Elastostatic assessment of several mixed/displacement-based laminated plate theories, differently accounting for transverse normal deformability

Abstract

Several multilayered physically-based plate theories are derived under different limiting assumptions on displacement, strain and stress fields, either in displacement-based or mixed Hu-Washizu and Helinger-Reissner form, and assuming different layerwise functions. Their features are reminiscent to those of theories published in the literature, or are entirely new. The present study aims to evaluate how different forms of description of the transverse normal deformation and stress affect accuracy. At the same time, the purpose is also to see if a much broader degree of generalization of what characterizing currently available physically-based zig-zag theories can be achieved through a redefinition of coefficients obtained by imposing the fulfillment of physical constraints, namely interfacial stress compatibility and local equilibrium equations across the thickness through use of symbolic calculus tool. Besides calculating exactly quantities, this tool enables users to choose representation form and zig-zag functions as desired, keeping fixed the d.o.f. to five. Challenging benchmarks with strong layerwise effects are considered, for which an accurate description of the transverse normal deformation effect is important. They include distributed/localized step loading and different boundary conditions. Effects of constraint stresses at supports are accounted for. Numerical results show that whenever the whole set of physical constraints is enforced across the thickness to redefine coefficients, the choice of the representation form and of zig-zag functions is immaterial and more importantly, accurate results are obtained with few variables and a low expansion order of solutions. Otherwise results are sensitive to the choices made.