Abstract in English:

Abstract This research aims to evaluate the impact of the initial cell configuration and the limit volume fraction on the generation of mechanical metamaterial cells. The procedure was developed using a methodology based on preprocessing, processing, and post processing to facilitate fast exploration of metamaterial cell space design. The initial cell consisted of a square or cube of material with a central circular or spherical void diameters of 10 mm, 20 mm, and 30 mm. Additionally, the generation process employed three volume fractions limits (30%, 40%, and 50%) and eleven objective functions. These functions intended to generate cells that maximize stiffness in one or multiple directions and cells with maximum compressibility or shear modulus. Some of the obtained cells with tailored mechanical properties exhibit novel geometrical configurations. The results highlight volume fraction as the most significant factor in the generation process, with well-defined metamaterial cells produced using an initial volume fraction of 50% and low to medium void diameters.

Abstract in English:

Abstract For the first time, this article uses higher-order IGA to study the high frequency of the functionally graded sandwich (FGS) square nanoplates with two different skin layers resting on elastic foundations. In this work, the elastic foundations use the Pasternak foundation (PF) model with a two-parameter as a spring stiffness (k1) and a shear layer stiffness (k2). The observation of small-scale effects in nanoplates is accomplished by incorporating nonlocal elasticity theory (NET) with a higher-order shear deformation theory (HSDT). The governing equation of nanoplates is derived from Hamilton's principle. An extensive parametric investigation has been conducted to illustrate the free vibration characteristics of FGS square nanoplates across both low and high frequency modes, placing a greater emphasis on the analysis of high frequency behaviour. Furthermore, the high eigenmodes and frequencies of the FGS circular/elliptical nanoplates are also added. Therefore, the findings presented here contribute to an improved understanding of the vibrations of FGS nanoplates at high frequencies.

Abstract in English:

Abstract A structural analysis of framed structures using the finite element method considering both the Bernoulli- Euler and the Timoshenko beam theories can be performed adopting cubic interpolation functions that yield analytical solutions for the displacements. However, these theories may not provide stress results with sufficient accuracy. In such cases, it is necessary to employ higher order beam formulations, that may require a high level of discretization. Therefore, this study proposes an enhanced Reddy beam element, obtained by considering interpolation functions calculated directly from the solution of the differential equation system. This solution minimizes the impact of structural discretization on the analysis, and framed structures can be effectively modeled considering the minimum number of elements required to describe the geometry. The results obtained by the proposed formulation were compared against classical beam theories and the Reddy beam model adopting conventional shape functions, showing the efficacy of the proposed element in simulating the elastic behavior of framed structures in a FEM-like procedure.