A family of higherorder single layer plate models meeting $C^0_z$  requirements for arbitrary laminates
Abstract
In the framework of displacementbased equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higherorder shear deformation theory (polynomial, trigonometric, hyperbolic, ...) to a multilayer $C^0_z$ higherorder shear deformation theory. The key idea is to enhance the description of the crosssectional warping: the odd highorder $C^1_z$ function of the basis model is replaced by one odd and one even highorder function and including the characteristic zigzag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are considered. The coefficients of these four warping functions are determined in such a manner that the interlaminar continuity as well as the homogeneity conditions at the plate's top and bottom surfaces are {\em a priori} exactly verified by the transverse shear stress field. These $C_z^0$ ESL models all have the same number of DOF as the original basis HSDT. Numerical assessments are presented by referring to a strongform Naviertype solution for laminates with arbitrary stacking sequences as well for a sandwich plate. In all practically relevant configurations for which laminated plate models are usually applied, the results obtained in terms of deflection, fundamental frequency and local stress response show that the proposed zigzag models give better results than the basis models they are issued from.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.00720
 Bibcode:
 2019arXiv190500720L
 Keywords:

 Physics  Classical Physics
 EPrint:
 Composite Structures, Elsevier, 2019, pp.111146