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Strategic Latency Unleashed: The Role of Technology in a Revisionist Global Order and the Implications for Special Operations Forces
The article of record may be found at https://cgsr.llnl.govThis work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory in part under Contract W-7405-Eng-48 and in part under Contract DE-AC52-07NA27344. The views and opinions of the author expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC. ISBN-978-1-952565-07-6 LCCN-2021901137 LLNL-BOOK-818513 TID-59693This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory in part under Contract W-7405-Eng-48 and in part under Contract DE-AC52-07NA27344. The views and opinions of the author expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC. ISBN-978-1-952565-07-6 LCCN-2021901137 LLNL-BOOK-818513 TID-5969
A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates
The Refined Zigzag Theory (RZT) has been widely used in the numerical analysis of multilayered
and sandwich plates in the last decay. It has been demonstrated its high accuracy in predicting global quantities, such as maximum displacement, frequencies and buckling loads, and local quantities such
as through-the-thickness distribution of displacements and in-plane stresses [1,2]. Moreover, the C0
continuity conditions make this theory appealing to finite element formulations [3]. The standard RZT,
due to the derivation of the zigzag functions, cannot be used to investigate the structural behaviour
of angle-ply laminated plates. This drawback has been recently solved by introducing a new set of
generalized zigzag functions that allow the coupling effect between the local contribution of the zigzag
displacements [4]. The newly developed theory has been named enhanced Refined Zigzag Theory (en-
RZT) and has been demonstrated to be very accurate in the prediction of displacements, frequencies,
buckling loads and stresses. The predictive capabilities of standard RZT for transverse shear stress
distributions can be improved using the Reissner’s Mixed Variational Theorem (RMVT). In the mixed
RZT, named RZT(m) [5], the assumed transverse shear stresses are derived from the integration of local
three-dimensional equilibrium equations. Following the variational statement described by Auricchio
and Sacco [6], the purpose of this work is to implement a mixed variational formulation for the en-RZT,
in order to improve the accuracy of the predicted transverse stress distributions. The assumed kinematic
field is cubic for the in-plane displacements and parabolic for the transverse one. Using an appropriate
procedure enforcing the transverse shear stresses null on both the top and bottom surface, a new set
of enhanced piecewise cubic zigzag functions are obtained. The transverse normal stress is assumed as
a smeared cubic function along the laminate thickness. The assumed transverse shear stresses profile
is derived from the integration of local three-dimensional equilibrium equations. The variational functional
is the sum of three contributions: (1) one related to the membrane-bending deformation with a
full displacement formulation, (2) the Hellinger-Reissner functional for the transverse normal and shear
terms and (3) a penalty functional adopted to enforce the compatibility between the strains coming
from the displacement field and new “strain” independent variables. The entire formulation is developed
and the governing equations are derived for cases with existing analytical solutions. Finally, to assess
the proposed model’s predictive capabilities, results are compared with an exact three-dimensional solution,
when available, or high-fidelity finite elements 3D models. References: [1] Tessler A, Di Sciuva
M, Gherlone M. Refined Zigzag Theory for Laminated Composite and Sandwich Plates. NASA/TP-
2009-215561 2009:1–53. [2] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. Assessment of the Refined
Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different
theories. Composite Structures 2013;106:777–92. https://doi.org/10.1016/j.compstruct.2013.07.019.
[3] Di Sciuva M, Gherlone M, Iurlaro L, Tessler A. A class of higher-order C0 composite and sandwich
beam elements based on the Refined Zigzag Theory. Composite Structures 2015;132:784–803.
https://doi.org/10.1016/j.compstruct.2015.06.071. [4] Sorrenti M, Di Sciuva M. An enhancement
of the warping shear functions of Refined Zigzag Theory. Journal of Applied Mechanics 2021;88:7.
https://doi.org/10.1115/1.4050908. [5] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. A Multi-scale
Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear
Stresses, Ibiza, Spain: 2013. [6] Auricchio F, Sacco E. Refined First-Order Shear Deformation Theory
Models for Composite Laminates. J Appl Mech 2003;70:381–90. https://doi.org/10.1115/1.1572901