Optimization of three-dimensional truss-like periodic materials considering isotropy constraints

Abstract

In recent years, much attention has been directed to the study of ultralight periodic cellular materials, such as the so called Periodic Truss Materials (PTMs), which are made up of truss-like unit cells. Application of these materials has its best potential in structures subjected to multifunctional, and sometimes conflicting, engineering requirements. Hence, optimization techniques can be employed to help finding the shape of the optimal unit cell for a given multifunctional application. Although the result can be geometrically complex, this difficulty can be minored in view of modern additive manufacturing technologies. This work presents a parameter/ topology optimization procedure to design the particular unit cell geometry (that is, finding the cross sections of the bars) that results in a macroscopic material with optimum homogenized elastic or/and thermal constitutive properties. Emphasis is devoted to analyze the effect of enforcing independently elastic or thermal isotropy in the macroscopic material behavior. Although isotropic behavior can be imposed through adequate cell symmetries, an equivalent effect can be achieved by satisfying equality constraints relating constitutive coefficients. A sequential quadratic programming algorithm (SQP) is adopted, thus enforcing equality constraints gradually and within a tolerance range. This results in an enlarged search space at intermediate stages, rendering an effective strategy to solve the optimization problem. Different 3D cases with engineering appeal are solved and the results discussed.

Potentiale additiv gefertigter Gitterstrukturen – ein Review

“…Dies ermöglicht auch die gezielte Nutzung von Anisotropie in der Bauteilgestaltung. [43] Auch die Querkontraktionszahl kann durch die gezielte Wahl der Elementarzelle beeinflusst werden, bis hin zu auxetischen Materialeigenschaften, also einer negativen Querkontraktionszahl [44,45]. Die Querkontraktionszahl muss dabei nicht homogen über das Bauteil verteilt sein, sondern kann einem definierten Verlauf folgen.…”

Concurrent optimization of structural topology and infill properties with a CBF-based level set method

“…18is hold. An isotropy polar plot index [70] is utilized in this research to visualize the isotropy of the infill structure throughout its optimization process, for an easy isotropy monitoring. The details are introduced as follows: For a unit cell with a rotation of angle , as shown in Fig.…”

“…To address this issue, an isotropic infill micro/meso structure is designed to be filled into the interior infill region. The isotropy of the infill structure is ensured by imposing the isotropy constraint [67][68][69][70] to the topology optimization process. As for the mapping, a local shape-preserving conformal mapping is employed in this research.…”

An Extended Multiscale Finite Element Method (EMsFEM) Analysis of Periodic Truss Metamaterials (PTMM) Designed by Asymptotic Homogenization

“…Muñoz-Rojas et al (2010) proposed the layout optimization (simultaneous cross sectional areas and coordinates as design variables) of truss-made unit cells for achieving optimum thermo-mechanical periodic truss metamaterials. Guth et al (2012Guth et al ( , 2015 optimized the layout of PTMMs including mechanical and thermal isotropic behavior as constraints in the optimization problem. All these works aimed at the optimization of material properties for a prescribed condition (shear stiffness, for instance) but they did not consider the pointwise response of a component made up of such material.…”