CMES-Vol. 93, No. 1, 2013

Open Access

ARTICLE

Theoretical Analysis of a Functionally Graded Shape Memory Alloy Beam under Pure Bending
Lijun Xue¹, Guansuo Dui^1,2, Bingfei Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 1-16, 2013, DOI:10.3970/cmes.2013.093.001
Abstract The Functionally Graded Shape Memory Alloy (FG-SMA) is a new kind of functional materials which possesses the excellent properties of both Shape Memory Alloy (SMA) and Functionally Graded Material (FGM). A macro constitutive model of FG-SMA is established by using the theory of the mechanics of composites and the existing SMA model. With this macro constitutive model, the mechanical behavior of a FG-SMA beam composed by elastic material A and SMA subjected to pure bending is investigated. The loading processes including elastic process and phase transformation process are discussed in detail and the analytical solutions… More >

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ARTICLE

Construction of Operator-Orthogonal Wavelet-Based Elements for Adaptive Analysis of Thin Plate Bending Problems
Y.M. Wang^1,2, Q. Wu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 17-45, 2013, DOI:10.3970/cmes.2013.093.017
Abstract A new kind of operator-orthogonal wavelet-based element is constructed based on the lifting scheme for adaptive analysis of thin plate bending problems. The operators of rectangular and skew thin plate bending problems and the sufficient condition for the operator-orthogonality of multilevel stiffness matrix are derived in the multiresolution finite element space. A new type of operator-orthogonal wavelets for thin plate bending problems is custom designed with high vanishing moments to be orthogonal with the scaling functions with respect to the operators of the problems, which ensures the independent solution of the problems in each scale. More >

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ARTICLE

Error Expansion of Classical Trapezoidal Rule for Computing Cauchy Principal Value Integral
Jin Li¹, De-hao Yu^{2, 3}
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 47-67, 2013, DOI:10.3970/cmes.2013.093.047
Abstract The composite classical trapezoidal rule for the computation of Cauchy principal value integral with the singular kernel 1/(x-s) is discussed. Based on the investigation of the superconvergence phenomenon, i.e., when the singular point coincides with some priori known point, the convergence rate of the classical trapezoidal rule is higher than the globally one which is the same as the Riemann integral for classical trapezoidal rule. The superconvergence phenomenon of the composite classical trapezoidal rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. Some numerical examples are provided More >

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ARTICLE

Half Space Acoustic Problems Analysis by Fast Multipole Boundary Face Method
Xianhui Wang¹, Jianming Zhang^1,2, Xingshuai Zheng¹, Fenglin Zhou¹
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.1, pp. 69-90, 2013, DOI:10.3970/cmes.2013.093.069
Abstract In this paper, a half space adaptive fast multipole boundary face method (FMBFM) is presented for solving the three-dimensional half space exterior acoustic problems. In the presented method, the Burton-Miller equation based on the conventional boundary integral equation (CBIE) and its hyper-singular boundary integral equation (HBIE) is used to deal with the fictitious eigenfrequencies problem. The half space Green’s function is employed, thus the tree structure in the fast multipole method can be used only for the real domain. The higher order elements and an adaptive tree structure are used to improve the efficiency of More >

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