Jin Ma, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 213-228, 2006, DOI:10.3970/cmes.2006.012.213

Abstract The generalized interpolation material point (GIMP) method, recently developed using a C¹ continuous weighting function, has solved the numerical noise problem associated with material points just crossing the cell borders, so that it is suitable for simulation of relatively large deformation problems. However, this method typically uses a uniform mesh in computation when one level of material points is used, thus limiting its effectiveness in dealing with structures involving areas of high stress gradients. In this paper, a spatial refinement scheme of the structured grid for GIMP is presented for simulations with highly localized stress gradients. A uniform structured background… More >

S. Gerace¹, K. Erhart¹, E. Divo^1,2, A. Kassab¹

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 35-68, 2011, DOI:10.3970/cmes.2011.081.035

Abstract The focus of this work is to demonstrate a novel approach to true CFD automation based on an adaptive Cartesian point distribution process coupled with a Meshless flow solution algorithm. As Meshless method solutions require only an underlying nodal distribution, this approach works well even for complex flow geometries with non-aligned domain boundaries. Through the addition of a so-called shadow layer of body-fitted nodes, application of boundary conditions is simplified considerably, eliminating the stair-casing issues of typical Cartesian-based techniques. This paper describes the approach taken to automatically generate the Meshless nodal distribution, along with the details of an automatic local… More >

J. Cugnoni¹, M. Galli²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 165-186, 2010, DOI:10.3970/cmes.2010.066.165

Abstract With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is… More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 161-190, 2009, DOI:10.3970/cmes.2009.050.161

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs over irregularly shaped domains. For a problem defined over Ω∈ℜ^d, the boundary of an irregularly shaped domain, Γ, is defined as a boundary curve that is a product of a Heaviside function along the normal direction and a piecewise continuous tangential curve. The link between the original wavelet based adaptive method presented in Libre, Emdadi, Kansa, Shekarchi, and Rahimian (2008, 2009) or LEKSR method and the generalized one is given through the use of simple Heaviside masking procedure. In addition… More >

Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 147-176, 2009, DOI:10.3970/cmes.2009.041.147

Abstract Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This paper, therefore, extends the strategy proposed by [Aftosmis and Berger (2002)] to compute the refinement threshold. The extended strategy computes the refinement threshold based on a user desired number of grid cells and adaptations, thereby ensuring high computational efficiency. Because our main interest is flow around wind turbines, the adaptation strategy has been optimized for flow around wind turbine airfoils. The… More >

Leevan Ling¹, Tomoya Takeuchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence… More >

Chany Lee¹, Chang-Hwan Im², Hyun-Kyo Jung³, Hong-Kyu Kim⁴, Do Wan Kim⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process for more efficient meshless analysis… More >

M. Manjuprasad¹, C. S. Manohar²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 23-54, 2007, DOI:10.3970/cmes.2007.019.023

Abstract A technique for adaptive random field refinement for stochastic finite element reliability analysis of structures is presented in this paper. Refinement indicator based on global importance measures are proposed and used for carrying out adaptive random field mesh refinements. Reliability index based error indicator is proposed and used for assessing the percentage error in the estimation of notional failure probability. Adaptive mesh refinement is carried out using hierarchical graded mesh obtained through bisection of elements. Spatially varying stochastic system parameters (such as Young's modulus and mass density) and load parameters are modeled in general as non-Gaussian random fields with prescribed… More >

J. Ma¹, H. Lu¹, B. Wang¹, S. Roy¹, R. Hornung², A. Wissink², R. Komanduri^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.2, pp. 135-152, 2005, DOI:10.3970/cmes.2005.008.135

Abstract In the simulation of a wide range of mechanics problems including impact/contact/penetration and fracture, the material point method (MPM), Sulsky, Zhou and Shreyer (1995), demonstrated its computational capabilities. To resolve alternating stress sign and instability problems associated with conventional MPM, Bardenhagen and Kober (2004) introduced recently the generalized interpolation material point (GIMP) method and implemented for one-dimensional simulations. In this paper we have extended GIMP to 2D and applied to simulate simple tension and indentation problems. For simulations spanning multiple length scales, based on the continuum mechanics approach, we present a parallel GIMP computational method using the Structured Adaptive Mesh… More >

S. Taschini¹, J. Müller², A. Greiner², M. Emmenegger¹, H. Baltes¹, J.G. Korvink²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 31-44, 2000, DOI:10.3970/cmes.2000.001.031

Abstract We present three techniques to accurately model the thermomechanical response of microsystem components: a new, accurate and stable Kirchhoff-Love multi-layered plate model implemented as an Argyris finite element, a model for the amplitude fluctuations of vibrational modes in micro-mechanical structures within a gaseous environment, and the consistent refinement of a finite element mesh in order to maximize the computational accuracy for a given mesh size. We have implemented these techniques in our in-house MEMS finite element program and accompanying Monte Carlo simulator. We demonstrate our approach to dynamic modeling by computing the thermomechanical response of a CMOS AFM beam. More >