Thermal Stresses in a Bimaterial Axisymmetric Disk-Approximate and Exact Solutions

복합 재료로 구성된 축대칭 원판에서의 열응력

  • 정철섭 (건양대학교 기계공학과) ;
  • 김기석 (한국원자력연구소 기계설계부)
  • Published : 1995.03.01

Abstract

It is well known that structures constructed by bonding two or more materials and then subjected to temperature change experience thermal stress. This stress results from thermal expansion mismatch of materials. The present paper derives formulas for the stresses in a bimaterial axisymmetric disk which is subjected to a uniform temperature change. First, an approximate solution following strength-of-materials principles is developed. However, the strength-of-materials solution has difficulty in predicting both the peak value of interfacial stresses and its associated distribution. Next, a solution consistent with the theory of elasticity is developed by way of an eigenfunction expansion approach. The eigenfunction analysis is compared with finite element stress analysis results for a specific numerical example. Finite element analysis results show that the interfacial stresses are adequately predicted by eigenfunction solution. Therefore, the method developed in this paper will be useful in determination of the interfacial stress state.

2가지 이상의 재질로 결합된 구조물이 온도 변화를 받으면 열응력이 발생한다. 이러한 응력은 재질간의 열팽창계수가 서로 상이하여 생긴다. 본 논문에서는 균일한 온도변화를 받는 복합 재료로 이루어진 축대칭 원판(disk)에 대한 응력상태를 구하는 공식을 유도하였다. 먼저, 재료역학원리를 이용하여 근사해를 구한 후, Eigenfunction series를 전개하여 탄성학적인 정확해(Exact Solution)를 구하였다. 또한 정확해는 유한요소법으로 구한 해와 비교하였다. 상기 근사해로는 연계면에서의 응력분포를 예측하는 데 어려움이 있었으나, 정확해는 유한요소법으로 구한 결과와 대체로 일치하고 있어 응력분포를 충분히 예측할 수 있었다. 따라서, 본 논문에서 구한 정확해(Exact Solution) 공식은 복합재료로 구성된 구조물의 연계면에서의 응력분포를 결정하는 데 유용하다.

Keywords

References

  1. Interantional Journal of Solids and Structures v.6 On the Problem of Edge Bonded Elastic Quater-Planes Loaded at the Boundary Bogy,D.B.
  2. Complex Variables and Applications(4th Ed.) Churchill,R.V.;Brown,J.W.
  3. Journal of Composite Materials v.3 The End Problem for a Laminated Elastic Strip-Ⅱ, Differential Expansion Stresses Hess,M.S.
  4. A Treatise on the Mathematical Theory of Elasticity(4th ed.) Love,A.E.H.
  5. Journal of Applied Mechanics, Trans. v.53 Stresses in Bi-Metal Thermostats Suhir,E.
  6. Journal of Applied Mechanics v.55 An Approximate Analysis of Stresses in Multilayeres Elastic Thin Films Suhir,E.
  7. Journal of Applied Mechanics v.56 no.3 Interfacial Stresses in Bimetal Thermostats Suhir,E.
  8. Journal of the Optical Society of America v.11 Analysis of Bi-Metal Thermostats Timoshenko,S.
  9. Theory of Plates and Shells Timoshenko,S.P.
  10. Theory of Elasticity(3rd Ed.) Timoshenko;Goodier
  11. Journal of Applied Physics v.53 no.3 Simple Stress Formula for Multilayered Thin Films on a Thick Substrate Vilms,J.;Kerps,D.