C. Jiang¹, Y.C. Bai¹, X. Han^1,2, H.M. Ning¹

CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 21-42, 2010, DOI:10.3970/cmc.2010.018.021

Abstract In this paper, an efficient interval optimization method based on a reliability-based possibility degree of interval (RPDI) is suggested for the design of uncertain structures. A general nonlinear interval optimization problem is studied in which the objective function and constraints are both nonlinear and uncertain. Through an interval order relation and a reliability-based possibility degree of interval, the uncertain optimization problem is transformed into a deterministic one. A sequence of approximate optimization problems are constructed based on the linear approximation technique. Each approximate optimization problem can be changed to a traditional linear programming problem, which can be easily solved by… More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 1-20, 2010, DOI:10.3970/cmc.2010.018.001

Abstract We are concerned with the reconstruction of an unknown space-dependent rigidity coefficient in a wave equation. This problem is known as one of the inverse scattering problems. Based on a two-point Lie-group equation we develop a Lie-group adaptive method (LGAM) to solve this inverse scattering problem through iterations, which possesses a special character that by using onlytwo boundary conditions and two initial conditions, as those used in the direct problem, we can effectively reconstruct the unknown rigidity function by aself-adaption between the local in time differential governing equation and the global in time algebraic Lie-group equation. The accuracy and efficiency… More >

Weichung Yeih¹, Chein-Shan Liu², Chung-Lun Kuo³, Satya N. Atluri⁴

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 275-302, 2010, DOI:10.3970/cmc.2010.017.275

Abstract In this paper, a multiple-source-point boundary-collocation Trefftz method, with characteristic lengths being introduced in the basis functions, is proposed to solve the direct, as well as inverse Cauchy problems of the Laplace equation for a multiply connected domain. When a multiply connected domain with genus p (p>1) is considered, the conventional Trefftz method (T-Trefftz method) will fail since it allows only one source point, but the representation of solution using only one source point is impossible. We propose to relax this constraint by allowing many source points in the formulation. To set up a complete set of basis functions, we… More >

J. Wang¹, D. C. C. Lam²

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 215-232, 2010, DOI:10.3970/cmc.2010.017.215

Abstract Selected elastic moduli of nanocomposites are higher than the elastic moduli of microcomposites. Molecular immobilization and crystallization at the interfaces had been proposed as potential causes, but studies suggested that these effects are minor and cannot be used to explain the magnitude observed in nanocomposites with >3nm particles. Alternately, molecular simulation of polymer deformation showed that rotation gradients can lead to additional molecular rotations and stiffen the matrix. The stiffening is characterized by the nanostiffening material parameter, l2. In this investigation, an analytical expression for nanostiffening in nanocomposites was developed using finite element analysis. The nanostiffening in nanocomposites was determined… More >

Qunfeng Liu¹, gping Shen²

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 59-76, 2010, DOI:10.3970/cmc.2010.017.059

Abstract Molecular Dynamics (MD) simulations have been performed using the EAM potential to investigate the deformation behaviors and mechanical properties of <100>/{100} gold nanowires with square cross-section at a certain strain rate under different temperatures ranging from 10 K to 700 K. It is found that <100>/{100} gold nanowires at high temperatures tend to form the extended stable nanobridges-Helical Multi-shell Structure (HMS), which is similar to the deformation behavior of <110> gold nanowires at room temperature reported in the previous experimental observations and simulations. The effect of temperature on the mechanical properties and deformation behaviors of gold nanowires was analyzed. The… More >

Taotao Hu¹, gping Shen^1,2

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 41-58, 2010, DOI:10.3970/cmc.2010.017.041

Abstract In this paper, an axisymmetric indentation model is set up to calculate the effects of the roughness of the thermally grown oxide (TGO) layer, which was modeled as a sinusoidal wave, on the indentation response of the thermal barrier coatings. It is found that the amplitude, wavelength, and thickness of the thermally grown oxide layer have obvious influences on the indentation response, while the effect of the indenter position can be neglected. In the top coating layer, residual stress mainly occurs below the indenter and around the nearest two peaks of the thermally grown oxide layer to the indenter. Only… More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 19-40, 2010, DOI:10.3970/cmc.2010.017.019

Abstract In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is offered. The solver utilized in… More >

S. Patala¹, C.A. Schuh¹

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 1-18, 2010, DOI:10.3970/cmc.2010.017.001

Abstract Recent advances in microstructural characterization have made it possible to measure grain boundaries and their networks in full crystallographic detail. Statistical studies of the complete boundary space using full crystallographic parameters (misorientations and boundary plane inclinations) are limited because the topology of the parameter space is not understood (especially for homophase grain boundaries). This paper addresses some of the complexities associated with the group space of grain boundaries, and resolves the topology of the complete boundary space for systems of two-dimensional crystals. Although the space of homophase boundaries is complicated by the existence of a `no-boundary' singularity, i.e., no boundary… More >

Zone-Ching Lin¹and Ren-Yuan Wang¹

CMC-Computers, Materials & Continua, Vol.16, No.3, pp. 247-272, 2010, DOI:10.3970/cmc.2010.016.247

Abstract The paper establishes a new three-dimensional quasi-steady molecular statics nanoscale abrasive cutting model to investigate the abrasive cutting behavior in the downpressing and abrasive cutting process of a workpiece in chemical mechanical polishing (CMP) process. The downpressing and abrasive cutting process is a continuous process. The abrasive cutting process is done after the single abrasive particle has downpressed and penetrated a workpiece to a certain depth of a workpiece. The paper analyzes the effects of the abrasive particles with different diameters on action force. It also analyzes the action force change of abrasive particles with different diameters on the projected… More >

W. F. Yuan^1,2, H. B. Zhang¹

CMC-Computers, Materials & Continua, Vol.16, No.2, pp. 117-126, 2010, DOI:10.3970/cmc.2010.016.117

Abstract Corrosion pits on a steel plate can reduce the strength of the plate. However, it is difficult to calculate the corrosion effect analytically since the pits are normally distributed on the plate's surface randomly. In this manuscript, a simple approach is proposed to convert the corroded plate into a perfect one. By this method, the corrosion pits are treated as inclusions embedded in the plate. Then the analytical mechanics model used for composite material can be adopted in the calculation of the steel plate's effective material properties. To verify the proposed approach, numerical simulation is conducted using finite element method. More >