Zhang JT¹, B Xu¹, M Li²

Phyton-International Journal of Experimental Botany, Vol.80, pp. 161-166, 2011, DOI:10.32604/phyton.2011.80.161

Abstract The content of active compounds in Glycyrrhiza uralensis may vary among populations in different regions, and be influenced by environmental variables. We determined the effects of soil and climate on contents of glycyrrhizic acid and liquiritin in various populations of Glycyrrhiza uralensis. Fifty individuals from 5 rangeland populations in arid and semi-arid regions of North China were collected and analyzed. The contents of glycyrrhizic acid and liquiritin were determined using the HPLC method. Contents of glycyrrhizic acid and liquiritin varied significantly among populations as follows: Chifeng > Hangjinqi > Minqin > Aletai > Kashi. These contents were More >

S. Atobe¹, H. Fukunaga¹, N. Hu²

CMC-Computers, Materials & Continua, Vol.26, No.1, pp. 67-90, 2011, DOI:10.3970/cmc.2011.026.067

Abstract This paper presents a method for identifying the location and force history of an impact force acting on CFRP structures such as laminated plates and stiffened panels. The identification method is an experimental one without using any analytical model of the structure. Here, experimental transfer matrices, which relate the impact force to the corresponding responses of PZT sensors, are used to identify the impact force. The transfer matrices are preliminarily constructed from the measured data obtained by impact tests with an impulse hammer. To identify the impact location, the arrival times of the flexural waves More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.25, No.3, pp. 239-264, 2011, DOI:10.3970/cmc.2011.025.239

Abstract For the computational applications in several areas, we propose a single-scale and a multi-scale diagonal preconditioners to reduce the condition number of Vandermonde matrix. Then a new algorithm is given to solve the inversion of the resulting coefficient matrix after multiplying by a preconditioner to the Vandermonde matrix. We apply the new techniques to the interpolation of data by using very high-order polynomials, where the Runge phenomenon disappears even the equidistant nodes are used. In addition, we derive a new technique by employing an m-order polynomial with a multi-scale technique to interpolate 2m+1 data. Numerical results More >

D. Brunner¹, M. Junge¹, P. Rapp¹, M. Bebendorf², L. Gaul¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.2, pp. 131-160, 2010, DOI:10.3970/cmes.2010.058.131

Abstract The simulation of the hydroacoustic sound radiation of ship-like structures has an ever-growing importance due to legal regulations. Using the boundary element method, the overall dimension of the problem is reduced and only integrals over surfaces have to be considered. Additionally, the Sommerfeld radiation condition is automatically satisfied by proper choice of the fundamental solution. However, the resulting matrices are fully populated and the set-up time and memory consumption scale quadratically with respect to the degrees of freedom. Different fast boundary element methods have been introduced for the Helmholtz equation, resulting in a quasilinear complexity.… More >

P. Redou¹, L. Gaubert¹, G. Desmeulles¹, P-A. Béal², C. Le Gal², V. Rodin³

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.1, pp. 11-40, 2010, DOI:10.3970/cmes.2010.070.011

Abstract Multi Interaction Systems, used in the context of Virtual Reality, are dedicated to real-time interactive simulations. They open the way to the in virtuo experimentation, especially useful in the domain of biochemical kinetics. To this purpose, chaotic and asynchronous scheduling of autonomous processes is based upon desynchronization of phenomena involved in the system. It permits interactivity, especially the capability to add or remove phenomena in the course of a simulation. It provides methods of resolution of ordinary differential systems and partial derivative equations. Proofs of convergence for these methods have been established, but the problem of More >

Chein-Shan Liu¹, Hong-Ki Hong¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279

Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications… 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… 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… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 253-276, 2009, DOI:10.3970/cmes.2009.043.253

Abstract Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a₀ + a₁x + ... + a_nxⁿ expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an interpolant. But, Runge gave a counterexample, demonstrating that the polynomial interpolation problem may be ill-posed. Very high-order polynomial interpolation is very hard to realize by numerical computations. In this paper we propose a… More >

R Sivaprasad^1,2, S Venkatesha¹, C S Manohar^1,3

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 179-208, 2009, DOI:10.3970/cmc.2009.009.179

Abstract The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on More >