Lamine kompozit ve sandviç plakaların şekil ve gerilme algılaması için yeni bir dört-düğüm noktalı ters-plaka elemanı

Öz

Kompozit malzemeler, çeşitli mühendislik yapılarının birincil yük taşıyıcı bileşenlerinin imalat sürecinde yaygın olarak kullanılmaktadır. Ancak, kompozitlerin yapısal bütünlüğünün, yapının hizmet ömrü boyunca meydana gelen hasarlardan dolayı azalması muhtemeldir. Duruma dayalı bakım programlaması için kompozit yapılara gerçek zamanlı şekil ve gerilme algılaması gerçekleştirebilen bir yapısal sağlık izleme sistemi entegre edilebilir. Bu çalışmada, Rafine Zikzak Teorisinin (RZT) temel olarak kullanıldığı ters sonlu elemanlar yöntemine (iFEM) dayanan yeni bir dört düğümlü ters plaka elemanı önerilmiştir. Buradaki iFEM-RZT formülasyonu, membran, eğilme, enine kayma ve zikzak kesit gerinimlerini içeren RZT'nin bütün gerinim ölçüleri kümesini kullanan ağırlıklı en küçük kareler fonksiyonunu en aza indirgemektedir. Mevcut elemanın temel faydası, herhangi bir yükleme bilgisi gerektirmemesi ve şekil algılaması için yalnızca yerleşik sensörlerden alınan gerinim ölçer ölçümlerini kullanmasıdır. Diğer bir avantajı, aynı zamanda genel bir lamine kompozit ve sandviç yapı sınıfının tam alan ve üç boyutlu yer değiştirmelerini ve gerilmelerini tahmin etmek içinde uygulanabilir olmasıdır. Mevcut elemanın potansiyel yeteneklerini göstermek için, farklı laminasyon tiplerine sahip olan bir lamine kompozit plaka üzerinde çeşitli vaka çalışmaları yapılmıştır. İFEM-RZT sonuçları ve son derece hassas sonlu elemanlar çözümleri arasındaki karşılaştırmaya göre, mevcut yaklaşımın üstün doğruluğu ortaya konmuştur.

Anahtar Kelimeler

• Yapısal Sağlık İzleme
• Ters Sonlu Elemanlar Yöntemi (iFEM)
• Rafine Zikzak Teorisi (RZT)
• Kompozit ve Sandviç Yapılar
• Şekil ve Gerilme Algılaması

A novel four-node inverse-plate element for shape and stress sensing of laminated composite and sandwich plates

Öz

Composite materials are widely utilized in manufacturing process of primary load bearing components of various engineering structures. However, the structural integrity of composites are likely to diminish due to damage accumulation over the service life of the structure. A structural health monitoring (SHM) system that can perform real-time shape and stress sensing can be integrated to composite structures for condition-based maintenance scheduling. In this study, a new four-node inverse-plate element, is proposed based on the inverse finite element method (iFEM) in which the Refined Zigzag Theory (RZT) is used as a basis. Herein the iFEM-RZT formulation minimizes a weighted least-squares functional that uses the complete set of strain measures of RZT, that include the membrane, bending, transverse shear and zigzag section strains. The main benefit of the present element is that it does not require any loading information and uses only strain gauge measurements taken from the on-board sensors to perform shape sensing. Another advantage is that it is also applicable to predict full field and three-dimensional displacements and stresses of a general class of laminated composite and sandwich structures. To demonstrate the potential capabilities of the present element, various case studies were performed on a laminated composite plate having different types of laminations. According to the comparison between iFEM-RZT results and highly accurate finite element solutions, the superior accuracy of the present approach was revealed.

Anahtar Kelimeler

• Structural Health Monitoring
• Inverse Finite Element Method (iFEM)
• Refined Zigzag Theory (RZT)
• Composite and Sandwich Structures
• Shape and Stress Sensing

Kaynakça

1. Herrmann, A.S., Zahlen, P.C., Zuardy, I., Sandwich structures technology in commercial aviation, Sandwich Structures 7: Advancing with Sandwich Structures and Materials, Springer, Netherlands, 13-26, 2005. doi:10.1007/1-4020-3848-8_2
2. Vadakke, V., Carlsson, L.A., Experimental investigation of compression failure of sandwich specimens with face/core debond, Composites Part B: Engineering, 35:6, 583-590, 2004. doi:10.1016/j.compositesb.2003.10.004
3. Zou, Y., Tong, L.P.S.G., Steven, G.P., Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures—a review, Journal of Sound and Vibration, 230:2, 357-378, 2000. doi:10.1006/jsvi.1999.2624
4. Tikhonov, A.N., Arsenin, V.Y., Solutions of Ill-Posed Problems, Winston and Sons, Washington, DC, 1977. doi:10.1137/1021044
5. Davis, M.A., Kersey, A.D., Sirkis, J., Friebele, E.J., Shape and vibration mode sensing using a fiber optic Bragg grating array, Smart Materials and Structures, 5:6, 759-765, 1996. doi:10.1088/0964-1726/5/6/005
6. Bogert, P.B., Haugse, E.D., Gehrki, R.E., Structural shape identification from experimental strains using a modal transformation technique, Proceedings of 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, VA, 2003. doi:10.2514/6.2003-1626
7. Tessler, A., Spangler, J.L., A variational principal for reconstruction of elastic deformation of shear deformable plates and shells, NASA TM-2003-212445, 2003.
8. Tessler, A., Spangler, J.L., A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells, Computer Methods in Applied Mechanics and Engineering, 19:2, 327-339, 2005. doi:10.1016/j.cma.2004.03.015

