Abstract
The nonlinear time-dependent displacement values of the curved (single/doubly) composite debonded shell structure are examined under different kinds of pulse loading in this research. The structural curved panel model is derived mathematically using the higher-order displacement theories containing the thickness stretching effect, whereas the sub-laminate approach is adopted for the inclusion of delamination between the subsequent layers. The structural geometry distortion under variable loading has been included in the current theoretical analysis through Green–Lagrange type of strain kinematics. Further, the governing differential equation order has been reduced with the help of 2D finite element formulation via the nine-noded isoparametric Lagrangian elements with variable degrees of freedom (eighty-one and ninety) for two different higher-order kinematics, respectively. The final equation of motion is solved computationally to evaluate the transient responses through an original computer code including the direct iterative technique and Newmark’s average acceleration method. The convergence criteria of the current numerical solution are established as a priori and the subsequent validity is demonstrated via comparing the current responses with available published data. Further, the comprehensive behavior of the debonded structure under the influence of the variable loads (time and area dependent) is evaluated by solving different numerical illustrations for variable geometrical configuration and described in detail.
Similar content being viewed by others
References
To CWS, Wang B (1998) Transient responses of geometrically nonlinear laminated composite shell structures. Finite Elem Anal Des 31:117–134. https://doi.org/10.1016/S0168-874X(98)00054-7
Yu TT, Yin S, Bui TQ, Hirose S (2015) A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates. Finite Elem Anal Des 96:1–10. https://doi.org/10.1016/j.finel.2014.11.003
Nath Y, Shukla KK (2001) Non-linear transient analysis of moderately thick laminated composite plates. J Sound Vib 247:509–526. https://doi.org/10.1006/jsvi.2001.3752
Yin S, Hale JS, Yu T, Bui TQ, Bordas SPA (2014) Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos Struct 118:121–138. https://doi.org/10.1016/j.compstruct.2014.07.028
Bui TQ, Nguyen MN, Zhang C (2011) A meshfree model without shear-locking for free vibration analysis of first-order shear deformable plates. Eng Struct 33:3364–3380. https://doi.org/10.1016/j.engstruct.2011.07.001
Amnieh HB, Zamzam MS, Kolahchi R (2018) Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically. Constr Build Mater 174:633–644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
Parhi A, Singh BN (2014) Stochastic response of laminated composite shell panel in hygrothermal environment. Mech Based Des Struct Mach 43:314–341. https://doi.org/10.1080/15397734.2014.888006
Panda SK, Singh BN, Parhi A, Singh BN (2017) Nonlinear free vibration analysis of shape memory alloy embedded laminated composite shell panel. Mech Adv Mater Struct 24:713–724. https://doi.org/10.1080/15376494.2016.1196777
Upadhyay AK, Pandey R, Shukla KK (2011) Nonlinear dynamic response of laminated composite plates subjected to pulse loading. Commun Nonlinear Sci Numer Simul 16:4530–4544. https://doi.org/10.1016/j.cnsns.2011.03.024
Tran LV, Lee J, Nguyen-van H, Nguyen-xuan H, Wahab MA (2015) Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory. Int J Non-Linear Mech 72:42–52. https://doi.org/10.1016/j.ijnonlinmec.2015.02.007
Zarei MS, Hajmohammad MH, Kolahchi R, Karami H (2018) Dynamic response control of aluminum beams integrated with nanocomposite piezoelectric layers subjected to blast load using hyperbolic visco-piezo-elasticity theory. J Sandw Struct Mater. https://doi.org/10.1177/1099636218785316
