Gusein Sh. Guseinov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.4, pp. 301-320, 2012, DOI:10.3970/cmes.2012.086.301

Abstract This paper deals with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit algorithm of reconstruction of the matrix from the two spectra is given. More >

Huimin Song¹, Dewey H. Hodges¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.3, pp. 239-278, 2012, DOI:10.3970/cmes.2012.085.239

Abstract The present paper presents a rigorous approach that can accurately and efficiently capture the linear, static and free-vibration behaviors of a beam-like structure by the rigorous combination of a one-dimensional beam model with a three-dimensional continuum model. This study focuses on coupling these disparate finite element types, putting them both into a single finite element model while making use of the asymptotically exact information available as part of the beam model, which itself is obtained by asymptotic dimensional reduction. The coupling is undertaken by use of appropriate transformation matrices at the interface together with stress More >

Gusein Sh. Guseinov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405

Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. More >

Jianxin Zhu, Zengsi Chen, Zheqi Shen

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 547-560, 2012, DOI:10.3970/cmes.2012.083.547

Abstract An acoustic waveguide with continuously varying sound speed is discussed in this paper. When the waveguide is open along the depth, the perfectly matched layer (PML) is used to terminate the infinite domain. Since the sound speed is gradually varied, the density is assumed as constant in each fluid layer. For this waveguide, it is shown that the mode relation is derived by using the differential transfer matrix method (DTMM). To solve leaky and PML modes, Newton's iteration is applied, and Chebyshev pseudospectral method is used for obtaining initial guesses. The solutions are with high More >

L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale… More >

P. Gayathri¹, R. Ganguli^1,2

Structural Durability & Health Monitoring, Vol.7, No.1&2, pp. 119-138, 2011, DOI:10.3970/sdhm.2011.007.119

Abstract The effect of random variation in composite material properties on the reliability of structural damage detection is addressed in this paper. A composite plate is considered as the structure and a finite element model is used for the simulation. Damage growth due to cyclic loading is addressed. Matrix crack induced delamination is emphasized in this paper. Thresholds for the damage accumulation are found using finite element simulations so that the structure can be subjected to inspections and removed from service safely. Uncertainty effects of composite material properties on the response of the structure are quantified More >

W. Zhang¹, X. Han^1,2, J. Liu¹, Z. H. Tan¹

CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 201-226, 2011, DOI:10.3970/cmc.2011.026.201

Abstract The uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters are widely existing and unsolved in the practical engineering. The insufficiency refers to the partly known parameters in the input and/or output, and the imprecision refers to the measurement errors of these ones. In this paper, a combined method is proposed to deal with such problems. In this method, the imprecision of these known parameters can be described by probability distribution with a certain mean value and variance. Sensitive matrix method is first used to transform the insufficient formulation in the More >

Şahin Emrah Amrahov¹, Iman N. Askerzade¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 207-216, 2011, DOI:10.3970/cmes.2011.076.207

Abstract We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side. It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix. This means that this theorem can be applicable only for a special form of linear systems, namely, only when the system consists of equations, each of which has exactly one variable. We prove an existence and uniqueness theorem, More >

Nizami Gasilov¹, Şahin Emrah Amrahov², Afet Golayoğlu Fatullayev¹, Halil İbrahim Karakaş¹, Ömer Akın³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 189-204, 2011, DOI:10.3970/cmes.2011.075.189

Abstract In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It… More >

Minghui Wang¹, Musheng Wei², Shanrui Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 173-182, 2011, DOI:10.3970/cmes.2011.077.173

Abstract The mapping from the symmetric solution set to its independent parameter space is studied and an iterative method is proposed for the least-squares minimum-norm symmetric solution of AXB = E. Numerical results are reported that show the efficiency of the proposed methods. More >