No abstract

The aim of this paper is to create novel 3D cubic negative stiffness structures (NSSs) with superior mechanical performances such as high energy absorption, shape recovery, super-elasticity, and reversibility. The conceptual design is based on an understanding of geometrical influences, non-linear buckling-type instability, snap-through mechanism, elasto-plastic deformation growth and plastic hinges. A finite element (FE) based computational model with an elasto-plastic material behavior is developed to design and analyze NSSs, saving time, material, and energy consumption. Material samples and meta-structures are 3D printed by selective laser sintering printing method. Material properties are determined via mechanical testing revealing that the printing process does not introduce much anisotropy into the fabricated parts. Experimental tests are then conducted to study the behavior of novel designs under loading-unloading cycles verifying the accuracy of the computational model. A good correlation is observed between experimental and numerical data revealing the high accuracy of the FE modeling. The structural model is then implemented to digitally design and test NSSs. Effects of the geometrical parameters of the negative stiffness members under three cyclic loading are investigated, and their implications on the non-linear mechanical behavior of NSSs under cyclic loading are put into evidence, and pertinent conclusions are outlined. In addition, the dissipated energy and loss factor values of the designed structures are studied and the proposed UC is presented for the energy absorbing systems. The results show that the structural and geometry of energy absorbers are key parameters to improve the energy absorption capability of the designed structures. This paper is likely to fill a gap in the state-of-the-art NS meta-structures and provide guidelines that would be instrumental in the design of NSS with superior energy absorption, super-elasticity and reversibility features.

<p style='text-indent:20px;'>In this paper, we first study the skew cyclic codes of length <inline-formula><tex-math id="M3">\begin{document}$ p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M4">\begin{document}$ R_3 = \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}, $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M5">\begin{document}$ p $\end{document}</tex-math></inline-formula> is a prime number and <inline-formula><tex-math id="M6">\begin{document}$ u^3 = 0. $\end{document}</tex-math></inline-formula> Then we characterize the algebraic structure of <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{F}_{p^{m}}\mathbb{F}_{p^{m}}[u^2] $\end{document}</tex-math></inline-formula>-additive skew cyclic codes of length <inline-formula><tex-math id="M8">\begin{document}$ 2p^s. $\end{document}</tex-math></inline-formula> We will show that there are sixteen different types of these codes and classify them in terms of their generators.</p>