Wei J, Shetty MS, Dharani LR (2006) Stress characteristics of laminated architectural glazing subjected to blast loading. Comput Struct 84:699–707. https://doi.org/10.1016/j.ijimpeng.2005.05.012
Louca LA, Pan YG, Harding JE (1998) Response of stiffened and unstiffened plates subjected to blast loading. Eng Struct 20:1079–1086. https://doi.org/10.1016/S0141-0296(97)00204-6
Nath Y, Alwar RS (1978) Non-linear static and dynamic of spherical shells response. Int J Non-Linear Mech 13:157–170. https://doi.org/10.1016/S0141-0296(97)00204-6
Sun W, Liu X, Zhang Y (2018) Analytical analysis of vibration characteristics for the hard-coating cantilever laminated plate. Proc Inst Mech Eng Part G J Aerosp Eng 232:813–824. https://doi.org/10.1177/0954410016688926
Birman V, Bert CW (1987) Behaviour of laminated plates subjected to conventional blast. Int J Impact Eng 6:145–155. https://doi.org/10.1016/0734-743X(87)90018-2
Zhang YX, Kim KS (2005) A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates. Comput Methods Appl Mech Eng 194:4607–4632. https://doi.org/10.1016/j.cma.2004.11.011
Zhang YX, Kim KS (2005) Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element. Comput Mech 36:331–342. https://doi.org/10.1007/s00466-004-0625-6
Turkmen HS, Mecitoglu Z (1999) Nonlinear structural response of laminated composite plates subjected to blast loading. AIAA J 37:1639–1647. https://doi.org/10.2514/2.646
Kazanci Z, Mecitoglu Z (2006) Nonlinear damped vibrations of a laminated composite plate subjected to blast load. AIAA J 44:2002–2008. https://doi.org/10.2514/1.17620
Ganapathi M, Patel BP, Makhecha DP (2004) Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory. Compos Part B 35:345–355. https://doi.org/10.1016/S1359-8368(02)00075-6
Naidu NVS, Sinha PK (2006) Nonlinear finite element analysis of laminated composite shells in hygrothermal environments. Compos Struct 69:387–395. https://doi.org/10.1016/j.compstruct.2004.07.019
Pai PF, Nayfeh AH, Oh K, Mook DT (1993) A refined nonlinear model of composite plates with integrated piezoelectric actuators and sensors. Int J Solids Struct 30:1603–1630. https://doi.org/10.1016/0020-7683(93)90193-B
Amara K, Tounsi A, Megueni A, Adda-Bedia EA (2006) Effect of transverse cracks on the mechanical properties of angle-ply composites laminates. Theor Appl Fract Mech 45:72–78
Fellah M, Tounsi A, Amara KH, Adda Bedia EA (2007) Effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates. Theor Appl Fract Mech 48:32–40. https://doi.org/10.1016/j.tafmec.2007.04.007
Szekrényes A (2016) Vibration and parametric instability analysis of delaminated composite beams. Int J Mater Metall Eng 10:821–838. https://doi.org/10.1999/1307-6892/10004740
Szekrényes A (2017) Antiplane-inplane shear mode delamination between two second-order shear deformable composite plates. Math Mech Solids 22:259–282. https://doi.org/10.1177/1081286515581871
Yi G, Yu T, Bui TQ, Ma C, Hirose S (2017) SIFs evaluation of sharp V-notched fracture by XFEM and strain energy approach. Theor Appl Fract Mech 89:35–44. https://doi.org/10.1016/j.tafmec.2017.01.005
Kang Z, Bui TQ, Saitoh T, Hirose S (2017) Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments. Theor Appl Fract Mech 87:61–77. https://doi.org/10.1016/j.tafmec.2016.10.006
Bui TQ, Nguyen NT, Van Lich L, Nguyen MN, Truong TT (2018) Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods. Theor Appl Fract Mech 96:642–657. https://doi.org/10.1016/j.tafmec.2017.10.005
Mishra PK, Pradhan AK, Pandit MK (2016) Delamination propagation analyses of spar wingskin joints made with curved laminated FRP composite panels. J Adhes Sci Technol 30:708–728. https://doi.org/10.1080/01694243.2015.1121851
