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Proper Orthogonal Decomposition for Nonlinear Radiative Heat Transfer Problems ; Masset, Luc ; Kerschen, Gaëtan et al in Proceedings of the ASME International Design Engineering Technical Conferences (2011) Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive ... [more ▼] Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlinear multiphysical systems. The paper focuses on Proper Orthogonal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The radiative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a raytracing method. A reduction procedure is proposed for this fully coupled nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic approach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes separately. The paper builds on previous work presented previously by the authors. The results are given for the RMS error between either approach and the original, full solution. [less ▲] Detailed reference viewed: 27 (7 ULg)Investigating the performance of model order reduction techniques for nonlinear radiative heat transfer problems ; Masset, Luc ; Kerschen, Gaëtan et al in Proceedings of the International Conference on Advanced Computational Methods in Engineering (2011) The problem of nonlinear radiative heat transfer is one of great importance to the aerospace industry. However, analysing large-scale, nonlinear, multiphysical, dynamical structures, by using mathematical ... [more ▼] The problem of nonlinear radiative heat transfer is one of great importance to the aerospace industry. However, analysing large-scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally expensive. This provides motivation for the development of Model-Order Reduction (MOR) techniques capable of reducing simulation times without the loss of important information. The objective is to demonstrate the method of Proper Orthogonal Decompostition (POD) as a technique for nonlinear MOR. The nonlinear radiative exchanges between a linear benchmark beam within an external box (Figure 1) are analysed and a reduction procedure for this fully coupled, nonlinear, multiphysical, thermomechanical system is established. The solution to the strongly coupled, thermomechanical equations of motion is found by making use of an extended version of the implicit generalized-alpha scheme. In the reduced model, the residual of the unreduced system of equations need to be evaluated at each Newton iteration of each time step. In order to optimise the efficiency of the reduction method it is shown that the internal forces can be split into their linear and nonlinear counterparts. Only the nonlinear terms change at each time step, thus only these terms need to remain in the iterative loop significantly reducing the number of parameters that are to be computed at each step. These efficiency improvements to the method are discussed and the results are given. [less ▲] Detailed reference viewed: 48 (6 ULg) |
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