Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 261-286, 2008, DOI:10.3970/cmes.2008.036.261

Abstract The inverse Sturm-Liouville problem finds its applications in the identification of mechanical properties and/or geometrical configurations of a vibrating continuous medium; however, this problem is hard to solve, either theoretically or numerically. Previously, Liu (2008a) has constructed a Lie-group shooting method to determine the eigenvalues, and the corresponding eigenfunctions, for the direct Sturm-Liouville problem. In this study, we are concerned with solving the inverse Sturm-Liouville problem, by developing a Lie-group of SL(2,R) to construct nonlinear algebraic equations (NAEs), when discrete eigenvalues are specified. Our purpose here is to use these NAEs to solve the unknown function More >

G. Veble^1,2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 243-260, 2008, DOI:10.3970/cmes.2008.036.243

Abstract A simple cost function is proposed that depends on the inviscid pressure distribution around an airfoil and that, when minimized, results in airfoils that promote laminar flow. Additional constraints specify the design point of the airfoil. The method allows for straightforward inclusion of multiple design points. The resulting airfoils are quantitatively similar to those already successfully used in practice. More >

Maria João M. Vasconcelos¹, João Manuel R. S. Tavares¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 213-242, 2008, DOI:10.3970/cmes.2008.036.213

Abstract In this work we developed methods to automatically extract significant points of objects like hand palms and faces represented in images that can be used to build Point Distribution Models automatically. These models are further used to segment the modelled objects in new images, through the use of Active Shape Models or Active Appearance Models. These models showed to be efficient in the segmentation of objects, but had as drawback the fact that the labelling of the landmark points was usually manually made and consequently time consuming. Thus, in this paper we describe some methods More >

G.J.A. Loeven^1,2, H. Bijl³

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 193-212, 2008, DOI:10.3970/cmes.2008.036.193

Abstract In this paper a Two-Step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters. Both steps are performed using the Probabilistic Collocation method. The first step consists of a sensitivity analysis to identify the most important parameters of the problem. The sensitivity derivatives are obtained using a first or second order Probabilistic Collocation approximation. For the most important parameters the probability distribution functions are propagated using the Probabilistic Collocation method using higher order approximations. The Two-Step approach is demonstrated for flow around a NACA0012 airfoil with eight uncertain parameters in the More >

L. Li, S. Liu, H. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 173-192, 2008, DOI:10.3970/cmes.2008.036.173

Abstract We study ductile fracture using Reproducing Kernel Particle Interpolation and the Gurson-Tvergaard-Needleman (GTN) model. The meshless simulations are compared with the available experimental results and previous finite element simulations for crack propagation. The results agree well with experimental results, and it is confirmed that the proposed method provides a convenient and yet accurate means for simulation of ductile fracture. More >

Yueting Zhou¹, Xing Li², Dehao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 147-172, 2008, DOI:10.3970/cmes.2008.036.147

Abstract A problem for bonded plane material with a set of curvilinear cracks, which is under the action of a rigid punch with the foundation of convex shape, has been considered in this paper. Kolosov-Muskhelishvili complex potentials are constructed as integral representations with the Cauchy kernels with respect to derivatives of displacement discontinuities along the crack contours and pressure under the punch. The contact of crack faces is considered. The considered problem has been transformed to a system of complex Cauchy type singular integral equations of first and second kind. The presented approach allows to consider More >

V. Vavourakis ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 119-146, 2008, DOI:10.3970/cmes.2008.036.119

Abstract In this paper, a new meshless Local Hypersingular Boundary Integral Equation method is presented for the analysis of two-dimensional elastostatic problems. The elastic domain is discretized by placing arbitrarily nodes on its boundary and interior. Given this set of nodes, the corresponding map of background triangles is constructed through a common triangulation algorithm. The local domain of each node consists of the union of triangles that this point lies, thus, creating a polygonal line of its local boundary. The local boundary integral equations of both displacements and stresses of the conventional Boundary Elements Method are… More >

S. Wong, Y. Shie

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 97-118, 2008, DOI:10.3970/cmes.2008.036.097

Abstract In this paper, we propose a Galerkin-based smoothed particle hydrodynamics (SPH) formulation with moving least-squares meshless approximation, applied to solid mechanics and large deformation. Our method is truly meshless and based on Lagrangian kernel formulation and stabilized nodal integration. The performance of the methodology proposed is tested through various simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena. More >

H. Nguyen-Van¹, N.Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 65-96, 2008, DOI:10.3970/cmes.2008.036.065

Abstract A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized More >

Giorgio Pini¹, Annamaria Mazzia¹, Flavio Sartoretto²,

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 43-64, 2008, DOI:10.3970/cmes.2008.036.043

Abstract Meshless methods have been explored in many 2D problems and they have been shown to be as accurate as Finite Element Methods (FEM). Compared to the extensive literature on 2D applications, papers on solving 3D problems by meshless methods are surprisingly few. Indeed, a main drawback of these methods is the requirement for accurate cubature rules. This paper focuses on the so called Meshless Local Petrov Galerkin (MLPG) methods. We show that accurate solutions of 3D potential problems can be attained, provided suitable cubature rules are identified, sparse data structures are efficiently stored, and strategies More >