Mishra PK, Pradhan AK, Pandit MK (2016) Inter-laminar delamination analyses of Spar Wingskin Joints made with flat FRP composite laminates. Int J Adhes Adhes 68:19–29. https://doi.org/10.1016/j.ijadhadh.2016.02.001
Ovesy HR, Totounferoush A, Ghannadpour SAM (2015) Dynamic buckling analysis of delaminated composite plates using semi-analytical finite strip method. J Sound Vib 343:131–143. https://doi.org/10.1016/j.jsv.2015.01.003
Mohammadi B, Shahabi F, Ghannadpour SAM (2011) Post-buckling delamination propagation analysis using interface element with de-cohesive constitutive law. Proc Eng 10:1797–1802. https://doi.org/10.1016/j.proeng.2011.04.299
Dimitri R, Tornabene F, Zavarise G (2018) Analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams. Compos Struct 187:535–553. https://doi.org/10.1016/j.compstruct.2017.11.039
Reddy JN, Liu CF (1985) A higher-order shear deformation theory of laminated elastic shells. Int J Eng Sci 23:319–330. https://doi.org/10.1016/0020-7225(85)90051-5
Hari Kishore MDV, Singh BN, Pandit MK (2011) onlinear static analysis of smart laminated composite plate. Aerosp Sci Technol 15:224–235. https://doi.org/10.1016/j.ast.2011.01.003
Jones RM (1975) Mechanics of composite materials. Taylor and Francis, Philadelphia
Reddy JN (2004) Mechanics of laminated composite plates and shells, Second edn. CRC Press, Florida
Singh VK, Panda SK (2014) Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels. Thin-Walled Struct 85:341–349. https://doi.org/10.1016/j.tws.2014.09.003
Mahapatra TR, Panda SK (2015) Thermoelastic vibration analysis of laminated doubly curved shallow panels using non-linear FEM. J Therm Stress 38:39–68. https://doi.org/10.1080/01495739.2014.976125
Cook RD, Malkus DS, Plesha ME (2000) Concepts and applications of finite element analysis. John Willy and Sons (Asia) Pvt Ltd, Singapore
Ju F, Lee HP, Lee KH (1995) Finite element analysis of free vibration of delaminated composite plates. Compos Eng 5:195–209. https://doi.org/10.1016/0961-9526(95)90713-L
Ju F, Lee HP, Lee KH (1995) Free vibration of composite plates with delaminations around cutouts. Compos Struct 31:177–183. https://doi.org/10.1016/0263-8223(95)00016-X
Kumar A, Shrivastava RP (2005) Free vibration of square laminates with delamination around a central cutout using HSDT. Compos Struct 70:317–333. https://doi.org/10.1016/j.compstruct.2004.08.040
Bathe K-J, Ram E, Wilso EL (1975) Finite-element formulations for large deformation dynamic analysis. Int J Numer Method Eng. 9:353–386. https://doi.org/10.1002/nme.1620090207
Bathe K-J (1982) Finite element procedure in engineering analysis. Prentice-Hall, New Jersey
Wang YY, Lam KY, Liu GR (2001) A strip element method for the transient analysis of symmetric laminated plates. Int J Solids Struct 38:241–259. https://doi.org/10.1016/S0020-7683(00)00035-4
Maleki S, Tahani M, Andakhshideh A (2012) Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings. Arch Appl Mech 82:615–630. https://doi.org/10.1007/s00419-011-0577-1
Kundu CK, Sinha PK (2006) Nonlinear transient analysis of laminated composite shells. J Reinf Plast Compos 25:1129–1147. https://doi.org/10.1177/0731684406065196
Parhi PK, Bhattacharyya SK, Sinha PK (2000) Finite element dynamic analysis of laminated composite plates with multiple delaminations. J Reinf Plast Compos 19:863–882. https://doi.org/10.1177/073168440001901103
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hirwani, C.K., Panda, S.K. Nonlinear transient analysis of delaminated curved composite structure under blast/pulse load. Engineering with Computers 36, 1201–1214 (2020). https://doi.org/10.1007/s00366-019-00757-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-019-00757-6