A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics

Abstract

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions are used, providing a more realistic representation of the deformation states of transverse shear-flexible plates than other similar theories. The formulation does not enforce full continuity of the transverse shear stresses across the plate's thickness, yet it is robust. Transverse shear correction factors are not required to yield accurate results. The theory avoids the shortcomings of earlier zigzag theories (such as shearforce inconsistency and difficulties in simulating clamped boundary conditions) which have limited their accuracy. This new theory requires only C 0 -continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. It should be useful for obtaining relatively efficient, accurate estimates of structural response, needed in designing high-performance load-bearing aerospace structures.A list of symbols can be found on page 363.

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part I: Model formulation

“…As an alternative ZZ function, the Refined Zigzag Theory (RZT) developed by Tessler, Di Sciuva and Gherlone [36][37][38][39] may be used. The kinematics of RZT are essentially those of a first-order shear deformation theory enhanced by ZZ variables ψ i (x, y) that are multiplied by piecewise continuous transverse functions φ (k)…”

Two-noded zigzag beam element accounting for shear effects based on an extended Euler Bernoulli theory

“…The beam segment is defined in the ( , ) x z Cartesian system, where x is the beam longitudinal axis and z is the thickness coordinate. The superscript k denotes quantities within the th k layer with Using the same notation as for the RZT [18,19,21,23], we propose the following displacement field for the th k layer…”

“…Different works [18][19][20] have shown that beam models requiring 1 C continuity for the deflection field, such as that presented in Eq. (1), have theoretical difficulties to represent correctly the shear strain and the shear stress distributions in a clamped support where the following kinematic conditions are required…”

“…Zigzag theories typically have as baseline the kinematics assumptions of the classical EulerBernoulli [14,15] and Timoshenko [16][17][18][19] beam theories (EBT and TBT). Some researchers consider that the 1 C continuity requirement for the deflection field of the EBT is a drawback versus the simpler 0 C requirement of the TBT [18,20].…”

“…Tessler et al [18,19] have recently developed a Refined Zigzag Theory (RZT) for beams and plates based in the TBT kinematic assumptions. In this theory the zigzag functions have the property of vanishing on the top and bottom surfaces of the laminate.…”