CMES-Vol. 62, No. 1, 2010

Open Access

ARTICLE

Particle Methods for a 1D Elastic Model Problem: Error Analysis and Development of a Second-Order Accurate Formulation
D. Asprone¹, F. Auricchio², G. Manfredi¹, A. Prota¹, A. Reali², G. Sangalli³
CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.062.001
Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative More >

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Topological Derivative-Based Optimization of Micro-Structures Considering Different Multi-Scale Models
E.A. de Souza Neto¹, S. Amstutz², S.M. Giusti³, A.A. Novotny³
CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 23-56, 2010, DOI:10.3970/cmes.2010.062.023
Abstract A recently proposed algorithm for micro-structural optimization, based on the concept of topological derivative and a level-set domain representation, is applied to the synthesis of elastic and heat conducting bi-material micro-structures. The macroscopic properties are estimated by means of a family of multi-scale constitutive theories where the macroscopic strain and stress tensors (temperature gradient and heat flux vector in the heat conducting case) are defined as volume averages of their microscopic counterparts over a Representative Volume Element (RVE). Several finite element-based examples of micro-structural optimization are presented. Three multi-scale models, providing an upper and a More >

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On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion
Roman Chapko¹, B. Tomas Johansson², Oleh Sobeyko¹
CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 57-76, 2010, DOI:10.3970/cmes.2010.062.057
Abstract We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the More >

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ARTICLE

Thin Film Flow Over and Around Surface Topography: a General Solver for the Long-Wave Approximation and Related Equations
P.H. Gaskell¹, Y.C. Lee², H.M. Thompson¹
CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 77-112, 2010, DOI:10.3970/cmes.2010.062.077
Abstract The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptive time stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the More >

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