Model order reduction for temperature-dependent nonlinear mechanical systems: A multiple scales approach

Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.

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Multiple scales analyses of the dynamics of weakly nonlinear mechanical systems

Applied Mechanics Reviews ◽

10.1115/1.1581884 ◽

2003 ◽

Vol 56 (5) ◽

pp. 455-492 ◽

Cited By ~ 43

Author(s):

MP Cartmell, ◽

SW Ziegler, ◽

R Khanin, ◽

DIM Forehand

Keyword(s):

Multiple Scales ◽

Mechanical Systems ◽

Perturbation Parameter ◽

Review Article ◽

Multiple Scales Method ◽

Weakly Nonlinear ◽

Time Scaling ◽

Nonlinear Mechanical ◽

Space Tethers ◽

Nonlinear Mechanical Systems

This review article starts by addressing the mathematical principles of the perturbation method of multiple scales in the context of mechanical systems which are defined by weakly nonlinear ordinary differential equations. At this stage the paper investigates some different forms of typical nonlinearities which are frequently encountered in machine and structural dynamics. This leads to conclusions relating to the relevance and scope of this popular and versatile method, its strengths, its adaptability and potential for different variant forms, and also its weaknesses. Key examples from the literature are used to develop and consolidate these themes. In addition to this the paper examines the role of term-ordering, the integration of the so-called small (ie, perturbation) parameter within system constants, nondimensionalization and time-scaling, series truncation, inclusion and exclusion of higher order nonlinearities, and typical problems in the handling of secular terms. This general discussion is then applied to models of the dynamics of space tethers given that these systems are nonlinear and necessarily highly susceptible to modelling accuracy, thus offering a rigorous and testing applications case-study area for the multiple scales method. The paper concludes with comments on the use of variants of the multiple scales method, and also on the constraints that the method can bring to expectations of modelling accuracy. This review article contains 134 references.

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Identification of temperature-dependent boundary conditions using MOR

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-05-2019-0404 ◽

2019 ◽

Vol 30 (2) ◽

pp. 1009-1022

Author(s):

Tobias Frank ◽

Steffen Wieting ◽

Mark Wielitzka ◽

Steffen Bosselmann ◽

Tobias Ortmaier

Keyword(s):

Boundary Conditions ◽

Model Order Reduction ◽

Order Reduction ◽

Complex Geometries ◽

Temperature Dependent ◽

Model Order ◽

Content Type ◽

Model Based Control ◽

Model Based ◽

Film Coefficient

Purpose A mathematical description of temperature-dependent boundary conditions is crucial in manifold model-based control or prototyping applications, where accurate thermal simulation results are required. Estimation of boundary condition coefficients for complex geometries in complicated or unknown environments is a challenging task and often does not fulfill given accuracy limits without multiple manual adaptions and experiments. This paper aims to describe an efficient method to identify thermal boundary conditions from measurement data using model order reduction. Design/methodology/approach An optimization problem is formulated to minimize temperature deviation over time between simulation data and available temperature sensors. Convection and radiation effects are expressed as a combined heat flux per surface, resulting in multiple temperature-dependent film coefficient functions. These functions are approximated by a polynomial function or splines, to generate identifiable parameters. A formulated reduced order system description preserves these parameters to perform an identification. Experiments are conducted with a test-bench to verify identification results with radiation, natural and forced convection. Findings The generated model can approximate a nonlinear transient finite element analysis (FEA) simulation with a maximum deviation of 0.3 K. For the simulation of a 500 min cyclic cooling and heating process, FEA takes a computation time of up to 13 h whereas the reduced model takes only 7-11 s, using time steps of 2 s. These low computation times allow for an identification, which is verified with an error below 3 K. When film coefficient estimation from literature is difficult due to complex geometries or turbulent air flows, identification is a promising approach to still achieve accurate results. Originality/value A well parametrized model can be further used for model-based control approaches or in observer structures. To the knowledge of the authors, no other methodology enables model-based identification of thermal parameters by physically preserving them through model order reduction and therefore derive it from a FEA description. This method can be applied to much more complex geometries and has been used in an industrial environment to increase product quality, due to accurate monitoring of cooling processes.

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