Model reduction and clustering techniques for crash simulations

Fehr, Jörg; Grunert, Dennis

doi:10.1002/pamm.201510053

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…[26][27][28] However, linear MOR methods for a nonlinear problem would result in a large error, and the usage of nonlinear MOR techniques is normally very expensive and code intrusive. 29,30 The nonlinear MOR methods may be divided into three main categories, the discrete empirical interpolation method (DEIM), 31,32 the a priori hyper reduction (APHR), 33 and the proper generalized decomposition (PGD) proposed methods based on the gappy proper orthogonal decomposition (POD) method. [34][35][36] Furthermore, the modal derivatives-based MOR method has been widely applied in the nonlinear dynamic analysis.…”

Section: The Basic Theory Of the Reslto Methodsmentioning

confidence: 99%

Efficient structure crash topology optimization strategy using a model order reduction method combined with equivalent static loads

Ren

Min

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part D:

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In this study, an efficient topology optimization method under crash loads is proposed by combining the equivalent static loads with a model order reduction method, which is referred as the reduced model–based equivalent static loads method for nonlinear dynamic response topology optimization method. Considering that some parts of the vehicle experience large nonlinear deformations, whereas others exhibit only small linear deformations in a vehicle crash scenario, the linear and nonlinear behavior parts are identified and the whole model of the complete structure is divided into nonlinear and linear sub-models. At each cycle, the model order reduction method is used in the linear sub-model during crash analysis to solve the low-density-elements-induced mesh distortion problem and accelerate this process. In the linear static topology optimization, the nonlinear sub-model that was initially used to describe the nonlinear behavior part is linearized by the equivalent static loads method and then reduced by the Guyan reduction method. Then, the reduced equivalent static load model is assembled into the linear sub-model that is defined as the design space to formulate a reduced topology optimization model of the complete structure and the reduced equivalent static loads that only act on master degrees of freedom are calculated. Finally, the linear static topology optimization is performed based on the reduced topology optimization model with the reduced equivalent static loads to enhance the efficiency and improve the numerical stability. The process is repeated until the convergence criterion is satisfied. The effectiveness of the proposed method is demonstrated by investing a numerical example. The results show that the proposed method provides a feasible strategy for the topology optimization under crash loads, which can effectively improve the numerical stability and convergence.

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Section: The Basic Theory Of the Reslto Methodsmentioning

confidence: 99%

Efficient structure crash topology optimization strategy using a model order reduction method combined with equivalent static loads

Ren

Min

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part D:

View full text Add to dashboard Cite

show abstract

“…The core of the method is to compute the coefficients of the regression O solving the optimization problem (7). In this part, the computation method of the coefficients is outlined.…”

Section: Numerical Computation Of the Coefficients Of The Reduced Ordmentioning

confidence: 99%

“…These methods allow the use of partial or incomplete data (sample mesh in the DEIM and truncated integration domain in the APHR) to build a reduced order model. It is proposed in [7,8] to identify the parts having a non-linear behaviour and the parts having a linear behaviour using a clustering technique and to solve the non-linear problem with the DEIM and the linear part with Krylov subspaces [9]. As well as the APHR [10], this recent method has been applied to crash simulation but it seems limited to particular parts or small models with a low number of parameters.…”

Section: Introductionmentioning

confidence: 99%

A parametric and non-intrusive reduced order model of car crash simulation

Guennec

Brunet

Daim

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…M e ·q e + k e (q e , t) = h e (1) with mass matrix M e ∈ R N×N , elastic stiffness vector k e (q e , t) ∈ R N and applied forces h e ∈ R N solved with explicit time solver (LS-DYNA) tremendous simulation times and energy consumption due to highly detailed Finite Element models. Apply model order reduction for speedup for separation and understanding effects, a racing kart crashing against a pole as a surrogate model for research crash simulations possess three basic sources of nonlinearities in mechanics: large deformation nonlinear material behavior multiple contact scenarios internal forces k e = k e (q e ,q e , t, .…”

mentioning

confidence: 99%

“….) are nonlinear Reduction Approach Substructuring: Separation of the model in parts with linear and parts with nonlinear behaviour [1]. Apply model reduction only to linear part with k e = K e · q e (K e is stiffness matrix).…”

mentioning

confidence: 99%