scholarly journals Multi-material topology optimization of lattice structures using geometry projection

2020 ◽  
Vol 363 ◽  
pp. 112895 ◽  
Author(s):  
Hesaneh Kazemi ◽  
Ashkan Vaziri ◽  
Julián A. Norato
Keyword(s):  
Topology Optimization ◽  
Lattice Structures ◽  
Geometry Projection

scholarly journals Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 678
Author(s):  
Zijun Wu ◽  
Renbin Xiao
Keyword(s):  
Topology Optimization ◽  
High Efficiency ◽  
Spline Interpolation ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Hierarchical Lattice ◽  
B Spline ◽  
Design Variables ◽  
Optimality Criteria Method

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

DESIGN OF STRUCTURAL PARTS BY USING MODERN SIMULATION PROCEDURES

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Boštjan Harl ◽  
Jožef Predan ◽  
Marko Kegl ◽  
Dejan Dinevski
Keyword(s):  
Topology Optimization ◽  
Stress Fields ◽  
Lattice Structures ◽  
The Finite Element Method ◽  
Optimization Software ◽  
And Topology ◽  
Load Carrying ◽  
Domain Configuration ◽  
Structural Parts ◽  
Manufacturing Technologies

This paper discusses modern simulation procedures used in design of structural load-carrying parts that are based on the Finite Element Method. The specific focus of the paper is the topology optimization usage within the context of two currently very interesting topics: configuration and optimization of lattice structures and modern additive manufacturing technologies. Both types of structures are presented together with their limits as well as their potentials for optimization. The discussion is illustrated by two numerical examples and experimentally obtained results. In the examples, a simple beam with three points load is optimized regarding to the different topology setups. The stress fields for different loaded optimized versions of structures are presented and the solutions are discussed and compared to the results of the experiment. A standalone topology optimization software CAESS ProTOp is used for the domain configuration and topology optimization in both examples.

A geometry projection method for the topology optimization of plate structures

2016 ◽  
Vol 54 (5) ◽  
pp. 1173-1190 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato ◽  
Arun L. Gain ◽  
Naesung Lyu
Keyword(s):  
Topology Optimization ◽  
Projection Method ◽  
Plate Structures ◽  
Geometry Projection

Lattice Structure Design for Additive Manufacturing: Unit Cell Topology Optimization

2019 ◽  
Author(s):  
Bradley Hanks ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Lattice Structure ◽  
Optimization Method ◽  
Structure Design ◽  
Unit Cell ◽  
Lattice Structures ◽  
Design For Additive Manufacturing ◽  
Structure Topology

Abstract Additive manufacturing is a developing technology that enhances design freedom at multiple length scales, from the macroscale, or bulk geometry, to the mesoscale, such as lattice structures, and even down to tailored microstructure. At the mesoscale, lattice structures are often used to replace solid sections of material and are typically patterned after generic topologies. The mechanical properties and performance of generic unit cell topologies are being explored by many researchers but there is a lack of development of custom lattice structures, optimized for their application, with considerations for design for additive manufacturing. This work proposes a ground structure topology optimization method for systematic unit cell optimization. Two case studies are presented to demonstrate the approach. Case Study 1 results in a range of unit cell designs that transition from maximum thermal conductivity to minimization of compliance. Case Study 2 shows the opportunity for constitutive matching of the bulk lattice properties to a target constitutive matrix. Future work will include validation of unit cell modeling, testing of optimized solutions, and further development of the approach through expansion to 3D and refinement of objective, penalty, and constraint functions.

A Topology Optimization Method for the Design of Orthotropic Plate Structures

2020 ◽  
Author(s):  
Hollis Smith ◽  
Julian Norato
Keyword(s):  
Topology Optimization ◽  
Projection Method ◽  
Anisotropic Material ◽  
Optimization Method ◽  
Rectangular Plates ◽  
Material Anisotropy ◽  
Fixed Amount ◽  
Plate Structures ◽  
Geometry Projection ◽  
Topology Optimization Method

Abstract This work introduces a topology optimization method for the design of structures composed of rectangular plates each of which is made of a predetermined anisotropic material. This work builds upon the geometry projection method with two notable additions. First, a novel geometric parameterization of plates represented by offset surfaces is formulated that is simpler than the one used in previous works. Second, the formulation presented herein adds support to the geometry projection method for geometric components with general anisotropic material properties. A design-generation framework is formulated that produces optimal designs composed exclusively of rectangular plates that may be made of a predetermined, generally anisotropic material. The efficacy of the proposed method is demonstrated with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material. The example reveals the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit detrimental performance if the plates are naively replaced with an anisotropic material. Although the example given in this work is in the context of orthotropic plates, since the formulation presented in this work supports arbitrary anisotropic materials, it may be readily extended to support the design of each component’s material anisotropy as a part of the optimization routine.

scholarly journals Design and Optimization of Lattice Structures: A Review

2020 ◽  
Vol 10 (18) ◽  
pp. 6374
Author(s):  
Chen Pan ◽  
Yafeng Han ◽  
Jiping Lu
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Voronoi Tessellation ◽  
High Strength ◽  
Research Literature ◽  
Main Concern ◽  
Lattice Structures ◽  
Uniform Lattice ◽  
And Topology ◽  
Bio Engineering

Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.

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