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Mevcut Rijitlik Denklemleri Kullanılarak Sonlu Elemanlarda Mafsal ve Elastik-Bağlantı Uygulaması Üzerine Pratik Bir Yaklaşım

Year 2022, Volume: 13 Issue: 3, 571 - 578, 30.09.2022
https://doi.org/10.24012/dumf.1092538

Abstract

Sonlu Eleman (SE) modellerinin birçok mühendislik problemi için kullanışlılığı, elemanın uç mafsal ve elastik-bağlantılar dahil olmak üzere çeşitli bağlantı tiplerini destekleme yeteneğine bağlıdır. Bununla birlikte, bir SE modeline uç bağlantıların eklenmesi eleman geliştirme sürecinde ek teorik çaba gerektirir. Alternatif olarak, ağ yapısında sıfır uzunluklu harici bağlantı elemanları kullanılabilir, ancak bu hem ağ tanımını hem de birleştirme işlemlerini güçleştirecektir. Bu çalışma, rijit bağlantılara sahip herhangi bir SE modeline ait mevcut rijitlik denklemlerinin, ek bir teorik çıkarım gerektirmeksizin, basit matris işlemleri uygulayarak hem uç mafsalları hem de elastik uç yayları destekleyecek şekilde kolaylıkla yeniden yapılandırılabileceğini göstermektedir. Bu kapsamda önerilen yöntem üç temel adımda özetlenebilir. İlk olarak, eleman denklemleri, elemana özel yeni serbestlik dereceleri tanımlanarak sistem denkleminden ayrılır. İkinci olarak, eleman ve sistem arasına elastik yaylar yerleştirilir. Son olarak, yeni serbestlikler ortaya çıkan denklemlerden yok edilerek eleman sistemle yeniden birleştirilir. Önerilen bu yöntemin genel SE modellerine kolaylıkla uygulanabilir olduğu ve hedeflenen mafsal ve elastik bağlantılara sahip yeni bir eleman oluşturabildiği çalışma kapsamında örneklerle doğrulanmıştır.

References

  • C. L. Amba-Rao, “Method of calculation of frequencies of partially fixed beams carrying masses,“ J. Acoust. Soc. Am., vol. 40, no. 2, pp. 367-371, Feb. 1996. DOI:10.1121/1.1910079.
  • R. Shahab et al., “Proposed Simplified Approach for the Seismic Analysis of Multi-Storey Moment Resisting Framed Buildings Incorporating Friction Sliders,” Buildings, vol. 9, no. 5, pp. 1-22, May 2019. DOI: 10.3390/buildings9050130.
  • H. Lin, J. Jhou, and R. Stearman, “Influence of Joint Fixity on the Structural Static and Dynamic Response of a Joined-Wing Aircraft: Part I: Static Response,“ SAE trans., vol. 98, pp. 221-234, no. 1, 1989. DOI: 10.4236/ojapps.2016.67047.
  • A. Bijalwan, A. Misra, “Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method,“ Open J. Appl. Sci., vol. 6, no. 7, pp. 465-477, July 2016. DOI: 10.4236/ojapps.2016.67047.
  • G. R. Monforton, T. S. Wu, “Matrix Analysis of Semi-Rigidly Connected Frames,” J. Struct. Div., vol. 89, no. 6, pp. 13-42, Dec. 1963. DOI: 10.1061/JSDEAG.0000997.
  • T.Q. Li, B.S. Choo, D.A. Nethercot, “Connection element method for the analysis of semi-rigid frames,” J. Constr. Steel Res., vol. 32, no. 2, pp. 143-171, 1995. DOI: 10.1016/0143-974X(95)93170-9.
  • W. McGuire, R. H. Gallagher, R. D. Ziemian, Matrix Structural Analysis. 2nd ed, USA: John Wiley & Sons Inc., 2000, pp. 393–398.
  • A. Y. Aköz, Enerji Yöntemleri. İstanbul, TR: Birsen Yayınevi, 2005, pp. 155–176.
  • M. Yilmaz, Sonlu Elamanlar Analizi: Teori ve Python Uygulamaları. İstanbul, TR: Birsen Yayınevi, 2022, pp. 125–132.
  • P. Nanakorn, “A two-dimensional beam–column finite element with embedded rotational discontinuities,” Comput. Struct., vol. 82, no. 9-10, pp. 753-762, Mar. 2004. DOI: 10.1016/j.compstruc.2004.02.008.
  • B. Biondi, S. Caddemi, “Closed form solutions of Euler–Bernoulli beams with singularities,“ Int. J. Solids Struct., vol. 42, no. 9-10, pp. 3027-3044, May. 2005. DOI: 10.1016/j.ijsolstr.2004.09.048.
  • M. E. Kartal et al., “Effects of Semi-Rigid Connection on Structural Responses,” Electron. J. Struct. Eng., vol. 10, pp. 22-35, Jan. 2010.
  • W. Zuo et al., “A complete development process of finite element software for body-in-white structure with semi-rigid beams in .NET framework,” Adv. Eng. Softw., vol. 45, no. 1, pp. 261-271, Mar. 2012. DOI: 10.1016/j.advengsoft.2011.10.005.
  • CSI, “SAP2000 Integrated Software for Structural Analysis and Design,” Computers and Structures Inc., Berkeley, California.
  • M. Yilmaz, “Easy pre/post-processing of finite elements with custom symbolic-objects: A self-expressive Python interface,” Comput. Struct., vol. 222, pp. 82-97, Oct. 2019. DOI: 10.1016/j.compstruc.2019.07.002.

