Open Access
ARTICLE
Hrvoje Gotovac1, Vedrana Kozulić2, Blaž Gotovac1
CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173
Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the threshold as a direct measure… More >
Open Access
ARTICLE
F.Y.Li1,2, G.Y.Li1
CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 199-220, 2010, DOI:10.3970/cmc.2010.015.199
Abstract In this paper, an uncertain multi-objective optimization method is suggested to deal with crashworthiness design problem of vehicle, in which the uncertainties of the parameters are described by intervals. Considering both lightweight and safety performance, structural weight and peak acceleration are selected as objectives. The occupant distance is treated as constraint. Based on interval number programming method, the uncertain optimization problem is transformed into a deterministic optimization problem. The approximation models are constructed for objective functions and constraint based on Latin Hypercube Design (LHD). Thus, the interval number programming method is combined with the approximation model to solve the uncertain… More >
Open Access
ARTICLE
Chein-Shan Liu1
CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 221-240, 2010, DOI:10.3970/cmc.2010.015.221
Abstract We propose a simple numerical scheme for solving the space- and time-fractional derivative Burgers equations: Dtαu + εuux = vuxx + ηDxβu, 0 < α, β ≤ 1, and ut + D*β(D*1-βu)2/2 = vuxx, 0 < β ≤ 1. The time-fractional derivative Dtαu and space-fractional derivative Dxβu are defined in the Caputo sense, while D*βu is the Riemann-Liouville space-fractional derivative. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ)γu(x,t) =: v(x,t,τ), where 0 < γ ≤ 1 is a parameter, such that the original equation is written as a new functional-differential… More >
Open Access
ARTICLE
Luming Shen1
CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 241-260, 2010, DOI:10.3970/cmc.2010.015.241
Abstract In this study, molecular dynamics (MD) simulations are performed to form glassy silica from meltedb-cristobalite using cooling rates of 2, 20 and 200 K/ps. The resulting glassy silica samples are then shocked at particle velocities ranging from 0.3 to 11 km/s in the MD simulations. The effect of the cooling rate on the shock wave velocity is observed for particle velocities below 2 km/s. Moreover, the simulated pressure and density of the shocked glassy silica increase as the cooling rate increases. As compared with the experimental data, the MD simulation can approximately identify the initiation of densification and predict the… More >
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