain smoothing operation, and the strain energy in each smoothing cell is expressed as an explicit form of the smoothed strain. The effect of the number of divisions of smoothing cells in elements is investigated in detail. It is found that using three smoothing cells for bending More >

S. S. Chen¹, Y. H. Liu^1,2, Z. Z. Cen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 39-56, 2008, DOI:10.3970/cmes.2008.028.039

Abstract In most engineering applications, solutions derived from the lower-bound theorem of plastic limit analysis are particularly valuable because they provide a safe estimate of the load that will cause plastic collapse. A solution procedure based on the meshless local Petrov-Galerkin (MLPG) method is proposed for lower-bound limit analysis. This is the first work for lower-bound limit analysis by this meshless local weak form method. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The discretized limit analysis problem is solved numerically with More >

B Radhika¹, S S P,a¹, C S Manohar^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 79-110, 2008, DOI:10.3970/cmes.2008.027.079

Abstract Reliability of nonlinear vibrating systems under stochastic excitations is investigated using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis tests, and the next stage involves More >

Jyoti Ranjan Majhi, Ranjan Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 25-36, 2008, DOI:10.3970/cmes.2008.027.025

Abstract The flapping equation for a rotating rigid helicopter blade is typically derived by considering 1) small flap angle, 2) small induced angle of attack and 3) linear aerodynamics. However, the use of nonlinear aerodynamics can make the assumptions of small angles suspect. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived in this paper with nonlinear aerodynamics . Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are More >

Zdenko Tonković¹, Jurica Sorić^1,2, Ivica Skozrit¹

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 75-90, 2008, DOI:10.3970/cmes.2008.026.075

Abstract An efficient numerical algorithm for modeling of cyclic elastoplastic deformation of shell structures is derived. The constitutive model includes highly nonlinear multi-component forms of kinematic and isotropic hardening functions in conjunction with von Mises yield criterion. Therein, the closest point projection algorithm employing the Reissner-Mindlin type kinematic model, completely formulated in tensor notation, is applied. A consistent elastoplastic tangent modulus ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite shell element, which is capable of geometrical nonlinearities including finite rotations. Numerical examples, More >

Q.W. Ma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 75-90, 2008, DOI:10.3970/cmes.2008.023.075

Abstract In the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, one needs a meshless interpolation scheme for an unknown function to discretise the governing equation. The MLS (moving least square) method has been used for this purpose so far. The MLS method requires inverse of matrix or solution of a linear algebraic system and so is quite time-consuming. In this paper, a new scheme, called simplified finite difference interpolation (SFDI), is devised. This scheme is generally as accurate as the MLS method but does not need matrix inverse and consume less CPU time More >