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타원 섬유가 포함된 복합재료에서의 탄성 해석

Elastic Analysis in Composite Including Multiple Elliptical Fibers

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한국복합재료학회 (The Korean Society For Composite Materials)|2011.12|Composites Research|제24권 제6호|pp. 37-48

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키워드

Composite Materials유한요소법Finite Element Method복합 재료Fiber Volume Fraction체적 적분방정식법섬유 체적분율Volume Integral Equation Method타원 함유체Elliptical Inclusion
주제분류재료공학

초록

체적 적분방정식법(Volume Integral Equation Method)이라는 새로운 수치해석 방법을 이용하여, 서로 상호작용을 하는 등방성 또는 이방성 타원 함유체를 포함하는 등방성 무한고체가 정적 인장하중을 받을 때 무한고체 내부에 발생하는 응력분포 해석을 매우 효과적으로 수행하였다. 즉, 등방성 기지에 다수의 등방성 또는 이방성 타원 함유체의 중심이 1) 정사각형 배열 형태 또는 2) 정육각형 배열 형태로 포함되어 있는 경우에, 다양한 타원을 포함하는 원형 실린더 함유체의 체적비에 대하여, 중앙에 위치한 타원 함유체와 등방성 기지의 경계면에서의 인장응력 분포의 변화를 구체적으로 조사하였다. 또한, 체적 적분 방정식법을 이용한 해를 유한요소법을 이용한 해 및 해석해와 비교해 봄으로서, 체적 적분방정식법을 이용하여 구한 해의 정확도를 검증하였다.

Abstract

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solids containing interacting multiple isotropic or anisotropic elliptical inclusions subject to remote uniaxial tension. The method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of the inclusions. Effects of the number of isotropic or anisotropic elliptical inclusions and various fiber volume fractions for the circular inclusion circumscribing its respective elliptical inclusion on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and finite element methods. The method is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic or anisotropic elliptical fibers.

참고문헌 (37)

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