PSI - Issue 28

Florian Vlădulescu et al. / Procedia Structural Integrity 28 (2020) 637–647 Vl ă dulescu and Constantinescu / Structural Integrity Procedia 00 (2019) 000–000

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spatial distribution, as designing a material with periodic and gradient density topologies, such as to enhance the overall material toughness, without compromising its strength and modulus. This can be achieved by combining experimentally hard and soft subdomains within the material, much in the spirit of tough materials developed by nature, such as bone and nacre, where the soft subdomains perform the role of crack trapping, while the hard subdomains provide strength and stiffness. A special attention is given nowadays to FE 2 methods that can be used for the analysis of heterogeneous materials at the continuum macroscale while simultaneously accounting for the microstructural details. FE 2 analyses typically comprise two levels of Finite Element (FE) simulations that are performed concurrently. At the macroscale level, the entire heterogeneous material or structure is discretized into homogenized continuum finite elements. Homogenized constitutive relations are not required for the macroscale calculations. Instead they are obtained from microscale level FE simulations on representative volume elements (RVE) of the material where the different phases of the heterogeneous material are explicitly modelled. The Direct FE 2 models are shown to give similar results to full FE meshes of heterogeneities throughout the entire domain with significantly less degrees of freedom. It was demonstrated that in-built capabilities of the commercial codes are naturally available with Direct FE 2 through examples (Choi and Chae 2015), involving large deformation, plasticity, and viscoelasticity. Homogenization based topology optimization (HMTO) was used by Cheng et al. (2017) to optimize components with cellular structure. In this methodology, the macroscopic (or effective) mechanical properties of cellular structures are described by anisotropic constitutive laws without modelling the microstructures in detail. The authors showed that based on a set of computational data, a formulation of relative density is proposed to represent the equivalent material properties of certain cellular structure. For optimization, the penalization formulation used in standard topology optimization by Bendsøe and Sigmund (1999) is replaced with the fitted homogenized model. This methodology would preserve the original design shape, as regions having optimal relative density as zero or close to zero would become low density cellular structure. This type of approach is also used in the ANSYS software. The authors used in their work ANSYS (version 16.1) to conduct the computational homogenization simulation. The homogenization procedure used an equivalent continuous solid to represent a cellular structure (Deshpande et al. 2001) by introducing a homogenized material constitutive law, which is a function of the cellular structure’s microstructure characterizing parameters as relative density and cell orientation as also done before by Simone and Gibson (1988). For a given cellular structure designers can obtain the microstructure characterizing parameters constitutive laws from computational micromechanics models or experimental tests. An analysis to maximize the first eigenfrequency of the lattice structure was done by Cheng et al. (2018) by considering the lattice infill as a continuum material with equivalent elastic properties obtained from asymptotic homogenization. The present study is done in two stages. Using a geometric model, a FE analysis is performed by using the software ANSYS 2019 R3 (2019a, 2019b, 2019c) as to obtain the first natural frequency of a mounting bracket used for an industrial robotic arm. Starting from this initial design, an optimized lattice model is obtained and in the next approach a homogenized model with variable material properties specially defined with this type of structural component is created. The path from lattice optimization to model homogenization is a solution as to simplify the numerical calculations and reduce costs. A comparison between the results on the increase of the fundamental frequency and decrease of mass obtained on the two design approaches is performed. In the second stage crack propagation was simulated in ANSYS by using the SMART (Separating Morphing and Adaptive Remeshing Technology) crack growth simulation. An initial artificial crack of 50 mm was generated along the axis of symmetry and off-axis. Comments on the practical use of this methodology are done. 2. Case study description In general, topological optimization is based on a set of loads and boundary conditions provided by one or more previous sets of results. The topological optimization analysis itself may be preceded by a structural analysis or several coupled structural analyses. Loads and boundary conditions defined in the upstream analysis are used to create an optimized structural component based on the objectives and constraints specified in the topological optimization analysis. It is necessary to use the same loads and boundary conditions in the validation analysis of the optimized design.