Stress concentration and neutral inclusion of multilayer structure = 다층구조의 내포에 의한 응력집중과 중립물질 연구

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This thesis is devoted to analyze the conductivity problem in the presense of an inclusion with multilayer structure. In the first part, we analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. When the core and shell have circular boundaries that are nearly touching, the gradient of the solution can be arbitrary large in the narrow gap when the conductivities degenerate to zero or infinity. We derive an asymptotic formula for the solution in terms of the single and double layer potentials with image line charges. In the second part, we introduce the new concept of the geometric multipole expansion for the two-dimensional conductivity problem of which basis functions are associated with the inclusion's geometry. As an application, we construct multi-coated neutral inclusions of general smooth shape that have negligible perturbation for low-order polynomial loadings. We also suggest a new method to reconstruct the shape of inclusion.
Advisors
Lim, Mikyoungresearcher임미경researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2019
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2019.2,[iv, 58 p. :]

Keywords

Gradient blow-up▼aconductivity equation▼abipolar coordinates▼ageometric multipolar expansion▼aneutral inclusion▼ashape reconstruction; 경도함수 발산▼a전도도 방정식▼a양극좌표계▼a코어-셸 구조▼a중립물질▼a모양 재구성

URI
http://hdl.handle.net/10203/264945
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=842149&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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