A Variational Numerical Method of Linear Elasticity through the Extended Framework of Hamilton's Principle

김 진규; Kim Jinkyu

doi:10.7734/COSEIK.2014.27.1.37

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2014 Vol.27, Issue 1 Preview Page Next Page

A Variational Numerical Method of Linear Elasticity through the Extended Framework of Hamilton's Principle

2014. pp. 37-43

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Abstract

동역학의 새로운 변분이론인 확장 해밀턴 이론은 수학물리학을 비롯한 공학에 있어 초기치-경계치 문제해석에 광범위하게 적용될수 있는 기반을 제공하는 것으로 본 논문에서는 이 이론을 기반으로 선형탄성 단자유도계에 적용한 새로운 수치해석법을 제안하였다. 곧, 변분이론의 특성을 감안해, 전체 time-step에 대한 수치해를 한번에 산정하는 해석법을 제안하였고, 주요 예제를 통해 이 해석법의 특성을 살펴보았다. 에너지 보존 시스템의 경우(비감쇠 시스템에 외력이 작용치 않는 경우), time-step에 관계없이 에너지와 모멘텀이 보존되는 symplecticity property를 가지고 있음을 확인할 수 있었고, 감쇠 시스템인 경우, time-step이 점점 작아질수록 정확한 해에 빠르게 수렴하는 것을 확인하였다.

키워드

Hamilton's principle, mixed variational formulation, numerical method, linear elasticity

해밀턴 이론, 혼합변분이론, 수치해석법, 선형탄성

The extended framework of Hamilton's principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation. Based upon such framework, a new variational numerical method of linear elasticity is provided for the classical single-degree-of-freedom dynamical systems. For the undamped system, the algorithm is symplectic with respect to the time step. For the damped system, it is shown to be accurate with good convergence characteristics.

키워드

Hamilton's principle, mixed variational formulation, numerical method, linear elasticity

해밀턴 이론, 혼합변분이론, 수치해석법, 선형탄성

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Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 27
No :1
Pages :37-43
Received Date : 2014-01-22
Revised Date : 2014-01-28
Accepted Date : 2014-01-29
DOI :https://doi.org/10.7734/COSEIK.2014.27.1.37

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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