Abstract

Abstract

Topology optimization has undergone tremendous development since its introduction by Bendsøe and Kikuci in 1988, especially in recent years, due to its involvement in revolutionary generative design techniques. This paper aims to lay the foundations of a generative design methodology powered by an alternative approach to the well-known density methods. Based on finite element analysis, the objective is to develop an optimization algorithm with the Young modulus of the elements as design variables. That way, while previous studies have focused on void/solid distributions, this study searches for a distribution of different E values that could be manufactured due to progress in metamaterials and additive manufacturing. A mimetic metamaterial was also developed to be coupled with the topological optimization, but will not be included in this paper. To assess the optimization algorithm, several analyses have been carried out under different load and boundary conditions. The outcome shows correlation with our initial hypothesis: elements under higher strains increase their stiffness value, while the opposite occurs for those under minor stresses. Consequently, the results present a structure with a Young modulus distribution that optimizes the strain energy, and therefore, reduces the displacements.

Abstract

Metamaterials are generated from an interrelated set of cells and can present a macroscopic behaviour that differs from the one that characterizes its basic constituents. Modelling the influence that the damage and fracture of the elemental constituents have in the macroscopic properties of the metamaterial is relevant for its mechanical analysis. Altering the resistant behaviour of the elements (changing their longitudinal elastic modulus), it is possible to approximate the effect of the damage in the complete structure.  It is considered as valid the substitution of the damage and plastic deformation phenomena by intermediate states contained in the linear elastic deformation regime. Each state is characterized by the elastic module of the element, whose geometry remains unmodified. In an iterative process, when the induced stress in the elements is greater than the one stablished as the limit, they progress through the different states, diminishing their elastic modulus until they are considered as fractured and are eliminated from the structure. Mass effects are ignored, and a stress-free structure is implemented to calculate each iteration. A simple algorithm is presented to simulate the effect of damage in metamaterial structures, applicable to any finite element software.

Abstract

This work analyzes structural waves that propagate freely along taut cables, characterized by a discrete array of scatter elements. The outcomes underline the role played by the periodic distribution of such elements, whose presence alters the response of the system when subjected to propagating waves. Namely, when the domain is perfectly periodic, band gaps are found in the spectrum of the problem. It is also shown that the introduction of a defect of periodicity can lead to the appearance of eigenvalues inside band gaps, corresponding to a motion localized around the defect.

Abstract

Abstract