Non-linear Dynamics Analysis of Multilayer Composite Shells with Enhanced Solid-Shell Elements
This paper presents the non linear dynamic response of multilayer composites with an enhanced solid-shell element. The transverse shear and transverse normal locking are treated using the Assumed Natural Strain formulation (ANS) . For the enhanced part, o
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Abstract This paper presents the non linear dynamic response of multilayer composites with an enhanced solid-shell element. The transverse shear and transverse normal locking are treated using the Assumed Natural Strain formulation (ANS). For the enhanced part, one, three and five parameters are examined. Comparisons of numerical results with those extracted from literature show the good performance of the developed formulation in the isotropic case. The three enhancement choices give the same results in the multilayer composite case. Keywords Nonlinear dynamic
Solid-shell elements Multilayer composites
1 Introduction Shell structures are widely used in aircraft and space systems due to their advantages of high stiffness and strength-to-weight ratios. Many shell elements which include 3D constitutive relations have been developed. Displacement-based solid elements are known to have poor performance in bending-dominated problems, such as in thin shells. To obtain the same performance as that of stress–resultant shell formulations with plane stress assumption, the class of volumetric shell or so-called solid-shell elements is a suitable alternative to pure volumetric element formulations. A. Hajlaoui E. Triki A. Frikha F. Dammak (&) Mechanical Modelisation and Manufacturing Laboratory (LA2MP), National Engineering School of Sfax, University of Sfax, B.P W3038, Sfax, Tunisia e-mail: [email protected] A. Hajlaoui e-mail: [email protected] E. Triki e-mail: [email protected] A. Frikha e-mail: [email protected] © Springer International Publishing Switzerland 2017 T. Fakhfakh et al. (eds.), Advances in Acoustics and Vibration, Applied Condition Monitoring 5, DOI 10.1007/978-3-319-41459-1_28
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To improve the bending behavior of low-order elements, the enhanced assumed strain, EAS, method was proposed by Simo and Rifai (1990). Klinkel et al. (1999), developed a solid-shell element with the ANS method for transverse strains and five parameters. Vu-Quoc and Tan (2003) proposed an EAS solid shell element with 7 parameters that pass the membrane and bending plate patch tests but does not completely eliminate volumetric locking (Hajlaoui et al. 2012). Betsch and Stein (1995) proposed a new interpolation function for thickness strains E33 for shell element and extended to solid-shell element by Klinkel et al. (1999). In the present eight-node solid-shell element, we use the EAS method. Three types of parameters have been analyzed: one, three and five parameters. For the transverse shear locking, the ANS formulation of Bathe and Dvorkin (1985) is used.
2 Basic Concept of the Non-linear Static Solid-Shell Element The fixed spatial coordinate system is defined by a triad (Ei), i = 1, 2, 3. Associated variables with the undeformed state will be denoted by upper-case letters and by a lower-case letters when referred to the deformed configuration. Parameterizations of the shell material points are carried out in terms of curvilinear coordinates n ¼ ðn1 ; n2 ; n3 Þ ¼ ðn; g; fÞ. T
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