Topology optimization of periodic microstructures with a penalization of highly localized buckling modes

2002 ◽  
Vol 54 (6) ◽  
pp. 809-834 ◽  
Author(s):  
Miguel M. Neves ◽  
Ole Sigmund ◽  
Martin P. Bendsøe
Keyword(s):  
Topology Optimization ◽  
Buckling Modes ◽  
Periodic Microstructures ◽  
Localized Buckling

Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

scholarly journals Topology optimization of modulated and oriented periodic microstructures by the homogenization method

2019 ◽  
Vol 78 (7) ◽  
pp. 2197-2229 ◽  
Author(s):  
Grégoire Allaire ◽  
Perle Geoffroy-Donders ◽  
Olivier Pantz
Keyword(s):  
Topology Optimization ◽  
Homogenization Method ◽  
Periodic Microstructures

scholarly journals 3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

2020 ◽  
Vol 401 ◽  
pp. 108994 ◽  
Author(s):  
Perle Geoffroy-Donders ◽  
Grégoire Allaire ◽  
Olivier Pantz
Keyword(s):  
Topology Optimization ◽  
Homogenization Method ◽  
Periodic Microstructures

Topology Optimization Under Linear Thermo-Elastic Buckling

2016 ◽  
Author(s):  
Shiguang Deng ◽  
Krishnan Suresh
Keyword(s):  
Topology Optimization ◽  
Augmented Lagrangian ◽  
Thermal Environment ◽  
Augmented Lagrangian Method ◽  
Compressive Load ◽  
Elastic Buckling ◽  
Buckling Modes ◽  
Thermally Induced ◽  
Stiffness Matrices ◽  
Level Set Approach

This paper focuses on topology optimization of structures subject to a compressive load in a thermal environment. Such problems are important, for example, in aerospace, where structures are prone to thermally induced buckling. Popular strategies for thermo-elastic topology optimization include Solid Isotropic Material with Penalization (SIMP) and Rational Approximation of Material Properties (RAMP). However, since both methods fundamentally rely on material parameterization, they are often challenged by: (1) pseudo buckling modes in low-density regions, and (2) ill-conditioned stiffness matrices. To overcome these, we consider here an alternate level-set approach that relies discrete topological sensitivity. Buckling sensitivity analysis is carried out via direct and adjoint formulations. Augmented Lagrangian method is then used to solve a buckling constrained compliance minimization problem. Finally, 3D numerical experiments illustrate the efficiency of the proposed method.

scholarly journals Topology optimization for designing periodic microstructures based on finite strain viscoplasticity

2020 ◽  
Vol 61 (6) ◽  
pp. 2501-2521
Author(s):  
Niklas Ivarsson ◽  
Mathias Wallin ◽  
Daniel A. Tortorelli
Keyword(s):  
Topology Optimization ◽  
Finite Strain ◽  
Periodic Microstructures

scholarly journals Structural stability and artificial buckling modes in topology optimization

2021 ◽  
Author(s):  
Anna Dalklint ◽  
Mathias Wallin ◽  
Daniel A. Tortorelli
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Structural Response ◽  
Energy Transition ◽  
Sensitivity Analyses ◽  
Load Path ◽  
Buckling Modes ◽  
Topology Optimization Problem ◽  
The Stability ◽  
Transition Scheme

AbstractThis paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

3D-Printable Unit Cell Design for Cubic and Orthotropic Porous Microstructures Using Topology Optimization Based on Optimality Criteria Algorithm

2018 ◽  
Vol 10 (06) ◽  
pp. 1850060 ◽  
Author(s):  
Alireza Moshki ◽  
Akbar Ghazavizadeh ◽  
Ali Asghar Atai ◽  
Mostafa Baghani ◽  
Majid Baniassadi
Keyword(s):  
Topology Optimization ◽  
Optimization Technique ◽  
Optimality Criteria ◽  
Unit Cell ◽  
Topology Design ◽  
Two Phase ◽  
Topology Identification ◽  
Young’S Moduli ◽  
Periodic Microstructures ◽  
Porous Microstructures

Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

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