A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates

Abstract

In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic. . . ) to a multilayer C 0 z higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C 1 z function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag 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 a priori exactly verified by the transverse shear stress field. These C 0 z ESL models all have the same number of DOF as the original basis HSDT. Numerical assessments are presented by referring to a strong-form Navier-type 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 zig-zag models give better results than the basis models they are issued from.

Isogeometric static analysis of laminated plates with curvilinear fibers based on Refined Zigzag Theory

“…In the LW theory [1][2][3][4][5][6], the thickness coordinate is split into a number of analysis layers and the kinematic displacement fields of each analysis layer have been independently described which makes the theory computationally expensive and dependent on the number of layers considered. The ESL theories [7][8][9][10][11] treat a heterogeneous laminated plate as a statically equivalent, single layer having a complex constitutive behavior, thereby reducing the 3-D continuum problem into 2-D space.…”