Основные понятия
Analysis of Koiter's model for elliptic membrane shells using the penalty method.
Аннотация
The content discusses the numerical approximation of Koiter's model for linearly elastic elliptic membrane shells using the Finite Element Method. It covers the obstacle problem, variational inequalities, and the penalty method for approximating the solution. The paper presents theoretical results, formulations, and numerical experiments to validate the mathematical findings.
- Introduction to Koiter's model for elliptic membrane shells.
- Background and notation in differential geometry.
- Formulation of an obstacle problem for linearly elastic shells.
- Classical formulation of Koiter's model for elliptic membrane shells.
- Approximation of the solution using the penalty method.
- Augmentation of regularity and mixed variational formulation.
- Numerical approximation of the solution via the Finite Element Method.
- Numerical simulations and conclusions.
Статистика
"The operator β is monotone, bounded, and non-expansive." (연산자 β는 단조, 유계이며 확장되지 않는다.)
"The Lipschitz constant for the operator β is L = 1." (연산자 β의 리프시츠 상수는 L = 1이다.)
Цитаты
"The penalised version of Problem Pε K(ω) is formulated as follows." (문제 Pε K(ω)의 패널라이즈 버전은 다음과 같이 제시된다.)