Rapid Modeling and Design Optimization of Multi-Topology Lattice Structure Based on Unit-Cell Library

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Yuan Liu ◽  
Shurong Zhuo ◽  
Yining Xiao ◽  
Guolei Zheng ◽  
Guoying Dong ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Lattice Structure ◽  
Structure Design ◽  
Parametric Modeling ◽  
Unit Cell ◽  
Element Analysis ◽  
Structure Generation ◽  
Cell Library ◽  
Unit Cells ◽  
Property Space

Abstract Lightweight lattice structure generation and topology optimization (TO) are common design methodologies. In order to further improve potential structural stiffness of lattice structures, a method combining the multi-topology lattice structure design based on unit-cell library with topology optimization is proposed to optimize the parts. First, a parametric modeling method to rapidly generate a large number of different types of lattice cells is presented. Then, the unit-cell library and its property space are constructed by calculating the effective mechanical properties via a computational homogenization methodology. Third, the template of compromise Decision Support Problem (cDSP) is applied to generate the optimization formulation. The selective filling function of unit cells and geometric parameter computation algorithm are subsequently given to obtain the optimum lightweight lattice structure with uniformly varying densities across the design space. Lastly, for validation purposes, the effectiveness and robustness of the optimized results are analyzed through finite element analysis (FEA) simulation.

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.

Integration of Design for Additive Manufacturing Constraints With Multimaterial Topology Optimization of Lattice Structures for Optimized Thermal and Mechanical Properties

2021 ◽  
Vol 144 (4) ◽  
Author(s):  
Vysakh Venugopal ◽  
Matthew McConaha ◽  
Sam Anand
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Material Properties ◽  
Effective Properties ◽  
Lattice Structure ◽  
Unit Cell ◽  
Lattice Structures ◽  
Element Analysis

Abstract The design of multimaterial lattice structures with optimized elasticity tensor, coefficient of thermal expansion (CTE), and thermal conductivity is the main objective of the research presented in this article. In addition, the additive manufacturability of the lattice structure is addressed using a prismatic density filter to eliminate support structures, and an octant symmetry filter is used to design symmetric lattices. A density-based topology optimization model is formulated with a homogenization method and solved using a sequential linear programming method to obtain the desired unit cell geometry of the lattice structure. The optimized unit cell obtained has high mechanical stiffness, a low CTE, and low thermal conductivity. A finite element analysis is carried out on the optimized lattice structure and an equivalent cube of computed effective properties (with the same loading and boundary conditions) to validate the computed homogenized material properties. The results from the finite element analysis show that the methodology followed to generate the lattice structure is accurate. Such lattice structures with tailored material properties can be used in aerospace parts that are subjected to mechanical and thermal loads. The complex multimaterial geometry produced from the topology optimization routine presented here is intended explicitly for the manufacture of parts using the directed energy deposition process with multiple material deposition nozzles.

Determination of Optimal Unit-Cell Size of Homogeneous Conformal Unit-Cell Lattice Structure Using Solid Shape Matching

2016 ◽  
Author(s):  
Mahmoud A. Alzahrani ◽  
Seung-Kyum Choi
Keyword(s):  
Cell Size ◽  
Solid Body ◽  
Strain Energy ◽  
Lattice Structure ◽  
Weight Ratio ◽  
Unit Cell ◽  
Optimal Size ◽  
Lattice Structures ◽  
Unit Cell Size ◽  
Unit Cells

With rapid developments and advances in additive manufacturing technology, lattice structures have gained considerable attention. Lattice structures are capable of providing parts with a high strength to weight ratio. Most work done to reduce computational complexity is concerned with determining the optimal size of each strut within the lattice unit-cells but not with the size of the unit-cell itself. The objective of this paper is to develop a method to determine the optimal unit-cell size for homogenous periodic and conformal lattice structures based on the strain energy of a given structure. The method utilizes solid body finite element analysis (FEA) of a solid counter-part with a similar shape as the desired lattice structure. The displacement vector of the lattice structure is then matched to the solid body FEA displacement results to predict the structure’s strain energy. This process significantly reduces the computational costs of determining the optimal size of the unit cell since it eliminates FEA on the actual lattice structure. Furthermore, the method can provide the measurement of relative performances from different types of unit-cells. The developed examples clearly demonstrate how we can determine the optimal size of the unit-cell based on the strain energy. Moreover, the computational cost efficacy is also clearly demonstrated through comparison with the FEA and the proposed method.

