A novel hybrid-Trefftz finite element for symmetric laminated composite plates
Source abstract
Abstract
A novel hybrid-Trefftz finite element (HTFE) for the analysis of symmetric laminated composite plates has been developed. Unlike the existing HTFE formulations, the derivation of this HTFE does not require the particular solutions of simultaneous governing partial differential equations. The Trefftz functions are constructed from the exact solutions of the homogeneous simultaneous governing partial differential equations in a straight forward manner without transforming them into a single governing equation. The HTFE is validated with the authenticated exact solutions. It is observed that this HTFE is an efficient finite element for analyzing laminated composite structures.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis of Composite Materials · Acoustic Wave Phenomena Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (23)
Show source-provided references
1. Cao, C., Yu, A., Qin, Q.H.: A novel hybrid finite element model for modeling anisotropic composites. Finite Elem. Anal. Des. 64, 36–47 (2013)10.1016/j.finel.2012.09.007 ↗
2. Cen, S., Shang, Y., Li, C.-F., Li, H.-G.: Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate. Int. J. Numer. Methods Eng. 98, 203–234 (2014)10.1002/nme.4632 ↗
3. Choo, Y.S., Choi, N., Lee, B.C.: A new hybrid-Trefftz triangular and quadrilateral plate elements. Appl. Math. Model. 34, 14–23 (2010)10.1016/j.apm.2009.03.022 ↗
4. Fu, Z.-J., Qin, Q.H., Chen, W.: Hybrid-Trefftz finite element method for heat conduction in nonlinear functionally graded materials. Eng. Comput. 28, 578–599 (2011)10.1108/02644401111141028 ↗
5. Fu, Z.-J., Chen, W., Yang, H.-T.: Boundary particle method for Laplace transformed time fractional diffusion equations. J. Comput. Phys. 235, 52–66 (2013)10.1016/j.jcp.2012.10.018 ↗
6. Fu, Z.-J., Xi, Q., Chen, W., Cheng, A.H.D.: A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations. Comput. Math. Appl. 76, 760–773 (2018)10.1016/j.camwa.2018.05.017 ↗
7. Jirousek, J.: Basis for development of large finite elements locally satisfying all filed equations. Comput. Methods Appl. Mech. Eng. 14, 65–92 (1978)10.1016/0045-7825(78)90013-0 ↗
8. Jirousek, J., Guex, L.: The hybrid-Trefftz finite element model and its application to plate bending. Int. J. Numer. Methods Eng. 23, 651–693 (1986)10.1002/nme.1620230410 ↗
9. Jirousek, J., Leon, N.: A powerful finite element for plate bending. Comput. Methods Appl. Mech. Eng. 12, 77–96 (1977)10.1016/0045-7825(77)90052-4 ↗
10. Karkon, M.: Hybrid-Trefftz formulation for analysis of anisotropic and symmetric laminated plates. Compos. Struct. 134, 460–474 (2015)10.1016/j.compstruct.2015.08.098 ↗
11. Karkon, M., Pajand-Rezaiee, M.: Hybrid-Trefftz formulation for analysis of thick orthotropic plates. Aerosp. Sci. Technol. 50, 234–244 (2016)10.1016/j.ast.2016.01.006 ↗
12. Kita, E., Kamiya, N.: Trefftz method: an overview. Adv. Eng. Softw. 24, 3–12 (1995)10.1016/0965-9978(95)00067-4 ↗
13. Natarajan, S., Annabattula, R.K., Bordas, S., Atroshchenko, E.: Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties. Asia Pac. J. Comput. Eng. (2017). https://doi.org/10.1186/s40540-017-00201310.1186/s40540-017-002013 ↗
14. Pagano, N.J.: Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 4, 20–34 (1970)10.1177/002199837000400102 ↗
15. Pandya, B., Kant, T.: Flexural analysis of laminated composites using refined higher-order C0 plate bending elements. Comput. Methods Appl. Mech. Eng. 66, 173–198 (1988)10.1016/0045-7825(88)90075-8 ↗
16. Petrolito, J.: Hybrid-Trefftz quadrilateral elements for thick plate analysis. Comput. Methods Appl. Mech. Eng. 78, 331–351 (1990)10.1016/0045-7825(90)90005-7 ↗
17. Petrolito, J.: Triangular thick plate elements based on a hybrid-Trefftz approach. Comput. Struct. 60, 883–894 (1996)10.1016/0045-7949(95)00453-X ↗
18. Petrolito, J.: Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements. Appl. Math. Model. 38, 5858–5869 (2014)10.1016/j.apm.2014.04.026 ↗
19. Qin, Q.H.: Dual varialtional formulation for Trefftz finite element method of elastic materials. Mech. Res. Commun. 31, 321–330 (2004)10.1016/j.mechrescom.2003.11.003 ↗
20. Qin, Q.H., Wang, H.: Matlab and C Programming for Trefftz Finite Element Method. CRC Press, Boca Raton (2008)10.1201/9781420072761 ↗
21. Reddy, J.N.: Mechanics of Laminated Composite Plates Theory and Analysis. CRC Press, Boca Raton (1997)
22. Reddy, J.N.: Energy and Variational Method in Applied Mechanics with an Introduction to the Finite Element Method, p. 110002. Wiely, New Delhi (2016)
23. Rezaiee-Pajand, M., Karkon, M.: Two efficient hybrid-Trefftz elements for plate bending analysis. Latin Am. J. Solids Struct. 9, 43–67 (2012)10.1590/S1679-78252012000100003 ↗