Structural Topology Optimization Through Explicit Boundary Evolution

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Weisheng Zhang ◽  
Wanying Yang ◽  
Jianhua Zhou ◽  
Dong Li ◽  
Xu Guo
Keyword(s):  
Topology Optimization ◽  
Optimal Designs ◽  
Structural Topology ◽  
B Spline ◽  
Numerical Examples ◽  
Optimization Framework ◽  
And Topology ◽  
Spline Curves ◽  
Structural Boundary ◽  
Moving Morphable Components

Traditional topology optimization is usually carried out with approaches where structural boundaries are represented in an implicit way. The aim of the present paper is to develop a topology optimization framework where both the shape and topology of a structure can be obtained simultaneously through an explicit boundary description and evolution. To this end, B-spline curves are used to describe the boundaries of moving morphable components (MMCs) or moving morphable voids (MMVs) in the structure and some special techniques are developed to preserve the smoothness of the structural boundary when topological change occurs. Numerical examples show that optimal designs with smooth structural boundaries can be obtained successfully with the use of the proposed approach.

A Moving Morphable Voids Approach for Topology Optimization With Closed B-Splines

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Bingxiao Du ◽  
Wen Yao ◽  
Yong Zhao ◽  
Xiaoqian Chen
Keyword(s):  
Topology Optimization ◽  
B Spline ◽  
B Splines ◽  
Spline Curves ◽  
Beam Design ◽  
Merging Process ◽  
Order Degree ◽  
Structural Boundary ◽  
Ks Function ◽  
Selection Of

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.

scholarly journals Data-Driven Additive Manufacturing Constraints for Topology Optimization

2018 ◽  
Author(s):  
Benjamin M. Weiss ◽  
Joshua M. Hamel ◽  
Mark A. Ganter ◽  
Duane W. Storti
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Optimal Designs ◽  
Data Driven ◽  
Constraint Function ◽  
Manufacturing Constraint ◽  
Gradient Based ◽  
Fixed Radius ◽  
Different Shapes ◽  
Moving Morphable Components

The topology optimization (TO) of structures to be produced using additive manufacturing (AM) is explored using a data-driven constraint function that predicts the minimum producible size of small features in different shapes and orientations. This shape- and orientation-dependent manufacturing constraint, derived from experimental data, is implemented within a TO framework using a modified version of the Moving Morphable Components (MMC) approach. Because the analytic constraint function is fully differentiable, gradient-based optimization can be used. The MMC approach is extended in this work to include a “bootstrapping” step, which provides initial component layouts to the MMC algorithm based on intermediate Solid Isotropic Material with Penalization (SIMP) topology optimization results. This “bootstrapping” approach improves convergence compared to reference MMC implementations. Results from two compliance design optimization example problems demonstrate the successful integration of the manufacturability constraint in the MMC approach, and the optimal designs produced show minor changes in topology and shape compared to designs produced using fixed-radius filters in the traditional SIMP approach. The use of this data-driven manufacturability constraint makes it possible to take better advantage of the achievable complexity in additive manufacturing processes, while resulting in typical penalties to the design objective function of around only 2% when compared to the unconstrained case.

scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

scholarly journals Data-Driven Additive Manufacturing Constraints for Topology Optimization

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Benjamin M. Weiss ◽  
Joshua M. Hamel ◽  
Mark A. Ganter ◽  
Duane W. Storti
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Optimal Designs ◽  
Data Driven ◽  
Constraint Function ◽  
Manufacturing Constraint ◽  
Gradient Based ◽  
Fixed Radius ◽  
Different Shapes ◽  
Moving Morphable Components

Abstract The topology optimization (TO) of structures to be produced using additive manufacturing (AM) is explored using a data-driven constraint function that predicts the minimum producible size of small features in different shapes and orientations. This shape- and orientation-dependent manufacturing constraint, derived from experimental data, is implemented within a TO framework using a modified version of the moving morphable components (MMC) approach. Because the analytic constraint function is fully differentiable, gradient-based optimization can be used. The MMC approach is extended in this work to include a “bootstrapping” step, which provides initial component layouts to the MMC algorithm based on intermediate solid isotropic material with penalization (SIMP) topology optimization results. This “bootstrapping” approach improves convergence compared with reference MMC implementations. Results from two compliance design optimization example problems demonstrate the successful integration of the manufacturability constraint in the MMC approach, and the optimal designs produced show minor changes in topology and shape compared to designs produced using fixed-radius filters in the traditional SIMP approach. The use of this data-driven manufacturability constraint makes it possible to take better advantage of the achievable complexity in additive manufacturing processes, while resulting in typical penalties to the design objective function of around only 2% when compared with the unconstrained case.

A New Approach for Simultaneous Shape and Topology Optimization Based on Implicit Topology Description Functions

2004 ◽  
Author(s):  
Xu Guo ◽  
Kang Zhao ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Numerical Experiments ◽  
Shape Derivative ◽  
Structural Topology ◽  
Numerical Instability ◽  
New Approach ◽  
Shape And Topology Optimization ◽  
Topology Description Function ◽  
And Topology ◽  
Non Local

In the present paper, a new approach for structural topology optimization based on implicit topology description function (TDF) is proposed. TDF is used to describe the shape/topology of a structure, which is approximated in terms of the nodal values. Then a relationship is established between the element stiffness and the values of the topology description function on its four nodes. In this way and with some non-local treatments of the design sensitivities, not only the shape derivative but also the topological derivative of the optimal design can be incorporated in the numerical algorithm in a unified way. Numerical experiments demonstrate that by employing this approach, the computational efforts associated with TDF (and level set) based algorithms can be saved. Clear optimal topologies and smooth structural boundaries free from any sign of numerical instability can be obtained simultaneously and efficiently.

A bio-inspired B-Spline Offset Feature for structural topology optimization

2021 ◽  
Vol 386 ◽  
pp. 114081
Author(s):  
Ying Zhou ◽  
Jihong Zhu ◽  
Haifei Zhan ◽  
Weihong Zhang ◽  
Yuantong Gu
Keyword(s):  
Topology Optimization ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
B Spline

Additive Manufacturing-Oriented Design of Graded Lattice Structures Through Explicit Topology Optimization

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Chang Liu ◽  
Zongliang Du ◽  
Weisheng Zhang ◽  
Yichao Zhu ◽  
Xu Guo
Keyword(s):  
Topology Optimization ◽  
Structure Design ◽  
Lattice Structures ◽  
New Approach ◽  
Optimization Framework ◽  
Concurrent Optimization ◽  
Design Variables ◽  
Graded Material ◽  
Graded Lattice ◽  
Moving Morphable Components

In the present work, a new approach for designing graded lattice structures is developed under the moving morphable components/voids (MMC/MMV) topology optimization framework. The essential idea is to make a coordinate perturbation to the topology description functions (TDF) that are employed for the description of component/void geometries in the design domain. Then, the optimal graded structure design can be obtained by optimizing the coefficients in the perturbed basis functions. Our numerical examples show that the proposed approach enables a concurrent optimization of both the primitive cell and the graded material distribution in a straightforward and computationally effective way. Moreover, the proposed approach also shows its potential in finding the optimal configuration of complex graded lattice structures with a very small number of design variables employed under various loading conditions and coordinate systems.

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