Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Behavior of Orthotropic Composite Plate Due to Random Poisson's Ratio

직교이방성 복합적층구조의 거동: 포아송비의 임의성에 의한 영향

  • 노혁천 (세종대학교 토목환경공학과)
  • Received : 2009.09.30
  • Accepted : 2009.11.11
  • Published : 2009.12.30
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Abstract

Composite materials have been employed in the various engineering applications due to high mechanical performances including high strength-weight ratio and high degree of free formability. Due to complex manufacturing process, however, it can have intrinsic randomness in the material constants which affect the deterministic behavior of the composite structures. In this study, we suggest a formulation for stochastic finite element analysis considering the spatial randomness of Poisson's ratio. Considering the reciprocal relation between elastic moduli and Poisson's ratios in the two mutually orthogonal axes, one of two values of Poisson's ratio can be expressed in terms of the other. Using this, the relation between stress resultants and strains is derived in the ascending order of power of the stochastic field function, which can be directly used in the formulation to obtain the coefficient of variation of responses. The adequacy of the proposed scheme is demonstrated by comparison with the results of Monte Carlo analysis.

복합재료는 재료적, 역학적으로 뛰어난 특성을 가진 재료로서 엔지니어링분야의 많은 부분에 적용되고 있다. 특히 무게 대비 강성비가 높은 특성을 가지고 있으며 다양한 형상에 대한 성형성도 뛰어나다. 그러나 재료의 특성상 두 가지 재료를 조합하여 제작하는 복잡한 과정은 재료상수에 높은 임의성을 야기할 가능성이 있다. 본 연구에서는 재료상수 중 포아송비의 공간적 임의성을 고려한 추계론적 유한요소해석 정식화를 제시한다. 직교이방성 복합적층구조의 두 재료축에 대한 상호관계를 적용하여 두 재료축방향의 포아송비를 하나의 대표값으로 나타내었고, 이를 합력-변형률관계에 적용하였다. 이를 통하여 합력-변형률관계를 포아송비의 변동항의 수학적 표현인 추계장함수의 차수에 따라 분해된 형태로 유도하였고, 이를 정식화에 적용하여 응답분산계수를 제시하였다. 제시한 응답분산계수는 몬테카를로 해석의 결과와 비교하였다.

Keywords

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