Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures
Source abstract
Abstract
A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton–Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Structural Load-Bearing Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (35)
Show source-provided references
1. Koizumi, M.: The concept of FGM Ceramics. Trans. Funct. Grad. Mater. 34, 3–10 (1993)
2. Reddy, J.N., Chin, C.D.: Thermomechanical analysis of functionally cylinders and plates. J. Therm. Stress. 21, 593–626 (1998)10.1080/01495739808956165 ↗
3. Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998)10.1016/S0020-7683(97)00253-9 ↗
4. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 58, 2177–2200 (2000)
5. Woo, J., Meguid, S.A.: Nonlinear analysis of functionally graded plates and shallow shells. Int. J. Solids Struct. 38, 7409–7421 (2001)10.1016/S0020-7683(01)00048-8 ↗
6. Yang, J., Shen, H.S.: Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermomechanical loads under various boundary conditions. Compos. Part B: Eng. 34, 103–115 (2003)10.1016/S1359-8368(02)00083-5 ↗
7. Yang, J., Shen, H.S.: Nonlinear analysis of functionally graded plates under transverse and in-plane loads. Int. J. Nonlinear Mech. 38, 467–482 (2003)10.1016/S0020-7462(01)00070-1 ↗
8. Ma, L.S., Wang, T.J.: Nonlinear bending and postbuckling of functionally graded circular plates under mechanical and thermal loadings. Int. J. Nonlin. Mech. 40, 3311–3330 (2003)
9. Na, K.S., Kim, J.H.: Nonlinear bending response of functionally graded plates under thermal loads. J. Therm. Stress. 29, 245–261 (2005)
10. Reddy, J.N., Arciniega, R.A.: Mechanical and thermal buckling of functionally graded ceramic–metal plates. In: Analysis and Design of Plated Structures: Stability. Woodhead Publishing, Cambridge, UK (2006)10.1201/9781439824658.ch6 ↗
11. Reddy, J.N., Arciniega, R.A.: Free vibration analysis of functionally graded plates. In: Analysis and Design of Plated Structures: Dynamics. Woodhead Publishing, Cambridge, UK (2006)10.1533/9781845692292.293 ↗
12. Arciniega, R.A., Reddy, J.N.: Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052 (2007)10.1016/j.ijsolstr.2006.08.035 ↗
13. Kim, K.D., Lomboy, G.R., Han, S.C.: Geometrically nonlinear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element. J. Compos. Mater. 42(5), 485–511 (2008)10.1177/0021998307086211 ↗
14. Barbosa, A.T., Ferreira, A.J.M.: Geometrically nonlinear analysis of functionally graded plates and shells. Mech. Adv. Mater. Struct. 17, 40–48 (2010)10.1080/15376490903082870 ↗
15. Tamura, I., Tomota, Y., Ozawa, H.: Strength and ductility of Fe–Ni–C alloys composed of austenite and martensite with various strength. Proceedings of the Third International Conference on Strength of Metals and Alloys, vol. 1, Cambridge: Institute of Metals, 611–5 (1973)
16. Nakamura, T., Wang, T., Sampath, S.: Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Mater. 48, 4293–4306 (2000)10.1016/S1359-6454(00)00217-2 ↗
17. Gu, Y., Nakamura, T., Prchlik, L., Sampath, S., Wallace, J.: Micro-indentation and inverse analysis to characterize elastic–plastic graded materials. Mater. Sci. Eng. A 345, 223–233 (2003)10.1016/S0921-5093(02)00462-8 ↗
18. Jin, J.H., Paulino, G.H., Dodds Jr., R.H.: Cohesive fracture modeling of elastic–plastic crack growth in functionally graded materials. Eng. Fract. Mech. 70(14), 1885–1912 (2003)10.1016/S0013-7944(03)00130-9 ↗
19. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M., Carrera, E.: Stress, vibration and buckling analyses of FGM plates: a state-of-the-art review. Compos. Struct. 120, 10–31 (2015)10.1016/j.compstruct.2014.09.070 ↗
20. Bao, G., Wang, L.: Multiple cracking in functionally graded ceramic/metal coatings. Int. J. Solids Struct. 32, 2853–2871 (1995)10.1016/0020-7683(94)00267-Z ↗
21. Delale, F., Erdogan, F.: The crack problem for a nonhomogeneous plane. ASME J. Appl. Mech. 50, 609–614 (1983)10.1115/1.3167098 ↗
22. Chung, Y.L., Chi, S.H.: The residual stress of functionally graded materials. J. Chin. Inst. Civil Hydraul. Eng. 13, 1–9 (2001)
23. Chi, S.H., Chung, Y.L.: Cracking in Sigmoid functionally graded coating. J. Mech. 18, 41–53 (2002)
24. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells, 2nd edn. CRC Press, Boca Raton (2004)10.1201/b12409 ↗
25. Moita, J.S., Barbosa, J.I., Mota Soares, C.M., Mota Soares, C.A.: Sensitivity analysis and optimal design of geometric nonlinear laminated plates and shells. Comput. Struct. 76, 407–420 (2000)10.1016/S0045-7949(99)00164-9 ↗
26. Hinton, E., Owen, R.R.J.: Finite Element Software for Plates and Shells. Pineridge Press, Swansea (1984)
27. Zienkiewicz, O.C.: The Finite Element Method. McGraw-Hill, New York (1977)
28. Bathe, K.J.: Finite Element Procedures in Engineering Analysis. Prentice-Hall Inc, Englewood Cliffs (1982)
29. Bathe, K.J., Ho, L.W.: A simple and effective element for analysis of general shell structures. Comput. Struct. 13, 673–681 (1981)10.1016/0045-7949(81)90029-8 ↗
30. Moita, J.S., Araújo, A.L., Martins, P.G., Mota Soares, C.M., Mota Soares, C.A.: Analysis of active-passive plate structures using a simple and efficient finite element model. Mech. Adv. Mater. Struct. 18, 159–169 (2011)10.1080/15376494.2010.496062 ↗
31. Moita, J.S., Mota Soares, C.M., Mota Soares, C.A.: Buckling behaviour of laminated composite structures using a discrete higher-order displacement model. Compos. Struct. 35, 75–92 (1996)10.1016/0263-8223(96)00025-6 ↗
32. Crisfield, M.A.: A fast incremental/iterative solution procedure that handles snap-through. Comput. Struct. 62, 13–55 (1980)
33. Supriyomo, M.H., Aliabadi, M.H.: Boundary element method for shear deformable plates with combined geometric and material nonlinearities. Eng. Anal. Boundary Elem. 30, 31–42 (2006)10.1016/j.enganabound.2005.08.005 ↗
34. Waidemam, L.: Formulação do método dos elementos de contorno para placas enrigecidas considerando-se não-linearidades física e geométrica. Tese de Doutorado, Universidade de S. Paulo, Escola de Engenharia de S. Carlos (2008) - In Portuguese. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-10092008-102729/en.php
35. ANSYS 14.0, Swanson Analysis Systems, Houston, USA (2011)