scholarly journals Analysis of strain energy and relaxation degree in different-shaped quantum dots using finite element method

2009 ◽  
Vol 58 (8) ◽  
pp. 5618
Author(s):  
Wang Tian-Qi ◽  
Yu Zhong-Yuan ◽  
Liu Yu-Min ◽  
Lu Peng-Fei
Keyword(s):  
Finite Element Method ◽  
Quantum Dots ◽  
Finite Element ◽  
Strain Energy ◽  
Element Method

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

The Strain Energy Tuning of the Shape Memory Alloy on the Post-Buckling of Composite Plates Using Finite Element Method

2012 ◽  
Vol 445 ◽  
pp. 577-582
Author(s):  
Zainudin A. Rasid ◽  
Saiful Amri Mazlan ◽  
Amran Ayob ◽  
Rizal Zahari ◽  
Dayang Laila Majid ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Strain Energy ◽  
Composite Plates ◽  
Post Buckling ◽  
Energy Tuning ◽  
Element Method

scholarly journals A HYBRID SMOOTHED FINITE ELEMENT METHOD (H-SFEM) TO SOLID MECHANICS PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340011 ◽  
Author(s):  
XU XU ◽  
YUANTONG GU ◽  
GUIRONG LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Solid Mechanics ◽  
Weighted Average ◽  
Accurate Solution ◽  
Numerical Studies ◽  
Smoothed Finite Element Method ◽  
Theoretical Results ◽  
Element Method

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter α is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper- and lower-bound solutions can always be obtained by adjusting α; (2) there exists a preferable α at which the H-SFEM can produce the ultrasonic accurate solution.

scholarly journals Development and Optimization for a New Planar Spring Using Finite Element Method, Deep Feedforward Neural Networks, and Water Cycle Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Ngoc Le Chau ◽  
Hieu Giang Le ◽  
Van Anh Dang ◽  
Thanh-Phong Dao
Keyword(s):  
Neural Network ◽  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Water Cycle ◽  
Feedforward Neural Network ◽  
The Finite Element Method ◽  
Water Cycle Algorithm ◽  
Balance Mechanism ◽  
Element Method

The gravity balance mechanism plays a vital role in maintaining the equilibrium for robots and assistive devices. The purpose of this paper was to optimize the geometry of a planar spring, which is an essential element of the gravity balance mechanism. To implement the optimization process, a hybrid method is proposed by combining the finite element method, the deep feedforward neural network, and the water cycle algorithm. Firstly, datasets are collected using the finite element method with a full experiment design. Secondly, the output datasets are normalized to eliminate the effects of the difference of units. Thirdly, the deep feedforward neural network is then employed to build the approximate models for the strain energy, deformation, and stress of the planar spring. Finally, the water cycle algorithm is used to optimize the dimensions of the planar spring. The results found that the optimal geometries of the spring include the length of 45 mm, the thickness of 1.029 mm, the width of 9 mm, and the radius of 0.3 mm. Besides, the predicted results determined that the strain energy, the deformation, and the stress are 0.01123 mJ, 33.666 mm, and 79.050 MPa, respectively. The errors between the predicted result and the verifying results for the strain energy, the deformation, and the stress are about 1.87%, 1.69%, and 3.06%, respectively.

scholarly journals About applying directly the alpha finite element method (\(\alpha\)FEM) for solid mechanics using triangular and tetrahedral elements

2010 ◽  
Vol 32 (4) ◽  
pp. 235-246 ◽  
Author(s):  
Nguyen Thoi Trung ◽  
Nguyen Xuan Hung
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Strain Energy ◽  
Solid Mechanics ◽  
Computational Cost ◽  
Quasi Equilibrium ◽  
Tetrahedral Elements ◽  
Factor Alpha ◽  
Element Method

An alpha finite element method (\(\alpha\)FEM) has been recently proposed to compute nearly exact solution in strain energy for solid mechanics problems using three-node triangular (\(\alpha\)FEM-T3) and four-node tetrahedral (\(\alpha\)FEM-T4) elements. In the \(\alpha\)FEM, a scale factor \(\alpha \in [0, 1]\) is used to combine the standard fully compatible model of the FEM with a quasi-equilibrium model of the node-based smoothed FEM (NS-FEM). This novel combination of the FEM and NS-FEM makes the best use of the upper bound property of the NS-FEM and the lower bound property of the standard FEM. This paper concentrates on applying directly the \(\alpha\)FEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using \(\alpha = 0.6\) for 2D problems and \(\alpha = 0.7\) for 3D problems.

A Novel Alpha Smoothed Finite Element Method for Ultra-Accurate Solution Using Quadrilateral Elements

2019 ◽  
Vol 17 (02) ◽  
pp. 1845008 ◽  
Author(s):  
Y. H. Li ◽  
M. Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Solid Mechanics ◽  
Strain Energy Function ◽  
Accurate Solution ◽  
Scale Factor ◽  
Quadrilateral Elements ◽  
Smoothed Finite Element Method ◽  
Element Method

Smoothed finite element method (S-FEM) based on triangular elements has recently been widely used for solving solid mechanics problems. In this paper, a novel [Formula: see text]S-FEM using quadrilateral elements ([Formula: see text]SFEM-Q4) is proposed to obtain ultra-accurate solutions in the displacement and strain energy for solid mechanics problems. This method combines node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM) and cell-based S-FEM (CS-FEM) equipped with a scale factor [Formula: see text] that controls contribution from each of these three different S-FEM models. This novel combination makes the best use of the upper bound property of the NS-FEM and the lower bound property of the CS-FEM (with 4 or more sub-smoothing domains for each element), and establishes a continuous strain-energy function of a scale factor [Formula: see text] for obtaining close-to-exact solutions. Our [Formula: see text]SFEM-Q4 also ensures the variational consistence and the compatibility of the displacement field, and hence guarantees to reproduce linear field exactly. Various solid mechanics problems are presented to validate the stability, effectiveness and ultra-accuracy of the proposed method.

An ABAQUS Implementation of the Cell-Based Smoothed Finite Element Method (CS-FEM)

2019 ◽  
Vol 17 (02) ◽  
pp. 1850127 ◽  
Author(s):  
X. Cui ◽  
X. Han ◽  
S. Y. Duan ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Software Package ◽  
Strain Energy ◽  
Computational Accuracy ◽  
Mesh Distortion ◽  
Processing Program ◽  
Smoothed Finite Element Method ◽  
Solution Accuracy ◽  
Element Method

The smoothed finite element method (S-FEM) has been developed recent years and is increasingly used for stress analysis for engineering design of structures, due to its high computational accuracy and outstanding robustness in against mesh distortion. However, there is currently no commercial S-FEM software package available for convenient engineering applications. This paper aims to integrate S-FEM into the [Formula: see text] software, because it is most widely used in engineering analyses and well integrated in computer aided engineering (CAE). From a family of S-FEM models, the cell-based finite element method (CS-FEM) is chosen to be implemented in ABAQUS, because a smoothing cell in the CS-FEM involves only one element, and hence the implementation can be achieved via the use of the user-defined element library (UEL). Since only nodal displacement results can be extracted when UEL subroutine is used in ABAQUS, a post-processing program is also developed to compute nodal strains/stresses and strain energy results that are useful in structure analysis and CAE. Our CS-FEM UEL is validated using four numerical examples under plane stress conditions. Compared with standard ABAQUS, the CS-FEM in ABAQUS improves the solution accuracy remarkably, and we have also confirmed the robustness of CS-FEM against heavily distorted meshes.

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