Abstract
A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software.
Highlights
Shell structures are becoming very popular due to their typical curved shapes that can characterize the structural behavior of these elements
The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect
The paper can be placed in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software
Summary
Shell structures are becoming very popular due to their typical curved shapes that can characterize the structural behavior of these elements. Starting from the same ideas of FGMs, the class of functionally-graded Carbon Nanotube-reinforced composites is becoming very popular due to the introduction of nanoparticles as the reinforcing phase in the composite medium [61,62,63,64,65,66,67,68,69] Even in this circumstance, the variation of the mechanical properties is obtained by defining the volume fraction distribution of the constituents by means of different through-the-thickness laws. A different kind of composite material has been developed to obtain a variation of its properties within the domain defined by the middle surface of the structure Such variability can be achieved by changing the orientation of the fiber in each point of the domain. A posteriori recovery procedure based on the three-dimensional equilibrium equations is proposed
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