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Linear Problems (linear + problem)

Distribution by Scientific Domains
Engineering66%

Selected Abstracts

Micromechanics of fibre glass composites at elevated temperatures

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002
Alexander Tesar
Abstract The micromechanical assessment of ultimate response of moulded fibre glass (MFG) composites used in structural engineering and acting at elevated temperatures is treated in the present paper. The advanced crystal simulation model of the MFG-material at elevated temperatures, based on Washizu's variational principle, is presented. The numerical treatment of non-linear problems possibly appearing is made using the updated Lagrangian formulation of motion. Each step of iteration approaches the solution of the linear problem and the feasibility of the parallel processing FETM-simulation approach is established. Some numerical and experimental results are presented in order to demonstrate the efficiency of procedures suggested. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Truck schedule recovery for solid waste collection in Porto Alegre, Brazil

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2008
Jing-Quan Li
Abstract This paper considers a truck schedule recovery problem in the context of solid waste collection in the city of Porto Alegre, Brazil. When a truck on a scheduled trip breaks down, a backup truck needs to be selected to serve the cargo on that trip and other trucks might be rescheduled in order to gain the minimum operating and delay costs. The problem consists of designing, in the case of a severe disruption in a trip, new schedules taking into account the existing trucks in the system and a set of unfinished and not initiated collection trips, on which the trucks collect the solid waste in fixed routes and empty the loads in one of the several operational recycling facilities. The main objective is to minimize the total distances traveled and delay costs, as well as to obtain balanced assignments of truck unloads into the recycling facilities, due to the social benefits of the solid waste program. We modeled the problem as a mixed-integer linear problem and used CPLEX to solve it. Finally, computational experiments are conducted on real-world data. The results show that our approach successfully reduces the distances traveled and delays, simultaneously balancing the number of trucks unloading at each recycling facility, in comparison with the current manual strategy. [source]

Limitations of a linear model for the hurricane boundary layer

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 641 2009
Stefanie Vogl
Abstract The linear model for the steady boundary layer of a rapidly rotating axisymmetric vortex is derived from a detailed scale analysis of the full equations of motion. The previously known analytic solution is re-appraised for vortices of hurricane scale and strength. The internal consistency of the linear approximation is investigated for such a vortex by calculating from the solution the magnitude of the nonlinear terms that are neglected in the approximation compared with the terms retained. It is shown that the nonlinear terms are not negligibly small in a large region of the vortex, a feature that is consistent with the scale analysis. We argue that the boundary-layer problem is well-posed only at outer radii where there is subsidence into the layer. At inner radii, where there is ascent, only the radial pressure gradient may be prescribed and not the wind components at the top of the boundary layer, but the linear problem cannot be solved in these circumstances. We examine the radius at which the vertical flow at the top of the boundary layer changes sign for different tangential wind profiles relevant to hurricanes and show that this is several hundred kilometres from the vortex centre. This feature represents a further limitation of the linear model applied to hurricanes. While the present analysis assumes axial symmetry, the same limitations presumably apply to non-axisymmetric extensions to the linear model. Copyright © 2009 Royal Meteorological Society [source]

Flow separation and rotor formation beneath two-dimensional trapped lee waves

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 620 2006
S. B. Vosper
Abstract Numerical simulations of trapped lee waves generated in flow over a two-dimensional ridge are presented. It is shown that for sufficiently large amplitude waves flow separation occurs beneath the wave crests when a no-slip lower boundary condition is applied. The occurrence of separation corresponds to rotor motion, or recirculation, under the wave crests. The dependence of the wave-induced horizontal flow perturbations near the ground on the wave amplitude, wavelength and surface roughness is examined. It is shown that the normalized critical wave amplitude, above which rotors form, is a function of the ratio of the lee-wave horizontal wavelength to the surface roughness length. This normalized wave amplitude is defined as the ratio of the lee-wave pressure amplitude within the boundary layer, to the square of the friction velocity. Linearized turbulent equations for motion beneath the wave crests are considered and numerical solutions to the linear problem are compared with results from the simulations. When the waves are of sufficiently small amplitude that flow separation does not occur, the linear flow perturbations are shown to agree closely with the results from the simulations. It is also shown that linear theory provides a useful prediction of the occurrence of rotor formation. © Crown copyright, 2006. [source]

A reduced integration solid-shell finite element based on the EAS and the ANS concept,Geometrically linear problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2009
Marco Schwarze
Abstract In this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu,Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional material models can be implemented without additional assumptions. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A fast multi-level convolution boundary element method for transient diffusion problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
C.-H. Wang
Abstract A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N3/2) for three two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Analysis of 3D problems using a new enhanced strain hexahedral element

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
P. M. A. Areias
Abstract The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell finite elements, is here explored in a versatile 3D low-order element which is identified as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including finite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent stiffness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several finite strain tests. Some examples involve finite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Explicit calculation of smoothed sensitivity coefficients for linear problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
R. A. Bia, ecki
Abstract A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary-element and finite-element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Fifth-order Hermitian schemes for computational linear aeroacoustics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2007
Article first published online: 17 APR 200, G. Capdeville
Abstract We develop a class of fifth-order methods to solve linear acoustics and/or aeroacoustics. Based on local Hermite polynomials, we investigate three competing strategies for solving hyperbolic linear problems with a fifth-order accuracy. A one-dimensional (1D) analysis in the Fourier series makes it possible to classify these possibilities. Then, numerical computations based on the 1D scalar advection equation support two possibilities in order to update the discrete variable and its first and second derivatives: the first one uses a procedure similar to that of Cauchy,Kovaleskaya (the ,,-P5 scheme'); the second one relies on a semi-discrete form and evolves in time the discrete unknowns by using a five-stage Runge,Kutta method (the ,RGK-P5 scheme'). Although the RGK-P5 scheme shares the same local spatial interpolator with the ,-P5 scheme, it is algebraically simpler. However, it is shown numerically that its loss of compactness reduces its domain of stability. Both schemes are then extended to bi-dimensional acoustics and aeroacoustics. Following the methodology validated in (J. Comput. Phys. 2005; 210:133,170; J. Comput. Phys. 2006; 217:530,562), we build an algorithm in three stages in order to optimize the procedure of discretization. In the ,reconstruction stage', we define a fifth-order local spatial interpolator based on an upwind stencil. In the ,decomposition stage', we decompose the time derivatives into simple wave contributions. In the ,evolution stage', we use these fluctuations to update either by a Cauchy,Kovaleskaya procedure or by a five-stage Runge,Kutta algorithm, the discrete variable and its derivatives. In this way, depending on the configuration of the ,evolution stage', two fifth-order upwind Hermitian schemes are constructed. The effectiveness and the exactitude of both schemes are checked by their applications to several 2D problems in acoustics and aeroacoustics. In this aim, we compare the computational cost and the computation memory requirement for each solution. The RGK-P5 appears as the best compromise between simplicity and accuracy, while the ,-P5 scheme is more accurate and less CPU time consuming, despite a greater algebraic complexity. Copyright © 2007 John Wiley & Sons, Ltd. [source]