3D FEM analysis of stress concentrations in a rectangular thick plate with PZT inclusions under bending

Abstract

The present study is a prior attempt to study the influence of the PZT inclusion(s) in the rectangular elastic plate under bending on the stress concentration of this plate utilizing 3D exact equations of the elasto- and piezo-elastostatics theories. The corresponding boundary-value problem is formulated within the scope of the three dimensional exact equations of electro-elasticity theory using the piecewise-homogeneous body model and is solved numerically by the three dimensional Finite Element Method. It is assumed that the plate has simply-supported mechanically and short-circuit conditions with respect to the electric potential along all its lateral edge surfaces and ideal contact conditions are provided at the interface surfaces between the PZT inclusion(s) and the elastic matrix. All algorithms and programs required for the numerical solution are made by the authors. The effects of various matrix materials, the size, volume fraction and location of the piezoelectric inclusion as well as the coupling effect between the mechanical and electrical fields, in addition to the effects of interaction between the neighboring PZT inclusions in a simply-supported rectangular thick plate under bending force on the stress distributions therein are investigated and discussed. It is established that PZT inclusion(s) within the rectangular plate under bending force causes a decrease in the values of normal stresses and causes an increase in the values of shear stresses at the interface between the matrix and PZT inclusion(s).

Keywords

• Stress Concentration
• 3D Finite Elements Method
• Piezoelectric Inclusions

References

1. REFERENCES
2. [1] Aksüt H. Piezoelektrik kompozitlerin elektromekanik özelliklerinin analizi. Yüksek Lisans Tezi. İstanbul: İTÜ Fen Bilimleri Enstitüsü; 2020.
3. [2] Wang B. Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material. Int J Solids Struct 1992;29:293–308. [CrossRef]
4. [3] Fan H, Qin S A. Piezoelectric sensor embedded in a non-piezoelectric matrix. Int J Eng Sci 1995;33:379–388. [CrossRef]
5. [4] Xu XL, Rajapakse RKND. Boundary element analysis of piezoelectric solids with defects. Comp Part B 1998;29B:665–669. [CrossRef]
6. [5] Gonenli C, Das O. Effect of crack location on buckling and dynamic stability in plate frame structures. J Braz Soc Mech Sci Eng 2021;43:311. [CrossRef]
7. [6] Das O, Ozturk H, Gonenli C. Finite element vibration analysis of laminated composite parabolic thick plate frames. Steel and Composite Structures 2020;35:43–59.
8. [7] Gonenli C, Ozturk H, Das O. Effect of crack on free vibration of a pre-stressed curved plate. Proceed Inst Mech Eng C 2022;236:811825. [CrossRef]

9. [8] Xiao ZM, Bai J. On piezoelectric inhomogeneity related problem-part I: a close-form solution for the stress field outside a circular piezoelectric inhomogeneity. Int J Eng Sci 1999;37:945–959. [CrossRef]
10. [9] Gao Y, Wang M, Zhao B. The remarkable nature of radially symmetric deformation of anisotropic piezoelectric inclusion. Acta Mech Solid Sinica 2008;21:278–282. [CrossRef]
11. [10] Mishra D, Park CY, Yoo SH, Pak YE. Closed-form solution for elliptical inclusion problem in antiplane piezoelectricity with far-field loading at an arbitrary angle. Eur J of Mech A/Solids 2013;40:186–197. [CrossRef]
12. [11] Mishra D, Yoo SH, Park CY, Pak YE. Elliptical ınclusion problem ın antiplane piezoelectricity: Stress concentrations and energy release rates. Int J Fract 2013;179:213–220. [CrossRef]
13. [12] Lee YT, Chen JT, Kuo SR. Null-field integral approach for the piezoelectricity problems with multiple elliptical inhomogeneties. Eng Analy with Bound Elements 2014;39:111–120. [CrossRef]
14. [13] Zhou ZD, Zhao SX, Kuang ZB. Stress and electric displacement analyses in piezoelectric media with an elliptic hole and a small crack. Int J Solids Struct 2005;42:2803–2822. [CrossRef]
15. [14] Yang BH, Gao CF. Plane problems of multiple piezoelectric inclusions in a non-piezoelectric matrix. Int J Eng Sci 2010;48:518–528. [CrossRef]
16. [15] Kirilyuk VS, Levchuk OI. Stress state of an orthotropic piezoelectric body with a triaxial ellipsoidal inclusion subject to tension. Int Appl Mech 2019;55:305–310. [CrossRef]
17. [16] Babuşcu Yeşil Ü, Yahnioğlu N, Uçan Y. Electrostatic analysis of rectangular thick plate containing piezoelectic prismatic inclusion wıth FEM. Omer Halisdemir Univ J Eng Sci 2019;8:69–81.
18. [17] Zienkiewicz OC, Taylor RL. The Finite Element Methods: Basic Formulation and Linear Problems. 4th ed. Oxford: Mc Graw-Hill Book Company; 1989.
19. [18] Yang J. An Introduction to The Theory of Piezoelectricity. New York: Springer; 2005.
20. [19] Yahnioğlu N. Eğrisel yapıya sahip kompozit malzemeden hazırlanmış yapı elemanlarının statiğine uygun sınırdeğer problemlerinin FEM ile incelenmesi. Doktora Tezi. İstanbul: Yıldızm Teknik Üniversitesi Fen Bilimleri Enstitüsü; 1996.