Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Volume Integral Equation Method for Multiple Isotropic Inclusion Problems in an Infinite Solid Under Uniaxial Tension

인장 하중을 받는 무한 고체에 포함된 다수의 등방성 함유체 문제 해석을 위한 체적 적분방정식법

  • Lee, Jung-Ki (Dept. of Mechanical and Design Engineering, Hongik Univ.)
  • 이정기 (홍익대학교 기계정보공학과)
  • Received : 2010.02.08
  • Accepted : 2010.06.08
  • Published : 2010.07.01
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Abstract

A volume integral equation method (VIEM) is introduced for solving the elastostatic problems related to an unbounded isotropic elastic solid; this solid is subjected to remote uniaxial tension, and it contains multiple interacting isotropic inclusions. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out; square and hexagonal packing of the inclusions are considered. The effects of the number of isotropic inclusions and different fiber volume fractions 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 clarified by comparing the results obtained by analytical and finite element methods. The VIEM is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic fibers.

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

Keywords

References

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