2차원 다층 반무한해를 이용한 지하구조계의 동적 경계요소 해석

Dynamic Boundary Element Analysis of Underground Structures Using Multi-Layered Half-Plane Fundamental Solutions

  • 발행 : 1997.12.01

초록

터널 등과 같은 지하구조계를 유한요소법 등의 수치적 방법으로 해석할 경우 인위적인 경제에서 파의 반사가 발생하게 되어 실제 결과의 큰 차이를 발생시킨다. 따라서 동역학적 하중을 받는 지하구조계는 실질적인 반무한 구조계로 고려되어야 한다. 특히 지하구조계는 실제 다층구조로 구성되어 있으므로 이러한 다층문제를 고려할 수 있어야 한다. 이를 위해 본 연구에서는 외부영역 경제적문제로 해석하기 위한 동적 수치기본해를 개발하였다. 주파수영역의 정적인 경우에 대한 엄밀 적분해와 Bessel 함수의 점근식을 이용한 적분을 통해 축대치문제를 2차원 문제로 보다 쉽게 적용할 수 있도록 하였다. 이와 같이 개발된 동적 수치기본해를 경제 적분 방정식에 적용하여 해석한 결과와 기존 해석결과와의 비교를 통해 그 효율성을 입증하였다. 또한 다층지반내 지하구조물에 대해 지반매체의 각 물성 및 공동의 깊이에 따른 민감도분석을 수해하여 지하구조계의 동적 거동특성 파악의 적용성을 다루었다.

In analysis of underground structures, the effects of artificial boundary conditions are considered as one of the major reasons for differences from experimental results. These phenomena can be overcome by using the boundary elements which satisfy the multi-layered half space conditions. The fundamental solutions of multi-layered half-space for boundary element method is formulated satisfying the transmission and reflection of waves at each layer interface and radiation conditions at bottom layer. The governing equations can be obtained from the displacements at each layer which are expressed in terms of harmonic functions. All types of waves can be included using the complete response from semi-infinite integrals with respect to horizontal wavenumbers using expansion of Fourier series and Hankel transformation. Two dimensional Green's functions are derived from cylindrical Navier equations and potentials performing infinite integration in y-direction. In this case, it is effective to transform into two dimensional problem using semi-analytical integration and sinusoidal Bessel function. Some verifications are given to show the accuracy and efficiency of the developed method, and numerical examples to demonstrate the dynamic behavior of underground with various properties.

키워드

참고문헌

  1. Finite-Element Modeling of Unbounded Media Wolf, J,P.;Song, C.
  2. Engineering Analysis with Boundary Elements v.8 On the Use of BEM for Wave Propagation in Infinite Domains Dominguez, J.;Meise, T.
  3. Bulletin of the Seismological Society of America v.73 On the Green's Functions for a Layered Half-Space, Part Ⅰ Luco, J.E.;Apsel, R. J.
  4. Journal of Applied Mechanics, Trans, ASME v.30 Diffraction of Steady Elastic Waves by Surfaces of Arbitrary Shape Banaugh, R. P.;Goldsmith, W.
  5. Computation Methods in Applied Mechanics in Engineering v.36 Dynamic Response of Line Tunnels by an Isoparametric Boundary Element Method Manolis, G. D.;Beskos, D. E.
  6. Boundary Element Techniques: Theory and Application in Engineering Brebbia, C. A.;Telles, J.C.F.;Wrobel, L.C.
  7. Boundary Element Methods in Engineering Science Baberjee, P.K.;Butterfield, R.
  8. Computational Mechanics v.9 Dynamic Structure-Soil-Structure Interaction by FEM and BEM Wang, S.;Schmid, G.
  9. International Journal for Numerical Methods in Engineering v.29 Some Observation on Time Domain and Frequency Domain Boundary Elements Von Estorff, O.;Pais, A. L.;Kausel, E.
  10. Boundary Element Methods in Elastodynamics Manolis, G.D.;Beskos, D.E.
  11. Bulletin of the Seismological Society of America v.54 Surface Waves in Multilayered Elastic Media, Part Ⅰ. Rayleigh and Love Waves from Buried Sources i a Miltilayered Elastic Half-Space Harkrider, D. G.
  12. Foundations of Solid Mechanics Karasudhi, P.
  13. Seismic Wave Propagation in Stratified Media Kennet, B.L.N.
  14. Wave Propagation in Elastic Solids Achenbach, J.D.