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Data-driven Formulation of a Super Element for FE Analysis of Lattice Structures

Ashrafian, Ali | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56113 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen; Hosseini, Ehsan
  7. Abstract:
  8. Additive manufacturing enables fabricating lattice structures with tailored mechanical responses based on lattice materials. Full exploitation of such a possibility requires reliable and efficient mechanical analysis tools to be explored by topology optimization algorithms for designing the interior architecture of the structures to meet the desired mechanical behavior. However, detailed mechanical analysis of lattice-based structures using the conventional finite element approach is prohibitively expensive due to lattices’ complex and fine features that demand adopting very fine space discretization. As an alternative, equivalent models based on the homogenization principle have widely been used for analyzing lattice structures. Nevertheless, the validity requirements of the homogenization method are not adequately met, particularly for heterogeneous and graded lattice structures. Furthermore, homogenization fails to capture the true behavior of the lattice near the boundaries, and is not reliable when lattice dimensions are reduced below a certain limit. As an alternative solution, we propose substituting lattice unit cells with our novel partially averaged superelements, to govern the macroscopic response of unit cells by approximating the absolute or relative displacement of their boundary with finite series of linearly independent functions. Particular arrangements are proposed to control the computational expense by ”coarsening the superelements”, and a multi-layer perceptron is trained to assign cellular boundary conditions. In case of an inhomogeneous lattice, multivariate polynomial regression models are developed to predict the PASE stiffness matrix based on the unit cell topology. As a demonstrative example, we represent the BCC unit cells by a 24-node superelement having 216 or 432 DoFs for linear and quadratic approximations, respectively. The structural stiffness matrix of the superelement is computed for various strut diameters and then assembled to analyze small and large-scale lattices. The efficiency of the proposed methodology for various loading and domain sizes with uniform and graded architectures are evaluated by comparing it with the outcomes of high-fidelity mechanical analyses. It is shown that PASE outperforms the homogenization technique in predicting the total strain energy by up to 32% where size effects are noticeable. The method of PASE further reveals a remarkable accuracy of 97% in predicting the boundary effects. Moreover, PASE retains its accuracy and computational efficiency for large-scale lattice structures, making it an efficient substitute for the mainstream homogenization methods
  9. Keywords:
  10. Multi-Scale Analysis ; Homogenization ; Substructures ; Additive Manufacturing ; Lattice Structures ; Finite Element Analysis

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