Iterative solution of isoparametric spectral element equations by low-order finite element preconditioning

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

Download Full-text

Self-updated four-node finite element using deep learning

Computational Mechanics ◽

10.1007/s00466-021-02081-7 ◽

2021 ◽

Author(s):

Jaeho Jung ◽

Hyungmin Jun ◽

Phill-Seung Lee

Keyword(s):

Finite Element ◽

Deep Learning ◽

Iterative Solution ◽

Solution Procedure ◽

Element Formulation ◽

Zero Energy ◽

Energy Mode ◽

Bending Modes ◽

Solution Accuracy ◽

Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

Download Full-text

Aero-Engine Blade Deformation Control of Milling Process

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.308-310.1198 ◽

2011 ◽

Vol 308-310 ◽

pp. 1198-1204

Author(s):

Hui Xian Chen ◽

Hao Li ◽

Hai Tao Feng ◽

Min Juan Du

Keyword(s):

Finite Element ◽

Finite Element Simulation ◽

Error Compensation ◽

Leaf Blade ◽

Tool Path ◽

Iterative Solution ◽

Helical Milling ◽

Machining Accuracy ◽

Element Simulation ◽

Compensation Plan

The leaf blade manufacture precision's influencing factors are numerous, and they have coupling relationship each other. So it is difficult to peel out a single factor on the influencing regularity of the blade's machining accuracy. By researching the engine blades of helical milling state under the existing fixture, the leaf blade deformable model based on the instantaneous milling strength was established. Meanwhile, the off-line multi-level error compensation plan was proposed based on the processing surface static error forecasts and compensation. In order to revise the primitive NC tool path code and eliminate the processing distortion inaccuracy, the elastic deformity on each knife position spot is solved on the basis of iterative solution, using the finite element simulation and milling strength model. By using ANSYS finite element simulation, it receives the real-time error compensation of the tool path. And then The experiment has proven the accuracy and the usability of the compensation plan.

Download Full-text

Time domain spectral element-based wave finite element method for periodic structures

Acta Mechanica ◽

10.1007/s00707-020-02917-y ◽

2021 ◽

Author(s):

Shuvajit Mukherjee ◽

S. Gopalakrishnan ◽

Ranjan Ganguli

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Time Domain ◽

Periodic Structures ◽

Spectral Element ◽

Element Method

Download Full-text

Model calculations in reconstructions of measured fields

Open Physics ◽

10.2478/bf02475556 ◽

2003 ◽

Vol 1 (1) ◽

Cited By ~ 1

Author(s):

Mihály Makai ◽

Yuri Orechwa

Keyword(s):

Mathematical Model ◽

Finite Element Method ◽

Finite Element ◽

Group Theory ◽

Point Group ◽

Iterative Solution ◽

The Finite Element Method ◽

Technological Systems ◽

Convergence Problem ◽

Model Calculations

AbstractThe state of technological systems, such as reactions in a confined volume, are usually monitored with sensors within as well as outside the volume. To achieve the level of precision required by regulators, these data often need to be supplemented with the solution to a mathematical model of the process. The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rule problems. We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.

Download Full-text