Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Masih Mahmoodi ◽  
Kamran Behdinan
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Second Order ◽  
Computational Time ◽  
Original Structure ◽  
Fe Model ◽  
Krylov Methods ◽  
Convergence Criteria ◽  
Large Scale Systems ◽  
Reduction Techniques

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

Permafrost Thawing-Pipeline Interaction Advanced Finite Element Model

2009 ◽  
Author(s):  
Jianfeng Xu ◽  
Basel Abdalla ◽  
Ayman Eltaher ◽  
Paul Jukes
Keyword(s):  
Finite Element ◽  
Energy Demand ◽  
Large Scale ◽  
Limit State ◽  
The Arctic ◽  
Ultimate Limit State ◽  
Fe Model ◽  
Field Development ◽  
Thaw Settlement ◽  
Permafrost Thawing

The increasing energy demand has promoted the interest in exploration and field development in the Arctic waters, which holds one quarter of the world’s petroleum reserves. The harsh conditions and fragile environment in the arctic region introduce many challenges to a sustainable development of these resources. One of the key challenges is the engineering consideration of warm pipelines installed in permafrost areas; found mainly in shallow waters and shore crossings. Evaluations have to be made during the pipeline design to avoid significant thaw settlement and large-scale permafrost degrading. In this paper, a three-dimensional (3D) finite element (FE) model was developed to study the interaction between buried pipelines transporting warm hydrocarbons and the surrounding permafrost. This interaction is a combination of several mechanisms: heat transfer from the pipeline, results in permafrost thawing and formation of thaw bulb around the pipeline. Consequently, the thaw settlement of soil beneath the pipeline base results in bending strains in the pipe wall. For safe operations, the pipe should be designed so that the induced strains do not exceed the ultimate limit state conditions. The developed model helps in accurate prediction of pipe strains by using finite element continuum modeling method as opposed to the more commonly used discrete (springs) modeling and hand calculations. It also assesses the real size of the thaw bulb and the corresponding settlement at any time, thus preventing an over-conservative design.

An Efficient and Accurate Prediction of the Stability of Percutaneous Fixation of Acetabular Fractures With Finite Element Simulation

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
V. B. Shim ◽  
J. Böshme ◽  
P. Vaitl ◽  
C. Josten ◽  
I. A. Anderson
Keyword(s):  
Finite Element ◽  
Posterior Wall ◽  
Acetabular Fractures ◽  
Fe Model ◽  
Open Approach ◽  
Percutaneous Fixation ◽  
Biomechanical Stability ◽  
Posterior Wall Fracture ◽  
Interfragmentary Movement ◽  
The Stability

Posterior wall fracture is one of the most common fracture types of the acetabulum and a conventional approach is to perform open reduction and internal fixation with a plate and screws. Percutaneous screw fixations, on the other hand, have recently gained attention due to their benefits such as less exposure and minimization of blood loss. However their biomechanical stability, especially in terms interfragmentary movement, has not been investigated thoroughly. The aims of this study are twofold: (1) to measure the interfragmentary movements in the conventional open approach with plate fixations and the percutaneous screw fixations in the acetabular fractures and compare them; and (2) to develop and validate a fast and efficient way of predicting the interfragmentary movement in percutaneous fixation of posterior wall fractures of the acetabulum using a 3D finite element (FE) model of the pelvis. Our results indicate that in single fragment fractures of the posterior wall of the acetabulum, plate fixations give superior stability to screw fixations. However screw fixations also give reasonable stability as the average gap between fragment and the bone remained less than 1 mm when the maximum load was applied. Our finite element model predicted the stability of screw fixation with good accuracy. Moreover, when the screw positions were optimized, the stability predicted by our FE model was comparable to the stability obtained by plate fixations. Our study has shown that FE modeling can be useful in examining biomechanical stability of osteosynthesis and can potentially be used in surgical planning of osteosynthesis.

scholarly journals Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation

2016 ◽  
Vol 63 (4) ◽  
pp. 475-494 ◽  
Author(s):  
Thomas Volzer ◽  
Peter Eberhard
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Message Passing ◽  
Large Scale ◽  
Message Passing Interface ◽  
Block Size ◽  
Reduction Process ◽  
Element Model ◽  
Multibody Simulation ◽  
Elastic Bodies

Abstract The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a moment-matching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the block size and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.