A Practical Approach to Implement Releases and Partial Fixities in Finite Elements Using Already Existing Stiffness Equations

Year 2022, Volume: 13 Issue: 3, 571 - 578, 30.09.2022
https://doi.org/10.24012/dumf.1092538

Abstract

The usefulness of Finite Element (FE) models for many engineering purposes depends on the element's ability to support a variety of end-connection types including releases and partial-fixities. However, adding such features to a FE model would require additional theoretical effort in the element development process. Alternatively, zero-length external connector-elements can be used in the mesh structure, but this will complicate both mesh definition and assemblage operations. This study shows that the existing stiffness equations of any FE model with regular rigid connections can be effectively employed to automatically define both end-releases and end-partial-fixities by simply applying a basic matrix-equation modification process without the need for any additional theoretical development on the element itself. Our process can be summarized in three basic steps. Firstly, element equations are separated from the system equation by defining element’s own degree-of-freedoms (DOFs). Secondly, elastic springs are introduced between the element and the system. Finally, the element is merged back into the system by eliminating its newly defined DOFs from the emerged equations. It has been verified by examples that, using these steps results in a new set of element equations with the desired end-releases/partial fixities and can be used in custom FE models.

References

  • C. L. Amba-Rao, “Method of calculation of frequencies of partially fixed beams carrying masses,“ J. Acoust. Soc. Am., vol. 40, no. 2, pp. 367-371, Feb. 1996. DOI:10.1121/1.1910079.
  • R. Shahab et al., “Proposed Simplified Approach for the Seismic Analysis of Multi-Storey Moment Resisting Framed Buildings Incorporating Friction Sliders,” Buildings, vol. 9, no. 5, pp. 1-22, May 2019. DOI: 10.3390/buildings9050130.
  • H. Lin, J. Jhou, and R. Stearman, “Influence of Joint Fixity on the Structural Static and Dynamic Response of a Joined-Wing Aircraft: Part I: Static Response,“ SAE trans., vol. 98, pp. 221-234, no. 1, 1989. DOI: 10.4236/ojapps.2016.67047.
  • A. Bijalwan, A. Misra, “Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method,“ Open J. Appl. Sci., vol. 6, no. 7, pp. 465-477, July 2016. DOI: 10.4236/ojapps.2016.67047.
  • G. R. Monforton, T. S. Wu, “Matrix Analysis of Semi-Rigidly Connected Frames,” J. Struct. Div., vol. 89, no. 6, pp. 13-42, Dec. 1963. DOI: 10.1061/JSDEAG.0000997.
  • T.Q. Li, B.S. Choo, D.A. Nethercot, “Connection element method for the analysis of semi-rigid frames,” J. Constr. Steel Res., vol. 32, no. 2, pp. 143-171, 1995. DOI: 10.1016/0143-974X(95)93170-9.
  • W. McGuire, R. H. Gallagher, R. D. Ziemian, Matrix Structural Analysis. 2nd ed, USA: John Wiley & Sons Inc., 2000, pp. 393–398.
  • A. Y. Aköz, Enerji Yöntemleri. İstanbul, TR: Birsen Yayınevi, 2005, pp. 155–176.
  • M. Yilmaz, Sonlu Elamanlar Analizi: Teori ve Python Uygulamaları. İstanbul, TR: Birsen Yayınevi, 2022, pp. 125–132.
  • P. Nanakorn, “A two-dimensional beam–column finite element with embedded rotational discontinuities,” Comput. Struct., vol. 82, no. 9-10, pp. 753-762, Mar. 2004. DOI: 10.1016/j.compstruc.2004.02.008.
  • B. Biondi, S. Caddemi, “Closed form solutions of Euler–Bernoulli beams with singularities,“ Int. J. Solids Struct., vol. 42, no. 9-10, pp. 3027-3044, May. 2005. DOI: 10.1016/j.ijsolstr.2004.09.048.
  • M. E. Kartal et al., “Effects of Semi-Rigid Connection on Structural Responses,” Electron. J. Struct. Eng., vol. 10, pp. 22-35, Jan. 2010.
  • W. Zuo et al., “A complete development process of finite element software for body-in-white structure with semi-rigid beams in .NET framework,” Adv. Eng. Softw., vol. 45, no. 1, pp. 261-271, Mar. 2012. DOI: 10.1016/j.advengsoft.2011.10.005.
  • CSI, “SAP2000 Integrated Software for Structural Analysis and Design,” Computers and Structures Inc., Berkeley, California.
  • M. Yilmaz, “Easy pre/post-processing of finite elements with custom symbolic-objects: A self-expressive Python interface,” Comput. Struct., vol. 222, pp. 82-97, Oct. 2019. DOI: 10.1016/j.compstruc.2019.07.002.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Murat Yılmaz 0000-0002-5895-7839

Early Pub Date September 30, 2022
Publication Date September 30, 2022
Submission Date March 24, 2022
Published in Issue Year 2022 Volume: 13 Issue: 3

Cite

IEEE M. Yılmaz, “A Practical Approach to Implement Releases and Partial Fixities in Finite Elements Using Already Existing Stiffness Equations”, DUJE, vol. 13, no. 3, pp. 571–578, 2022, doi: 10.24012/dumf.1092538.
DUJE tarafından yayınlanan tüm makaleler, Creative Commons Atıf 4.0 Uluslararası Lisansı ile lisanslanmıştır. Bu, orijinal eser ve kaynağın uygun şekilde belirtilmesi koşuluyla, herkesin eseri kopyalamasına, yeniden dağıtmasına, yeniden düzenlemesine, iletmesine ve uyarlamasına izin verir. 24456