-

Öz

Implementation of Improved Finite Elements Over Circular Cross-Section Subjected to Effect of Non-Uniform Wind In this study, a finite element program based on p-version finite element method (pFEM) and augmented by blending function method is coded. The program has a solid 3 dimensional finite element defined in cartesian coordinates, by which application of continuous or discontinuous nonlinear loads are taken into account and exact representation of curved edge and/or surface boundary is performed. With the aid of the coded program, a series of static analyses under defined wind loads for uniform and non-uniform loadings according to TS 498 and non-uniform loading according to pr EN 1991-1-4 are carried out on an industrial chimney with a circular cross-section. It is concluded that the coded program gives reliable results. Due to the capability of modeling of non-uniform loadings it is observed that the standards may lead to vastly different results

Anahtar Kelimeler

• p-version finite element method (pFEM), finite elements, blending function method, finite element having curved surfaces, non-uniform loading, wind loading

Doğrusal Olmayan Rüzgâr Etkisindeki Dairesel Kesitlerde Geliştirilmiş Sonlu Elemanlar Uygulaması

Öz

Bu çalışmada p-yöntemine dayalı Sonlu Elemanlar Yöntemi (pSEY) ve Karma Fonksiyon Yöntemi ile zenginleştirilmiş bir sonlu eleman programı hazırlanmıştır. Program, kartezyen eksen takımında tanımlı doğrusal yerdeğiştirmelere ile doğrusal olmayan sürekli veya süreksiz yüklemelerin dikkate alınabildiği, eğrisel kenar ve/veya yüzeyli olabilen dörtgen prizma şeklindeki üç boyutlu bir sonlu elemana sahiptir. Program ile dairesel kesitli bir sanayi bacasının TS 498'e göre doğrusal olmayan ve düzgün rüzgâr yüklemeleri; pr EN 1991-1-4'e göre sadece doğrusal olmayan rüzgâr yüklemesi altında statik analizleri yapılmıştır. Sonuç olarak geliştirilen programın güvenilir sonuçlar verdiği ve doğrusal olmayan yük modellemesinin yapılabilirliği sayesinde ilgili standartların ne kadar farklı sonuçlar verebildiği görülmüştür

Anahtar Kelimeler

• p-yöntemi, sonlu elemanlar, karma fonksiyon yöntemi, eğrisel yüzeyli sonlu eleman, doğrusal olmayan yükleme, rüzgâr yüklemesi

Kaynakça

1. TS 498, Yapı Elemanlarının boyutlandırılmasında Alınacak Yüklerin Hesap Değerleri, TSE ICS 91.040, Ankara, 1997.
2. prEn 1991-1-4, Eourocode 1:Actions On Structures-Part 1-1: General Actions- Densities, Self-Weight, Imposed Loads For Buildings, EN, Brussels, 2002.
3. Babuška, I. ve Suri, M., 1994. The p and h-p Versions of the Finite Element Method, Basic Principles and Properties, SIAM Review, 36, 4, 578-632.
4. Gupta, A.K., Fang, T.H. ve Chen, H., 1991. Computational Efficiency of p- and h- Version Elements, Communications in Applied Numerical Methods, 7, 2, 87-92.
5. Houmat, A., 2004. Three-Dimensional Hierarchical Finite Element Free Vibration Analysis of Annular Sector Plates, Journal of Sound and Vibration 276, 181-273.
6. Rank, E., Düster, A., Nübel, V., Preusch, K. ve Bruhns, O.T., 2005. High Order Finite Elements For Shells, Computer Methods in Applied Mechanics and Engineering, 194, 2494-2512.
7. Babuška, I. ve Dorr, M.R., 1981. Error Estimates for The Combined h and p Versions of The Finite Element Method, Numerische Mathematik, 37, 2, 257-277.
8. Babuška, I., Griebel M. ve Pitkaranta, J., 1989. The Problem of Selecting the Shape Functions for a p-type Finite Element, International Journal for Numerical Methods in Engineering, 28, 1891-1908.

