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Finite Element Analysis of Thermally-Induced Bistable Plate Using Four Plate Elements

Authors: Jixiao Tao, Xiaoqiao He


The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Finite element method, geometrical nonlinearity, bistable, quadrilateral plate elements.

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[1] O. Bilgen, A. F. Arrieta, M. I. Friswell, and P. Hagedorn 2013 Dynamic control of a bistable wing under aerodynamic loading Smart. Mater. Struct. 22 025020
[2] X. Lachenal, S. Daynes, and P. M. Weaver 2013 Review of morphing concepts and materials for wind turbine blade applications Wind Energy. 16 283-307
[3] S. Daynes and P. M. Weaver 2013 Review of shape-morphing automobile structures: concepts and outlook P. I. Mech. Eng. D-J. Aut. 227 1603-1622
[4] A. F. Arrieta, P. Hagedorn, A. Erturk, and D. J. Inman 2010 A piezoelectric bistable plate for nonlinear broadband energy harvesting Appl. Phys. Lett. 97 104102
[5] A. F. Arrieta, T. Delpero, A. E. Bergamini, and P. Ermanni 2013 Broadband vibration energy harvesting based on cantilevered piezoelectric bi-stable composites Appl. Phys. Lett. 102 173904
[6] M. W. Hyer 1981 Some observations on the cured shape of thin unsymmetric laminates J. Compos.Mater. 15 175-194
[7] M.-L. Dano and M. W. Hyer 1998 Thermally-induced deformation behavior of unsymmetric laminates Int. J. Solids. Struct. 35 2101-2120
[8] W. Hufenbach, M. Gude, L. Kroll, A. Sokolowski, and B. Werdermann 2001 Adjustment of residual stresses in unsymmetric fiber-reinforced composites using genetic algorithms Mech. Compos. Mater. 37 71-78
[9] W. Hufenbach, M. Gude, and L. Kroll 2002 Design of multistable composites for application in adaptive structures Compos. Sci. Technol. 62 2201-2207
[10] M. Gigliotti, M. R. Wisnom, and K. D. Potter 2004 Loss of bifurcation and multiple shapes of thin
[0/90] unsymmetric composite plates subject to thermal stress Compos. Sci. Technol. 64 109-128
[11] M.-L. Dano and M. W. Hyer 2002 Snap-through of unsymmetric fiber-reinforced composite laminates Int. J. Solids. Struct. 39 175-198
[12] C. G. Diaconu, P. M. Weaver, and A. F. Arrieta 2009 Dynamic analysis of bi-stable composite plates J. Sound. Vib. 322 987-1004
[13] Z. Zhang, H. Wu, G. Ye, J. Yang, S. Kitipornchai, and G. Chai 2016 Experimental study on bistable behaviour of anti-symmetric laminated cylindrical shells in thermal environments Compos. Struct. 144 24-32
[14] S. Daynes, K. Potter, and P. Weaver 2008 Bistable prestressed buckled laminates Compos. Sci. Technol. 68 3431-3437
[15] H. Li, F. Dai, P. M. Weaver, and S. Du 2014 Bistable hybrid symmetric laminates Compos. Struct. 116 782-792
[16] X. Q. He, L. Li, S. Kitipornchai, C. M. Wang, and H. P. Zhu 2012 Bi-Stable Analyses of Laminated Fgm Shells Int. J. Struct. Stab. Dy. 12 311-335
[17] Z. Zhang, B. Chen, C. Lu, H. Wu, H. Wu, S. Jiang, et al. 2017 A novel thermo-mechanical anti-icing/de-icing system using bi-stable laminate composite structures with superhydrophobic surface Compos. Struct. 180 933-943
[18] D. N. Betts, R. A. Guyer, P.-Y. Le Bas, C. R. Bowen, D. Inman, and H. A. Kim 2014 Modelling the Dynamic Response of Bistable Composite Plates for Piezoelectric Energy Harvesting
[19] Y. X. Zhang and K. S. Kim 2004 Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates International Journal for Numerical Methods in Engineering. 61 1771-1796
[20] S. Tawfik, X. Tan, S. Ozbay, and E. Armanios 2006 Anticlastic Stability Modeling for Cross-ply Composites J. Compos.Mater. 41 1325-1338
[21] A. Haldar, J. Reinoso, E. Jansen, and R. Rolfes 2018 Thermally induced multistable configurations of variable stiffness composite plates: Semi-analytical and finite element investigation Compos. Struct. 183 161-175 G. O. Young, “Synthetic structure of industrial plastics (Book style with paper title and editor),” in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New York: McGraw-Hill, 1964, pp. 15–64.