S. Tangaramvong¹, F. Tin-Loi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.3, pp. 217-256, 2009, DOI:10.3970/cmes.2009.042.217

Abstract Classical limit analysis is extended to include the effects of 2nd-order geometric and material nonlinearities, as well as the inclusion of limited ductility constraints. For the class of frame structures considered, the material constitutive model adopted can simultaneously accommodate the effects of combined axial and flexural force as well as local softening instability through the use of piecewise linearized yield surfaces. The main feature of the approach developed is to compute, in a single step, an upper bound to the maximum load. Corresponding displacements and stresses can be obtained as a by-product of the analysis. The problem is formulated as… More >

Hung-Chang Lee¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001

Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They provide single-step explicit time integrators… More >

X.G. Yuan^1,2, H.W. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 201-224, 2009, DOI:10.3970/cmes.2009.040.201

Abstract The radially symmetric motion of the pre-existing micro-void centered at an incompressible hyperelastic sphere under the dynamic surface tensile loads relating to time is investigated in this paper. Some interesting conclusions are obtained by qualitatively analyzing the solutions of the motion equation of micro-void in detail; meanwhile, numerical simulations are used for understanding the obtained conclusions. In particular, it is proved that the motion of the micro-void with time would present a nonlinearly periodic oscillation if the values of the constant tensile load, the material and the structure parameters are given and that the oscillation amplitudes of the micro-void are… More >

Cha’o-Kuang Chen^1,2, Hsin-Yi Lai¹, Chin-Chia Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 155-174, 2009, DOI:10.3970/cmes.2009.040.155

Abstract Electrostatically-actuated micro circular plates are used in many micro-electro-mechanical systems (MEMS) devices nowadays such as micro pumps and optical switches. However, the dynamic behavior of these circular plates is not easily analyzed using traditional analytic methods due to the complexity of the interactions between the electrostatic coupling effects. Accordingly, this study develops an efficient computational scheme in which the nonlinear governing equation of the coupled electrostatic force acting on the micro circular plate is solved using a hybrid differential transformation / finite difference approximation method. In deriving the dynamic equation of motion of the micro plate, explicit account is taken… More >

Sergia Colli¹, Massimiliano Gei¹, Davide Bigoni^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 29-62, 2009, DOI:10.3970/cmes.2009.040.029

Abstract Incremental plane strain deformations superimposed upon a uniformly stressed and deformed nonlinear elastic (compressible) body are treated by developing {\it ad hoc} boundary integral equations that, discretized, lead to a novel boundary element technique. The approach is a generalization to compressible elasticity of results obtained by Brun, Capuani, and Bigoni (2003, Comput. Methods Appl. Mech. Engrg. 192, 2461-2479), and is based on a Green's function here obtained through the plane-wave expansion method. New expressions for Green's tractions are determined, where singular terms are solved in closed form, a feature permitting the development of a optimized numerical code. An application of… More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six 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 strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

P. Bettini, E. Brusa, M. Munteanu, R. Specogna, F. Trevisan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 215-242, 2008, DOI:10.3970/cmes.2008.033.215

Abstract Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is affected by the nonlinearity of the electromechanical coupling. Sometimes an additional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibited in bending. To overcome the computational limits of the available numerical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implementation of a \emph {Non incremental sequential approach} is firstly proposed. The so-called \emph… More >

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 form in the sphere as… 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 (ODEs). Subsequently, Gear's method is… 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 where… More >