# Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIDeformation Problem for Glued Elastic Bodies and an Alternative Iteration Method

Mathematical Analysis of Continuum Mechanics and Industrial Applications III: Deformation Problem... [We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it is nothing but an alternating minimizing method of the total energy. The convergence to a monolithic formulation and the alternating iteration method are numerically studied with the finite element method.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Mathematical Analysis of Continuum Mechanics and Industrial Applications IIIDeformation Problem for Glued Elastic Bodies and an Alternative Iteration Method

Part of the Mathematics for Industry Book Series (volume 34)
Editors: Itou, Hiromichi; Hirano, Shiro; Kimura, Masato; Kovtunenko, Victor A.; Khludnev, Alexandr M.
13 pages

/lp/springer-journals/mathematical-analysis-of-continuum-mechanics-and-industrial-KgQ37BEl0r
Publisher
Springer Singapore
© Springer Nature Singapore Pte Ltd. 2020
ISBN
978-981-15-6061-3
Pages
81 –94
DOI
10.1007/978-981-15-6062-0_6
Publisher site
See Chapter on Publisher Site

### Abstract

[We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it is nothing but an alternating minimizing method of the total energy. The convergence to a monolithic formulation and the alternating iteration method are numerically studied with the finite element method.]

Published: Aug 30, 2020

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