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Journal ArticleDOI

Effect of fictitious rotational stiffness coefficient on natural frequencies

22 Aug 1989-Journal of Sound and Vibration (Elsevier Science)-Vol. 133, Iss: 1, pp 177-179
About: This article is published in Journal of Sound and Vibration.The article was published on 1989-08-22. It has received 2 citations till now. The article focuses on the topics: Stiffness.
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Journal ArticleDOI
TL;DR: In this article, the perturbation method and Pade approximants are used to compute the eigenvalues of linear problems, which can deal with problems with close or multiple eigen values.

2 citations

Journal Article
TL;DR: In this paper, the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements is investigated.
Abstract: The choice of finite element to use in order to predict nonlinear static or dynamic response of complex structures becomes an important factor. Then, the main goal of this research work is to focus a study on the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements. In this purpose: First, simple triangular and quadrilateral flat shell finite elements are implemented in an incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear analysis. The triangular element is a combination of DKT and CST elements, while the quadrilateral is a combination of DKQ and the bilinear quadrilateral membrane element. In both elements, the sixth degree of freedom is handled via introducing fictitious stiffness. Secondly, in the same code, the sixth degrees of freedom in these elements is handled differently where the in-plane rotational d.o.f is considered as an effective d.o.f in the in-plane filed interpolation. Our goal is to compare resulting shell elements. Third, the analysis is enlarged to dynamic linear analysis by direct integration using Newmark’s implicit method. Finally, the linear dynamic analysis is extended to geometrically nonlinear dynamic analysis where Newmark’s method is used to integrate equations of motion and the Newton-Raphson method is employed for iterating within each time step increment until equilibrium is achieved. The obtained results demonstrate the effectiveness and robustness of the interpolation of the in-plane rotational d.o.f. and present deficiencies of using fictitious stiffness in dynamic linear and nonlinear analysis. Keywords—Flat shell, dynamic analysis, nonlinear, Newmark, drilling rotation.

1 citations


Cites background from "Effect of fictitious rotational sti..."

  • ...Furthermore, some research works on the effect of varying α constant determined that satisfactory results are obtained as α is smaller value [6,5,7]....

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References
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Journal ArticleDOI
TL;DR: In this paper, a detailed comparison of the predicted eigenfrequencies of twisted rotating plates as obtained by using two different shape functions is presented, and results of a brief study of cambered plates are presented.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the development of finite element procedures for the analysis of thin shells is presented, together with a discussion of the four types of approximations involved in the application of the method.

50 citations