#### Vol. 5, No. 2, 2010

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

### Alexander Tessler, Marco Di Sciuva and Marco Gherlone

Vol. 5 (2010), No. 2, 341–367
##### 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 shear-force 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.

##### Keywords
first-order shear deformation plate theory, zigzag kinematics, laminated composite plates, sandwich plates, virtual work principle
##### Milestones
Received: 23 March 2009
Revised: 7 August 2009
Accepted: 13 August 2009
Published: 30 August 2010
##### Authors
 Alexander Tessler Structural Mechanics and Concepts Branch NASA Langley Research Center Mail Stop 190 Hampton, VA 23681-2199 United States Marco Di Sciuva Department of Aeronautics and Space Engineering Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy Marco Gherlone Department of Aeronautics and Space Engineering Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy