Abstract
A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).
Highlights
Fibre-reinforced laminated and sandwich composites are fundamental to obtain a faster speed, longer range, larger payloads, less engine power, and a better operating economy of land, sea, and aerospace vehicles
The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.))
A rather large dispersion of results is shown for uς and for the transverse normal stress, while the transverse shear stress is erroneously provided by HRZZ, HRZZ4, MHWZZA, MHWZZA4, MHR, and MHR4 only across the first layer
Summary
Fibre-reinforced laminated and sandwich composites are fundamental to obtain a faster speed, longer range, larger payloads, less engine power, and a better operating economy of land, sea, and aerospace vehicles. It is necessary to better clarify what effects have an a priori assumption of certain zig-zag amplitudes at certain interfaces, or even to all of the interfaces such as in MZZ, in order to save costs To contribute to this matter, in this paper, zig-zag theories in displacement-based and mixed form are particularized from the ZZA 3D zig-zag theory [29], assuming different layerwise functions. The accuracy and the efficiency of these theories, which for the most part allow a redefinition of the coefficients layer-by-layer so as to satisfy all of the physical constraints and account for the normal transverse deformability effect ( in different ways), are assessed considering the free vibration and the response behaviour of blast-loaded multilayered and sandwich plates.
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