M. Iura¹, Y. Suetake², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 249-258, 2003, DOI:10.3970/cmes.2003.004.249

Abstract An accuracy of finite element solutions for 3-D Timoshenko's beams, obtained using a co-rotational formulation, is discussed. The co-rotational formulation has often been used with an assumption that the relative deformations are small. A fundamental question, therefore, has been raised as to whether or not the numerical solutions obtained approach the solutions of the exact theory. In this paper, from theoretical point of view, we investigate the accuracy of the co-rotational formulation for 3-D Timoshenko's beam undergoing finite strains and finite rotations. It is shown that the use of the conventional secant coordinates fails to give satisfactory numerical solutions. We… More >

Chyou-Chi Chien, Tong-Yue Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 213-226, 2001, DOI:10.3970/cmes.2001.002.213

Abstract This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from previous literature. Since a fifth-order… More >

CMC-Computers, Materials & Continua, Vol.47, No.3, pp. 179-201, 2015, DOI:10.3970/cmc.2015.047.179

Abstract Discontinuous smoothed particle hydrodynamics (DSPH) method based on traditional SPH method, which can be used to simulate discontinuous physics problems near interface or boundary. Previous works showed that DSPH method has a good application prospect [Xu et al, 2013], but further verification and improvement are demanded. In this paper, we investigate the accuracy of DSPH method by some numerical models. Moreover, to improve the accuracy of DSPH method, first order and second order multidimensional RDSPH methods are proposed by following the idea of restoring particle consistency in SPH (RSPH) method which has shown good results in the improvement of particle… More >

Hrvoje Gotovac¹, Vedrana Kozulić², Blaž Gotovac¹

CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173

Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the threshold as a direct measure… More >