Shape optimization analysis for thermal elastic deformation problems in three dimensions based on the adjoint variable and the finite element methods

2021 ◽  
Vol 2021.58 (0) ◽  
pp. E024
Author(s):  
Satoshi HIROSE ◽  
Takahiko KURAHASHI ◽  
Eiji KATAMINE
Keyword(s):  
Finite Element ◽  
Shape Optimization ◽  
Elastic Deformation ◽  
Finite Element Methods ◽  
Three Dimensions ◽  
Adjoint Variable ◽  
Optimization Analysis

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

Two low-order nonconforming finite element methods for the Stokes flow in three dimensions

2018 ◽  
Vol 39 (3) ◽  
pp. 1447-1470 ◽  
Author(s):  
Jun Hu ◽  
Mira Schedensack
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stokes Flow ◽  
Three Dimensions ◽  
Nonconforming Finite Element ◽  
Discrete Problem ◽  
Piecewise Affine ◽  
Korn Inequality ◽  
Nonconforming Finite Element Methods ◽  
Low Order

Abstract In this paper, we propose two low-order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the nonconforming FEM of Kouhia & Stenberg (1995, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Eng, 124, 195–212). The finite element spaces proposed in this paper consist of two globally continuous components (one piecewise affine and one enriched component) and one component that is continuous at the midpoints of interior faces. We prove that the discrete Korn inequality and a discrete inf–sup condition hold uniformly in the mesh size and also for a nonempty Neumann boundary. Based on these two results, we show the well-posedness of the discrete problem. Two counterexamples prove that there is no direct generalization of the Kouhia–Stenberg FEM to three space dimensions: the finite element space with one nonconforming and two conforming piecewise affine components does not satisfy a discrete inf–sup condition with piecewise constant pressure approximations, while finite element functions with two nonconforming and one conforming component do not satisfy a discrete Korn inequality.

scholarly journals Finite element methods for fractional PDEs in three dimensions

2020 ◽  
Vol 100 ◽  
pp. 106041 ◽  
Author(s):  
Zongze Yang ◽  
Yufeng Nie ◽  
Zhanbin Yuan ◽  
Jungang Wang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Three Dimensions ◽  
Fractional Pdes
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