A Meta-Modeling Procedure for Updating the Finite Element Model of an Arch Bridge Model

2013 ◽  
Vol 540 ◽  
pp. 79-86
Author(s):  
De Jun Wang ◽  
Yang Liu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Analysis ◽  
Large Scale ◽  
Model Updating ◽  
Element Model ◽  
Fe Model ◽  
Large Scale Structures ◽  
Bridge Model ◽  
Scale Structures

Finite element (FE) model updating of structures using vibration test data has received considerable attentions in recent years due to its crucial role in fields ranging from establishing a reality-consistent structural model for dynamic analysis and control, to providing baseline model for damage identification in structural health monitoring. Model updating is to correct the analytical finite element model using test data to produce a refined one that better predict the dynamic behavior of structure. However, for real complex structures, conventional updating methods is difficult to be utilized to update the FE model of structures due to the heavy computational burden for the dynamic analysis. Meta-model is an effective surrogate model for dynamic analysis of large-scale structures. An updating method based on the combination between meta-model and component mode synthesis (CMS) is proposed to improve the efficiency of model updating of large-scale structures. The effectiveness of the proposed method is then validated by updating a scaled suspender arch bridge model using the simulated data.

Numerical investigation on the stability of human upper cervical spine (C1–C3)

2021 ◽  
pp. 1-13
Author(s):  
Waseem Ur Rahman ◽  
Wei Jiang ◽  
Guohua Wang ◽  
Zhijun Li
Keyword(s):  
Finite Element ◽  
Cervical Spine ◽  
Axial Rotation ◽  
Upper Cervical Spine ◽  
Fe Model ◽  
Facet Joints ◽  
Flexion Extension ◽  
Upper Cervical ◽  
The Stability

BACKGROUND: The finite element method (FEM) is an efficient and powerful tool for studying human spine biomechanics. OBJECTIVE: In this study, a detailed asymmetric three-dimensional (3D) finite element (FE) model of the upper cervical spine was developed from the computed tomography (CT) scan data to analyze the effect of ligaments and facet joints on the stability of the upper cervical spine. METHODS: A 3D FE model was validated against data obtained from previously published works, which were performed in vitro and FE analysis of vertebrae under three types of loads, i.e. flexion/extension, axial rotation, and lateral bending. RESULTS: The results show that the range of motion of segment C1–C2 is more flexible than that of segment C2–C3. Moreover, the results from the FE model were used to compute stresses on the ligaments and facet joints of the upper cervical spine during physiological moments. CONCLUSION: The anterior longitudinal ligaments (ALL) and interspinous ligaments (ISL) are found to be the most active ligaments, and the maximum stress distribution is appear on the vertebra C3 superior facet surface under both extension and flexion moments.

Conventional and Evolutionary Order Reduction Techniques for Complex Systems

2021 ◽  
Vol 16 (4) ◽  
pp. 74-98
Author(s):  
Abha Kumari ◽  
C. B. Vishwakarma
Keyword(s):  
Large Scale ◽  
Order Reduction ◽  
Original System ◽  
Conventional Technique ◽  
Stability Equation ◽  
Padé Approximations ◽  
Time Frequency ◽  
Reduction Techniques ◽  
Pade Approximations ◽  
The Stability

Order reduction of the large-scale linear dynamic systems (LSLDSs) using stability equation technique mixed with the conventional and evolutionary techniques is presented in the paper. The reduced system (RS) is obtained by mixing the advantages of the two methods. For the conventional technique, the numerator of the RS is achieved by using the Pade approximations and improved Pade approximations, whereas the denominator is obtained by the stability equation technique (SET). For the evolutionary technique, numerator of the RS is obtained by minimizing the integral square error (ISE) between transient responses of the original and the RS using the genetic algorithm (GA), and the denominator is obtained by the stability equation method. The proposed RS retains almost all the essential properties of the original system (OS). The viability of the proposed technique is proved by comparing its time, frequency responses, time domain specifications, and ISE with the new and popular methods available in the literature.

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