서지주요정보
안정화 방법을 이용하는 Mindlin 판 요소의 수학적 특성 및 수치적 분석 = Mathmatical and numerical analyses of the mindlin plate element using the stabilization method
서명 / 저자 안정화 방법을 이용하는 Mindlin 판 요소의 수학적 특성 및 수치적 분석 = Mathmatical and numerical analyses of the mindlin plate element using the stabilization method / 이용주.
저자명 이용주 ; Lee, Yong-Joo
발행사항 [대전 : 한국과학기술원, 1993].
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소장정보

등록번호

8003314

소장위치/청구기호

학술문화관(문화관) 보존서고

DME 93009

휴대폰 전송

도서상태

이용가능

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반납예정일

초록정보

A combined mixed functional is proposed for analysis of linear elastic problems. The functional is a modification of the Hellinger-Reissner functional and a generalization of the Slivker's mixed functional. It is constructed by linearly combining the hellinger-Reissner functional and the total potential energy. The resulting bilinear form is shown to be positive definite and V-elliptic or V-coercive according to the combination parameter, which guarantee the existence and uniqueness of the solution. The equivalence theorem between mixed elements and reduced/selective integration elements is applied and the stabilization matrices are obtained for the continuum elements. By performing the error analysis, the combined mixed model is shown to have optimal convergence rate. This means that the stabilization methods have the same convergence rate as the displacement-based model. The combined mixed functional is applied to the Mindlin plate problem. Existence and uniqueness of the solution of the proposed mixed model are proven. The stabilization matrix of Belytschko is obtained for the four-node plate element based on the equivalence theorem between mixed elements and reduced/selectively integrated elements. Using the present method, stabilization matrices can be obtained for higher-order elements and triangular elements without any difficulty. The combined mixed model is shown to have optimal convergence rate from the error analysis under the assumption of the finite thickness. The stabilization parameter of Belytschko is modified and numerically tested. For the numerical verification of the combined mixed model, eigenvalues of the stiffness matrix of a typical rectangular element are obtained for various combinations of approximating polynomials. The structure of them is shown to conform to that theoretically predicted. From the numerical analyses of the rectangular plates under the uniformly distributed loads, the stabilization parameter is shown to be insensitive to Young's modulus, Poisson's ratio, thickness and area. It is also shown that the combined mixed element is not sensitive to stabilization parameter with reasonable meshes and that the element is free from the shear locking and spurious zero energy modes.

서지기타정보

서지기타정보
청구기호 {DME 93009
형태사항 xiv, 153 p. : 삽도 ; 26 cm
언어 한국어
일반주기 부록 : A, 선형 탄성 문제에서의 양일차 특성. - B, Mindlin 판 해석을 위한 안정화 행렬의 유도와 그의 수학적 특성
저자명의 영문표기 : Yong-Joo Lee
지도교수의 한글표기 : 이병채
지도교수의 영문표기 : Byung-Chai Lee
학위논문 학위논문(박사) - 한국과학기술원 : 기계공학과,
서지주기 참고문헌 : p. 108-118
주제 Convergence.
Numerical analysis.
Equivalence relations.
Elastic analysis (Engineering)
Matrices.
안정화.
수치 해법. --과학기술용어시소러스
수렴. --과학기술용어시소러스
탄성 역학. --과학기술용어시소러스
행렬식. --과학기술용어시소러스
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