A new zig-zag theory and C0 plate bending element for composite and sandwich plates

Abstract

A higher-order zig-zag theory for laminated composite and sandwich structures is proposed. The proposed theory satisfies the interlaminar continuity conditions and free surface conditions of transverse shear stresses. Moreover, the number of unknown variables involved in present model is independent of the number of layers. Compared to the zig-zag theory available in literature, the merit of present theory is that the first derivatives of transverse displacement have been taken out from the in-plane displacement fields, so that the C 0 interpolation functions is only required during its finite element implementation. To obtain accurately transverse shear stresses by integrating three-dimensional equilibrium equations within one element, a six-node triangular element is employed to model the present zig-zag theory. Numerical results show that the present zig-zag theory can predict more accurate in-plane displacements and stresses in comparison with other zig-zag theories. Moreover, it is convenient to obtain transverse shear stresses by integration of equilibrium equations, as the C 0 shape functions is only used when implemented in a finite element.

A unified theory for constitutive modeling of composites

“…The first-order sheardeformation theory was derived based on the assumption that the transverse normal remains straight and rigid, but does not necessarily remain normal. Many assumptions have been proposed in the literature including equivalent single-layer assumptions [Reddy 1984;Mantari et al 2012], layerwise assumptions [ Plagianakos and Saravanos 2009;Icardi and Ferrero 2010], and zigzag assumptions [Carrera 2003;Xiaohui et al 2011]. Recently, Carrera [2012] developed a unified formulation to systematically construct all these models based on a priori assumptions [Demasi and Yu 2012].…”

Mode shapes and frequencies of thin rectangular plates with arbitrarily varying non-homogeneity along two concurrent edges

“…During the past few decades, due to the development of high speed digital computers and numerical methodologies such as Lagrange multiplier technique (Ramkumar et al, 1987), hierarchical finite element method (Bardell, 1991), Kantorovich method (Sakata et al, 1996), finite strip method (Ashour, 2006), methods based on Green functions (Huang et al, 2007), Chebyshev collocation technique (Gupta et al, 2007), quintic splines methods (Lal and Dhanpati, 2007), hybrid method (Kerboua et al, 2007), superposition method (Bhaskar and Sivaram, 2008), boundary knot method (Shi et al, 2009), element-free kp-Ritz method (Zhao et al, 2009), discrete singular convolution method (Civalek et al, 2010), finite cosine integral transform method (Zhong et al, 2014), finite element method (Xiaohui et al, 2011;Houmat, 2012), differential transform method (Semnani et al, 2013), symplectic geometry method (Hu et al, 2012), Ritz method (Eftekhari and Jafari, 2013), unified formulation-cell based smoothed finite element method (Natarajan et al, 2013), local Kriging meshless method (Zhang et al, 2014), etc, a huge amount of work analyzing the dynamic behaviour of plates of various geometries with different boundary conditions has been reported in the literature. In the recent years, differential quadrature (DQ) method introduced by Bellman and Casti (1971) and Bert et al (1988) and its improved versions proposed by Shu and Richards (1992) as generalized differential quadrature (GDQ) method, Striz et al (1995) as harmonic differential quadrature (HDQ) method, Shu and Chew (1997) as Fourier expansionbased differential quadrature (FDQ) method, Liu and Wu (2001) as generalized differential quadrature rule (GDQR), Karami and Malekzadeh (2013) as new differential quadrature (NDQ) method, Krowiak (2006aKrowiak ( , 2006b as spli...…”

Untitled

“…[ Plagianakos and Saravanos 2009;Icardi and Ferrero 2010], and zigzag assumptions [Carrera 2003;Xiaohui et al 2011]. Recently, Carrera [2012] developed a unified formulation to systematically construct all these models based on a priori assumptions [Demasi and Yu 2012].…”