Thermal Deformation Analysis of Electronic Device using Finite Element Method and Moire Interferometry

2002 ◽  
Vol 2002.15 (0) ◽  
pp. 333-334
Author(s):  
Mitsugu TODO ◽  
Yasuyuki MORITA ◽  
Kazuo ARAKAWA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Deformation ◽  
Electronic Device ◽  
Moiré Interferometry ◽  
Deformation Analysis ◽  
Moire Interferometry ◽  
Element Method

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

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.

Deformation analysis for cold rolling of Al-Cu double layered sheet by physical modeling and finite element method

2013 ◽  
Vol 19 (5) ◽  
pp. 1069-1076 ◽  
Author(s):  
C. H. Jeon ◽  
S. W. Han ◽  
B. D. Joo ◽  
C. J. Van Tyne ◽  
Y. H. Moon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cold Rolling ◽  
Physical Modeling ◽  
Deformation Analysis ◽  
Element Method
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