p-수렴 완전층별모델에 의한 일면패치로 보강된원공 적층판의 휨효과
Bending Effect of Laminated Plates with a Circular Hole Repaired by Single-Sided Patch Based on p-Convergent Full Layerwise Model
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초록
기존에 설치되어 있는 구조물의 양면대칭 패치보강은 항상 면내거동만을 유발하나 시공상 어려움이 있다. 반면에 일면 패치보강의 경우 인장력의 증가에 따라 중립축의 위치가 대칭이 아니므로 휨에 대한 강성도가 증가하게 되며, 결과적으로 적층판의 휨을 심화시키게 된다. 이 연구에서는 일면 패치보강된 적층판의 두께방향은 물론이고 원공주위의 응력집중계수를 산정하기 위해 p-수렴 완전층별모델을 제안하였다. 가정된 변위장의 정의를 위해, 임의의 층에서 변위-변형률 관계와 3차원 구성방정식은 2차원 및 3차원 계층적 형상함수의 조합이 사용된다. 원형경계의 기하형상을 나타내기 위해 초유한사상 기법이 사용되며, 다른 외삽법을 사용하지 않고 각 층마다 절점에서의 응력값을 직접적으로 얻기위해 가우스-로바토 수치적분이 수행되었다. 제안된 모델의 정확도와 단순성은 기존의 3차원 유한요소해석과 실험에 의해 구해진 결과들과의 비교를 통해 검증되었다. 또한 정사각형, 원형, 고리형 형상의 다양한 패치보강에 따른 휨효과를 조사하였다.
Abstract
Double symmetric patch repair of existing structures always causes membrane action only, however, in many cases this technique is not practical. On the other hand, the bending stiffness of the patch and the skin increases as tensile loading is increased and affects the bending deformation significantly in the case of single-sided patch repair. In this study, the p-convergent full layerwise model has been proposed to determine the stress concentration factor in the vicinity of a circular hole as well as across the thickness of plates with single-sided patch repair. In assumed displacement field, the strain-displacement relations and 3-D constitutive equations of a layer are obtained by the combination of 2-D and 3-D hierarchical shape functions. The transfinite mapping technique has been used to represent a circular boundary and Gauss-Lobatto numerical integration is implemented in order to directly obtain stresses occurred at the nodal points of each layer without other extrapolation techniques. The accuracy and simplicity of the present model are verified with comparison of the previous results in literatures using experiment and conventional 3-D finite element. Also, the bending effect has been investigated with various patch types like square, circular and annular shape.
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