scholarly journals Deformation Analysis of the Glass Preform in the Progress of Precision Glass Molding for Fabricating Chalcogenide Glass Diffractive Optics with the Finite Element Method

Micromachines ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1543
Author(s):  
Yue Liu ◽  
Yintian Xing ◽  
Hang Fu ◽  
Chuang Li ◽  
Chao Yang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Surface Profile ◽  
Deformation Analysis ◽  
Deformation Model ◽  
Machining Parameters ◽  
The Finite Element Method ◽  
Glass Molding ◽  
Precision Glass Molding ◽  
Element Method

Precision glass molding (PGM) technology is a cost-efficient process for the production of micro/nanostructured glass components with complex surface geometries. The stress distribution, surface profile, and reduced refractive index of the molded lens are based on the lens being fully formed. The process of the deformation of the glass preform is rarely discussed, especially in the case of multi-machining parameters in the experiment. The finite element method (FEM) was adopted to analyze the glass preform deformation. Due to the phenomenon of incomplete deformation of the glass preforms in the experiments, two groups of finite element simulations with different boundary conditions were carried out with MSC.Marc software, to reveal the relationship between the deformation progress and the parameters settings. Based on the simulation results, a glass preform deformation model was established. The error between the model result and the simulation result was less than 0.16. The establishment method of the glass preform deformation model and the established model can be used as a reference in efficiently optimizing PGM processing parameters when the designed lens has two different base radii of curvature.

The Finite-Element Method—Part I

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Plane Elasticity ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular elements to the St. Venant torsion problem and proceeded to formulate the problem using the principle of minimum potential energy. Similar ideas were used later by several investigators to obtain the approximate solutions to certain boundary-value problems. It was Clough who first introduced the term “finite elements” in the study of plane elasticity problems. The equivalence of this method with the well-known Ritz method was established at a later date, which made it possible to extend the applications to a broad spectrum of problems for which a variational formulation is possible. Since then numerous studies have been reported on the theory and applications of the finite-element method. In this and next chapters the finite-element formulations necessary for the deformation analysis of metal-forming processes are presented. For hot forming processes, heat transfer analysis should also be carried out as well as deformation analysis. Discretization for temperature calculations and coupling of heat transfer and deformation are discussed in Chap. 12. More detailed descriptions of the method in general and the solution techniques can be found in References [3-5], in addition to the books on the finite-element method listed in Chap. 1. The path to the solution of a problem formulated in finite-element form is described in Chap. 1 (Section 1.2). Discretization of a problem consists of the following steps: (1) describing the element, (2) setting up the element equation, and (3) assembling the element equations. Numerical analysis techniques are then applied for obtaining the solution of the global equations. The basis of the element equations and the assembling into global equations is derived in Chap. 5. The solution satisfying eq. (5.20) is obtained from the admissible velocity fields that are constructed by introducing the shape function in such a way that a continuous velocity field over each element can be denned uniquely in terms of velocities of associated nodal points.

An Application of Finite-Element Method To The Deformation Analysis of Coated Plain-Weave Fabrics

1982 ◽  
Vol 11 (4) ◽  
pp. 310-327
Author(s):  
H. Irokazu ◽  
M. Inami ◽  
Yoshio Nakahara
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Uniaxial Stress ◽  
Deformation Analysis ◽  
Strength Analysis ◽  
The Finite Element Method ◽  
Membrane Structures ◽  
Plain Weave ◽  
Weave Fabric ◽  
Element Method

Methods for analysing coated plain-weave fabric which has properties of nonlinear elasticity have not yet been satisfactorily developed. In this paper, a method which is promis ing for use in engineering applications like the strength analysis of membrane structures is presented. The finite element method using a rectangular element consisting of plain-weave fabric and coating material which is assumed to be an isotropic elastic plate of plane stress is applied to the method. Verification of the me thod is made by using uniaxial stress-strain responses. A square piece of coated plain-weave fabric with a square hole in it is analyzed as an example of application of the present method. Key Words: coated plain-weave fabrics; finite element method; nonlinearly elastic biaxial response; geometrically nonlinear prob lem ; incremental approach.

SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS

2010 ◽  
Vol 07 (03) ◽  
pp. 513-524 ◽  
Author(s):  
S. J. LIU ◽  
H. WANG ◽  
H. ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Large Deformations ◽  
Meshfree Methods ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
First Time ◽  
Element Method

The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

scholarly journals Thermal Deformation Analysis of Cutting Tools by the Finite Element Method

1975 ◽  
Vol 41 (485) ◽  
pp. 512-519 ◽  
Author(s):  
Toshihiko AKIYAMA ◽  
Hisashi KAKUCHI ◽  
Tateshi KISHINAMI ◽  
Katsumasa SAITO
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Deformation ◽  
Cutting Tools ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method
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