9. Babuška, I. ve Suri, M., 1987. The Optimal Convergence Rate of The p-Version of The Finite Element Method, SIAM Journal on Numerical Analysis, 27, 4, 750-776.
10. Babuška, I., Szabό, B.A. ve Katz, I.N., 1981. The p-Version Finite Element Method, SIAM Journal on Numerical Analysis, 18, 515-545.
11. Carnevali, P., Morris, R.B., Tsuji, Y. ve Taylor, G., 1993. New Basis Functions and Computational Procedures for p-Version Finite Element Analysis, International Journal for Numerical Methods in Engineering, 36, 3759-3779.
12. Chilton, L. ve Suri, M., 1997. On The Selection of A Locking-free hp Element for Elasticity Problems, International Journal for Numerical Methods in Engineering, 40, 2045-2062.
13. Deuflhard, P., Leinen, P. ve Yserentant, 1988. Concepts of An Adaptive Hierarchical Finite Element Code, Technical Report SC-88-5, Konrad-Zuse-Zentrum, Berlin, Germany.
14. Duarte, C.A., Babuška, I. ve Oden, J.T., 2000. Generalized Finite Element Methods for Three-Dimensional Structural Mechanic Problems, Computers and Structures, 77, 2, 215-232.
15. Promwungkwa, A., 1998. Data Structure and Error Estimation For An Adaptive p- Version Finite Element Method in 2-D and 3-D Solids, Doktora Tezi, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
16. Rank, E., Düster, A., Nübel, V., Preusch, K. ve Bruhns, O.T., 2005. High Order Finite Elements For Shells, Computer Methods in Applied Mechanics and Engineering, 194, 2494-2512.
17. Rank, E., Rücker, M., Düster, A. ve Bröker, H., 2001. The Efficiency of The p- Version Finite Element Method in A Distirbuted Computing Environment, International Journal for Numerical Methods in Engineering, 52, 589-604.
18. Robinson, J., 1986. An Introduction to Hierarchical Displacement Elements and the Adaptive Technique, Finite Elements in Analysis and Design, 2, 377-388.
19. Szabό, B.A., 1990. The p- and h-p Versions of the Finite Element Method in Solid Mechanics, Computer Methods in Applied Mechanics and Engineering, 80, 185-195.
20. Szabό, B.A. ve Babuška, I. 1991. Finite Element Analysis, John Wiley & Sons, New York, 368 s.
21. Netz, T., Düster, A., ve Hartmann, S., 2013. High-order finite elements compared to low-order mixed element formulations, Journal of Mathematics and Mechanics, 93, 2- 3, 163-176.
22. Watkins, D.S., 1974. Blending Functions and Finite Elements, Doktora Tezi, The University of Calgary, Alberta.
23. Cavendish, J.C. ve Wixom, J.A., 1975. Finite Element Mesh Generation For Planar and Shell Type Structures, General Motors Research Laboratories, Warren, Michigan.
24. S., Bekiroğlu, “p-Yöntemine Dayalı Üç Boyutlu Sonlu Elemanlar İle Yapıların Elastostatik ve Elastodinamik Analizi” Doktora Tezi, KTÜ Fen Bilimleri Enstitüsü, 2010.
25. Gordon, W., 1971. Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation, SIAM Journal on Numerical Analysis, 8, 1, 158- 177.
26. Gordon, W. ve Hall, C., 1973a. Construction of Curvilinear Co-ordinate Systems and Applications to Mesh Generation, International Journal for Numerical Methods in Engineering, 7, 4, 461-477.
27. Gordon, W. ve Hall, C., 1973b. Transfinite Element Methods: Blending-Function Interpolation over Arbitrary Curved Element Domains, Numerische Mathematik, 21, 109-129.
28. Marshall, J.A. ve Mitchell, A.R., 1978. Blending Interpolants in Finite Element Method, International Journal for Numerical Methods in Engineering, 12, 1, 77-83.
29. Cavendish, J.C. ve Hall, C.A., 1984. A New Class of Transitional Blended Finite Elements for The Analysis of Solid Structures, International Journal for Numerical Methods in Engineering, 20, 2, 241-253.
30. Cavendish, J.C. ve Hall, C.A., 1984. A New Class of Transitional Blended Finite Elements for The Analysis of Solid Structures, International Journal for Numerical Methods in Engineering, 20, 2, 241-253.
31. Dey, S., 1997. Geometry-Based Three-Dimensional hp-Finite Element Modeling and Computations, Doktora Tezi, Rensselaer Polytechnic Institute, Troy, New York.
32. Düster, A., 2001. High Order Finite Elements For Three-Dimensional, Thin-Walled Nonlinear Continua, Doktora Tezi, Technishe Univesitӓt Münhen, Germany.
33. Királyfalvi, G. ve Szabό, B.A., 1997. Quasi-Regional Mapping For The p-Version of The Finite Element Method, Finite Elements in Analysis and Design, 27, 85-97.
34. Liu, Y., 1998. p-Adaptive Hybrid/Mixed Finite Element Method, Doktora Tezi, The Ohio State University, ABD.
35. Alfeld, P., 1985. Multivariate Perpendicular Interpolation, SIAM Journal on Numerical Analysis, 22, 1, 95-106.
36. Mӓkipelto, J., 2005. Exact Geometry Description With Unstructured Triangular Meshes For Shape Optimzation, 11th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro.
37. Danış, H. ve Görgün, M., 2005. Marmara Depremi ve Tüpraş Yangını, Deprem Sempozyumu, Kocaeli, 1362-1369.