9. Tessler, A., Spangler, J.L., Inverse FEM for full-field reconstruction of elastic deformations in shear deformable plates and shells, Proceedings of 2nd European Workshop on Structural Health Monitoring. Munich, Germany, 2004.
10. Vazquez, S.L., Tessler, A., Quach, C.C., Cooper, E.G., Parks, J., Spangler J.L., Structural health monitoring using high-density fiber optic strain sensor and inverse finite element methods, NASA TM-2005-213761, 2005.
11. Kefal, A., Oterkus, E., Tessler, A., Spangler, J.L. A quadrilateral inverse-shell element with drilling degrees of freedom for shape sensing and structural health monitoring. Engineering Science and Technology, an International Journal, 19, 1299-1313, 2016. doi:10.1016/j.jestch.2016.03.006
12. Kefal, A., Oterkus, E., Displacement and stress monitoring of a chemical tanker based on inverse finite element method, Ocean Engineering, 112, 33-46, 2016. doi:10.1016/j.oceaneng.2015.11.032
13. Kefal, A., Oterkus, E., Displacement and stress monitoring of a Panamax containership using inverse finite element method, Ocean Engineering, 119, 16-29, 2016. doi:10.1016/j.oceaneng.2016.04.025
14. Kefal, A., Mayang, J.B., Oterkus, E., Yildiz, M., Three dimensional shape and stress monitoring of bulk carriers based on iFEM methodology, Ocean Engineering, 147, 256-267, 2018. doi:10.1016/j.oceaneng.2017.10.040
15. Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., Shape sensing of 3D frame structures using an inverse finite element method, International Journal of Solids and Structures, 49:22, 3100-3112, 2012. doi:10.1016/j.ijsolstr.2012.06.009
16. Gherlone, M., Cerracchio, P., Mattone, M., Di Sciuva, M., Tessler, A., An inverse finite element method for beam shape sensing: theoretical framework and experimental validation, Smart Materials and Structures, 23:4, 045027, 2014. doi:10.1088/0964-1726/23/4/045027
17. Zhao, Y., Du, J., Bao, H., Xu, Q., Optimal Sensor Placement Based on Eigenvalues Analysis for Sensing Deformation of Wing Frame Using iFEM, Sensors, 18(8), 2424, 2018. doi:10.3390/s18082424
18. Mooij C., Martinez, M., Benedictus, R., iFEM benchmark problems for solid elements, Smart Materials and Structures, In-Press, 2019. doi:10.1088/1361-665X/ab136f
19. Miller, E.J., Manalo, R., Tessler, A., Full-Field Reconstruction of Structural Deformations and Loads from Measured Strain Data on a Wing Test Article using the Inverse Finite Element Method, NASA TM-2016-219407, 2016.
20. Kefal, A., Yildiz, M., Modeling of Sensor Placement Strategy for Shape Sensing and Structural Health Monitoring of a Wing-Shaped Sandwich Panel Using Inverse Finite Element Method, Sensors, 17:12, 2775, 2017. doi:10.3390/s17122775.
21. Tessler, A., Di Sciuva, M., Gherlone, M., A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics, Journal of Mechanics of Materials and Structures, 5:2, 341-367, 2010. doi:10.2140/jomms.2010.5.341
22. Cerracchio, P., Gherlone, M., Di Sciuva, M., Tessler, A., A novel approach for displacement and stress monitoring of sandwich structures based on the inverse finite element method, Composite Structures, 127, 69-76, 2015. doi:10.1016/j.compstruct.2015.02.081
23. Kefal, A., Tessler, A., Oterkus, E., An enhanced inverse finite element method for displacement and stress monitoring of multilayered composite and sandwich structures, Composite Structures, 179, 514-540, 2017. doi:10.1016/j.compstruct.2017.07.078
24. Kefal, A., Tessler, A., Oterkus, E., An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells, NASA/TP-2018-220079, 2018.
25. Tessler, A., Hughes, T.J.R., An improved treatment of transverse shear in the Mindlin-type four-node quadrilateral element, Computer Methods in Applied Mechanics and Engineering, 39:3, 311-335, 1983. doi:10.1016/0045-7825(83)90096-8