A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates

A refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

“…Based on physical considerations and after some algebraic transformations, the number of unknowns becomes independent of the number of layers. Whitney [1969] has extended the work of Ambartsumyan [1969] for symmetric laminated composites with arbitrary orientation and a quadratic variation of the transverse stresses in each layer. A family of models, called zig-zag models, was first employed in [di Sciuva 1986], then in [Bhaskar and Varadan 1989;Lee et al 1992;Cho and Parmerter 1993].…”

“…The finite element method is also applied [Kant and Gupta 1988;Vinayak et al 1996;Subramanian 2001;Zhang and Kim 2005]. In the framework of thermomechanical problems, different approaches have been developed, including mixed formulations [Tessler et al 2001] and displacement-based ones [Rolfes et al 1998;Ali et al 1999;Rohwer et al 2001;Robaldo 2006]. …”

First-Order Displacement-Based Zigzag Theories for Composite Laminates and Sandwich Structures: A Review

“…In the ZZ models (as in ESL models), the number of kinematic unknowns does not depend on the number of layers. The in-plane displacements combine the smooth (generally, polynomial) functions defined across the entire laminate thickness (linear [37,38,39,40,41,52,55,56,57] or higher-order polynomial, [42,43,44,45,46,51,53,58,59] with the piecewise linear (i.e., zigzag) distributions. The zigzag contributions enable a more realistic modeling of the in-plane crosssectional distortion in multilayered composites, giving rise to a computationally efficient theory for the modeling of relatively thick laminated composite and sandwich structures.…”

“…Another first-order zigzag theory largely used in the literature [53,58,81,82,83,84,85] is the Murakami's zigzag theory [52], which shares with RZT the same kinematics, but different zigzag functions. As will be seen later, Murakami's zigzag functions are basically of geometrical nature, in the sense that the jump in their thickness-wise derivative depends only on the thickness of each layer, when the same jump in the derivative of the RZT zigzag functions depends on the lay-up and on the transverse shear elastic compliance of the layers.…”

Generalized plane strain thermoelastic deformation of laminated anisotropic thick plates

“…We refer the reader to Tauchert (1991), Noor and Burton (1992), Jones (1975) and Reddy (1997) for a historical perspective and for a review of various approximate theories. The validity of approximate plate theories and ®nite-element solutions can be assessed by comparing their predictions with the analytical solutions of the three-dimensional equations of anisotropic thermoelasticity (Noor et al, 1994;Murakami, 1993;Ali et al, 1999). Srinivas and Rao (1972) obtained a threedimensional solution for the¯exure of laminated, isotropic, simply supported plates.…”