scholarly journals Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Wolfgang Witteveen ◽  
Florian Pichler
Keyword(s):  
Finite Element ◽  
Model Order Reduction ◽  
Mechanical Response ◽  
Order Reduction ◽  
Contact Forces ◽  
Computational Time ◽  
Present Contribution ◽  
Model Order ◽  
Friction Forces ◽  
Trial Vector

The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.

Efficient Virtual Tribomechadynamics by Means of Joint Modes for Detailed Investigation of Complex Local Stick and Slip Behavior Inside a Joint

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Florian Pichler ◽  
Wolgang Witteveen ◽  
Lukas Koller
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Global Dynamics ◽  
Model Order ◽  
Friction Forces ◽  
Generic Structure ◽  
Trial Vector ◽  
Element Method

Abstract In the last years, the numerical and experimental research effort on joint nonlinearities and tribomechadynamics has increased. Thereby, local sticking and slipping effects as well as the influence of friction caused damping on the global dynamics are of interest. Conventional computational approaches like model order reduction techniques or the finite element method lead either to insufficient result quality or a high computational burden. For the efficient numerical consideration of jointed structures in combination with model order reduction, joint modes based on trial vector derivatives have been presented. These joint modes enable accurate computation of local nonlinear contact and friction forces together with efficient time integration even for high fidelity finite element models. This article describes the application of joint modes for efficient virtual tribomechadynamics. Therefore, a generic structure including a bolted joint is used. It is investigated if these joint modes reproduce local friction stress, and sticking/slipping areas comparable to the nonlinear finite element method within reasonable computational times. Moreover, global damping effects are studied at different preload levels and related to local sticking/slipping behavior. The numerical studies confirm that joint modes lead to accurate results with low computation effort and hence allow an efficient and detailed virtual investigation of complex joints. In addition, this publication shows that the consideration of tangential stiffness for the computation of joint modes remarkably increases the local result quality.

An Exact and General Model Order Reduction Technique for the Finite Element Solution of Elastohydrodynamic Lubrication Problems

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
W. Habchi ◽  
J. S. Issa
Keyword(s):  
Finite Element ◽  
General Model ◽  
Model Order Reduction ◽  
Elastohydrodynamic Lubrication ◽  
Order Reduction ◽  
Reduction Technique ◽  
Operating Conditions ◽  
Computational Time ◽  
Splitting Algorithm ◽  
Model Order

This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature.

Model Order Reduction of Visco-Thermal Acousto-Elastic Interaction in High-Pressure Centrifugal Compressors

2015 ◽  
Author(s):  
Jithin Jith ◽  
Sunetra Sarkar
Keyword(s):  
Finite Element ◽  
Supercritical Co2 ◽  
Model Order Reduction ◽  
Computational Cost ◽  
Order Reduction ◽  
Elastic Interaction ◽  
Computational Time ◽  
Centrifugal Impeller ◽  
Centrifugal Compressors ◽  
Model Order

Centrifugal compressors used in applications like enhanced oil recovery using gas re-injection and Carbon capture and sequestration operate at very high pressures and often have to to deal with supercritical CO2 which is considerably viscous. Increased viscosity leads to energy dissipation and introduces damping in the acousto-elastic interaction between supercritical CO2 and the impeller of a centrifugal compressor, thereby altering the frequency response of the system especially near resonant frequencies. In this paper, the damping introduced by visco-thermal effects in such acousto-elastic systems is accounted for in a numerically efficient manner. The acoustics in the fluid are modelled using the Boundary Layer Impedance (BLI) model and the centrifugal impeller as a linear elastic structure. The coupled acousto-elastic system is then solved using the finite element method. The finite element solution becomes computationally expensive especially when working with large three-dimensional models. In order to reduce the computational cost, a model order reduction technique based on a multi-point second-order Arnoldi (SOAR) procedure is developed. It is demonstrated that the reduced order model significantly brings down the computational time while being sufficiently accurate.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

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