Zhiming Gao², Yichen Ma³

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 135-164, 2010, DOI:10.3970/cmes.2010.066.135

Abstract Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier-Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently More >

D. C. C. Lam¹, L-H Keung¹, P. Tong²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 73-100, 2010, DOI:10.3970/cmes.2010.066.073

Abstract Additional molecular rotations in long chained macromolecules lead to additional size dependence. In this investigation, we developed the higher order viscoelasticity framework and conducted experiments to determine the higher order material length scale parameters needed to describe the higher order viscoelastic behavior in the new framework. In the first part of the investigation of high order deformation behavior of macromolecular solids, the higher-order viscoelasticity theories for Maxwell and Kelvin-Voigt materials, and models of higher-order viscoelastic beam deflection creep are developed in this study. We conducted creep bending experiments with epoxy beams to show that the… 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 >

A. Papacharalampopoulos², G. F. Karlis², A. Charalambopoulos³, D. Polyzos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 45-74, 2010, DOI:10.3970/cmes.2010.058.045

Abstract A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain More >

X.P. Shen, A. Diaz¹, T. Sheehy²

CMC-Computers, Materials & Continua, Vol.20, No.3, pp. 205-224, 2010, DOI:10.3970/cmc.2010.020.205

Abstract This paper presents a case study for the design of a mud-weight window (MWW) with three-dimensional (3-D), finite-element (FE) tools for subsalt wells. The trajectory of the target well penetrates a 7 km thick salt body. A numerical scheme has been proposed for calculating the shear failure gradient (SFG) and fracture gradient (FG) with 3-D FE software. User subroutines have been developed to address non-uniform pore-pressure distribution. A series of FE calculations were performed to obtain the MWW of the target wellbore, which consists of the SFG and FG for the subsalt sections. Although no… 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 More >

Veturia Chiroiu¹, Ligia Munteanu¹, Pier Paolo Delsanto²

CMC-Computers, Materials & Continua, Vol.16, No.1, pp. 75-100, 2010, DOI:10.3970/cmc.2010.016.075

Abstract Conventional continuum theories are unable to capture the observed indentation size effects, due to the lack of intrinsic length scales that represent the measures of nanostructure in the constitutive relations. In order to overcome this deficiency, the Toupin-Mindlin strain gradient theory of nanoindentation is formulated in this paper and the size dependence of the hardness with respect to the depth and the radius of the indenter for multiple walled carbon nanotubes is investigated. Results show a peculiar size influence on the hardness, which is explained via the shear resistance between the neighboring walls during the More >

Shuling Hu¹, Shengping Shen^1,2

CMC-Computers, Materials & Continua, Vol.13, No.1, pp. 63-88, 2009, DOI:10.3970/cmc.2009.013.063

Abstract The electric field gradient effect is very strong for nanoscale dielectrics. In addition, neither the surface effect nor electrostatic force can be ignored. In this paper, the electric Gibbs free energy variational principle for nanosized dielectrics is established with the strain/electric field gradient effects, as well as the effects of surface and electrostatic force. As regards the surface effects both the surface stress and surface polarization are considered. From this variational principle, the governing equations and the generalized electromechanical Young-Laplace equations, which take into account the effects of strain/electric field gradient, surface and electrostatic force, More >

Zai You Yan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.1, pp. 1-20, 2009, DOI:10.3970/cmes.2009.046.001

Abstract It is well-known that the velocity potential and its first normal derivative on the structure surface can be easily found in the boundary element method for problems of potential flow. Based on an investigation in progress, the gradient of the normal derivative of the velocity potential will be very helpful in the treatment of the so-called hypersingular integral. Through a coordinate transformation, such gradient can be expressed by the combination of the first and the second normal derivatives of the velocity potential. Then one interesting problem is how to find the second normal derivative of More >

Hossein M. Shodja^{1, 2, 3}, Alireza Hashemian^{2, 4}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 57-58, 2009, DOI:10.3970/icces.2009.013.057

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations More >