Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 395-432, 2011, DOI:10.3970/cmes.2011.073.395

Abstract In this paper we solve a system of nonlinear algebraic equations (NAEs) of a vector-form: F(x) = 0. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we derive a system of nonlinear ordinary differential equations (ODEs) with a fictitious time-like variable t as an independent variable: x^· = λ[αF + (1−α)B^TF], where λ and α are scalars and B_ij = ∂F_i/∂x_j. From this set of nonlinear ODEs, we derive a purely iterative algorithm for finding the solution vector x, without having to invert the Jacobian (tangent stiffness matrix)… More >

G. Desmeulles, S. Bonneaud, P. Redou>, V. Rodin, J. Tisseau

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.3, pp. 299-330, 2009, DOI:10.3970/cmes.2009.047.299

Abstract Virtual reality can enable computer scientists and domain experts to perform in virtuo experiments of numerical models of complex systems. Such dynamical and interactive experiments are indeed needed when it comes to complex systems with complex dynamics and structures. In this context, the question of the modeling tool to study such models is crucial. Such tool, called a virtuoscope, must enable the virtual experimentation of models inside a conceptual and experimental framework for imagining, modeling and experimenting the complexity of the studied systems. This article describes a conceptual framework and a meta model, called RéISCOP, that enable the construction and… More >

D. Kourounis¹, L.N. Gergidis¹, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.3, pp. 185-202, 2008, DOI:10.3970/cmes.2008.028.185

Abstract The sensitivity of analytical solutions of the direct acoustic scattering problem in prolate spheroidal geometry on the wavenumber and shape, is extensively investigated in this work. Using the well known Vekua transformation and the complete set of radiating "outwards'' eigensolutions of the Helmholtz equation, introduced in our previous work ([Charalambopoulos and Dassios(2002)], [Gergidis, Kourounis, Mavratzas, and Charalambopoulos (2007)]), the scattered field is expanded in terms of it, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. An approach is employed for the determination of the expansion coefficients, which is optimal in the sense, that minimizes the… More >

L.N. Gergidis, D. Kourounis, S. Mavratzas, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 157-176, 2007, DOI:10.3970/cmes.2007.021.157

Abstract A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. Two approaches concerning the determination… More >

T. Nishioka¹, Y. Kobayashi¹, T. Fujimoto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 231-238, 2007, DOI:10.3970/cmes.2007.017.231

Abstract First, for growing cracks in elastic-plastic materials, an incremental variational principle is developed to satisfy the boundary conditions near newly created crack surfaces. Then using this variational principle, a moving finite element method is formulated and developed, based on the Delaunay automatic triangulation. Furthermore, theoretical backgrounds on numerical prediction for fracture path of curving crack using T* integral are explained. Using the automatic moving finite element method, fracture-path prediction simulations are successfully carried out. More >

Y. Guo¹, J. A. Nairn¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 295-308, 2004, DOI:10.3970/cmes.2004.006.295

Abstract The Material Point Method (MPM), which is a particle-based, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of crack-tip parameters, such as J-integral and stress intensity factors, from MPM calculations involving explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture parameters. The MPM results… More >

Farid F. Abraham¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 63-70, 2000, DOI:10.3970/cmes.2000.001.515

Abstract A challenging paradigm in the computational sciences is the coupling of the continuum, the atomistic and the quantum descriptions of matter for a unified dynamic treatment of a single physical problem. We described the achievement of such a goal. We have spanned the length scales in a concerted simulation comprising the finite-element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions. We illustrate and validate the methodology for crack propagation in silicon. More >

L. Ma¹, A.S. Kobayashi², S. N. Atluri³, P.W. Tan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 19-26, 2000, DOI:10.3970/cmes.2000.001.471

Abstract Experimentally determined T_ε^* and CTOA resistance curves were used to simulate numerically, stable crack growth and the ensuing crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimen with multiple site damage (MSD) subjected to monotonically/cyclically increasing loading. The T_ε^* integral correctly predicted the crack growth and linkup history as well as the onset of rapid fracture in MSD specimens. The CTOA criterion also predicted the crack growth history but in its present form, could not predict crack linkup and rapid fracture. More >

Kang Qiong^1,*, Xinting Li²

CMC-Computers, Materials & Continua, Vol.58, No.1, pp. 121-133, 2019, DOI:10.32604/cmc.2019.03723

Abstract The introduction of graph-theoretical structure descriptors represents an important step forward in the research of predictive models in chemistry and falls within the lines of the increasing use of mathematical and computational methods in contemporary chemistry. The basis for these models is the study of the quantitative structure-property and structure-activity relationship. In this paper, we investigate Great rhom-bitrihexagonal which is a kind of dodecagon honeycomb net-work covered by quadrangle and hexagon. Many topological indexes of Great rhom-bitrihexagonal have being investigated, such as sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index, fifth, harmonic index, Randić connectivity index, first Zagreb index, second Zagreb… More >

Wenjie Liu^1,2,*, Zhenyu Chen², Jinsuo Liu³, Zhaofeng Su⁴, Lianhua Chi⁵

CMC-Computers, Materials & Continua, Vol.56, No.2, pp. 211-223, 2018, DOI: 10.3970/cmc.2018.02288

Abstract The delegating private quantum computation (DQC) protocol with the universal quantum gate set {X,Z,H,P,R,CNOT} was firstly proposed by Broadbent et al. [Broadbent (2015)], and then Tan et al. [Tan and Zhou (2017)] tried to put forward a half-blind DQC protocol (HDQC) with another universal set {H,P,CNOT,T}. However, the decryption circuit of Toffoli gate (i.e. T) is a little redundant, and Tan et al.’s protocol [Tan and Zhou (2017)] exists the information leak. In addition, both of these two protocols just focus on the blindness of data (i.e. the client’s input and output), but do not consider the blindness of computation… More >