Topology Optimization of Periodic Structures With Substructuring

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Junjian Fu ◽  
Liang Xia ◽  
Liang Gao ◽  
Mi Xiao ◽  
Hao Li
Keyword(s):  
Topology Optimization ◽  
Linear System ◽  
Periodic Structures ◽  
Computational Cost ◽  
Optimization Method ◽  
Displacement Fields ◽  
Element Analysis ◽  
Level Set Function ◽  
Static Condensation ◽  
Unit Cells

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

Application of Regional Strain Energy in Topology Optimization With Inertia Relief Analysis

2013 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Ren-Jye Yang ◽  
Ching-Hung Chuang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Strain Energy ◽  
Computational Cost ◽  
Structure Design ◽  
Protective Structure ◽  
Element Analysis ◽  
Regional Strain ◽  
Unbalanced Loads ◽  
Energy Formulation

In finite element analysis, inertia relief solves the response of an unconstrained structure subject to constant or slowly varying external loads with static analysis computational cost. It is very attractive to utilize it in topology optimization to design structures under unbalanced loads, such as in impact and drop phenomena. In this paper, regional strain energy formulation and inertia relief is integrated into topology optimization to design protective structure under unbalanced loads. For background, the equations of inertia relief are introduced and a commonly used solving method is revisited. Then the regional strain energy formulation for topology optimization with inertia relief is proposed and its sensitivity is derived from the adjoint method. Based on the solving method, the sensitivity is evaluated term by term to simplify the results. The simplified sensitivity can be calculated easily using the output of commercial finite element packages. Finally, the effectiveness of this formulation is shown in the first example and the proposed regional strain energy formulation for topology optimization with inertia relief are presented and discussed in the protective structure design examples.

Biomimetic Micropore of Bearing Human Bone in the Design and Optimization Based on Finite Element Analysis and Simulation

2010 ◽  
Vol 37-38 ◽  
pp. 230-233
Author(s):  
Li Jun Yang ◽  
Xi Nan Dang ◽  
Li Li Wang ◽  
Lian Zhou
Keyword(s):  
Unit Cell ◽  
Human Bone ◽  
Boolean Operation ◽  
Artificial Bone ◽  
Element Analysis ◽  
Tissue Properties ◽  
Design And Optimization ◽  
Unit Cells ◽  
Average Modulus ◽  
Cylindrical Holes

Modeling, design and fabrication of tissue scaffolds with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. Based on comparison and analysis of the two kinds of existing unit cells, the new micropore unit cell with a sphere hole in the middle and three cylindrical holes in the edge was gained. The negative model of bearing human bone was designed according to the new unit cell. Boolean Operation to the negative mode and entity contour profile, then the interconnected scaffold of artificial bone with certain porosity and gradient micropore was obtained. The results of simulation show that the average modulus of the model is 8.5Gpa, and the porosity is from 25.8% to 42.7%. It can meet the mechanical and biomimetic requests of bearing human artificial bone.

Finite Element Analysis and Topology Optimization Design for Motional Board of Injection Molding Machine

2014 ◽  
Vol 607 ◽  
pp. 573-576
Author(s):  
En Guang Zhang ◽  
Li Wang ◽  
Wen Ju Shan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Topology Optimization ◽  
Injection Molding ◽  
Optimization Design ◽  
Structure Design ◽  
Molding Machine ◽  
Element Analysis ◽  
Injection Molding Machine ◽  
Load Carrying

The structure and the load-carrying capability of the front board of injection molding machine are more complex. The error of the approximation algorithm employed in engineering is larger so that the board may become invalid in the process of using, The finite element analysis can obtain the stress distribution in the parts so as to improve the accuracy of calculation and the quality of design; through The topology optimization analysis will take the initiative to find the optimal plan, which provides the theoretical basis for the improvement of the load-carrying capability and the structure design of board. This paper have conducted a parametric design, finite element analysis and the topology optimization design for a motional board of the injection molding machine using “Advanced simulation” of NX8.0, and get a quantitative conclusion of that the motional board volume is reduced and its stiffness is significantly enhanced.

scholarly journals STEADY STATE FINITE ELEMENT ANALYSIS OF A SINGLE STACK COLD PLATE WITH HEAT LOSSES

2017 ◽  
Vol 19 (1) ◽  
pp. 77-90 ◽  
Author(s):  
G. A. Quadir ◽  
Shiao Lin Bell ◽  
K. N. Seetharamu ◽  
A. Y. Hassan
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Single Unit ◽  
Heat Losses ◽  
Unit Cell ◽  
Bottom Surface ◽  
Cold Plate ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Unit Cells

Steady state analysis of a single stack cold plate used for the cooling of electronic components is carried out using the finite element method. The present methodology takes into account the heat losses from the top and bottom surfaces of the stack. In addition dimensionless parameters are used in the analysis. The analysis is divided into two parts: a single unit cell analysis and the analysis of the assembly of several unit cells. The results from the present analysis of a single unit cell for single stack cold plate without heat losses compare well with those available in the literature. The analyses of the assembly of unit cells with heat losses from the top and bottom surface of the stack show that the single unit cell can be considered to be the representative of the stacks only when there are no heat losses.

Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

2020 ◽  
Author(s):  
Liwei Wang ◽  
Siyu Tao ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Latent Variable ◽  
Distance Measure ◽  
Material Design ◽  
Cell Types ◽  
Unit Cell ◽  
Data Driven ◽  
Single Class ◽  
Unit Cells

Abstract The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

scholarly journals Compressive Properties of Al-Si Alloy Lattice Structures with Three Different Unit Cells Fabricated via Laser Powder Bed Fusion

Materials ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 2902 ◽  
Author(s):  
Xiaoyang Liu ◽  
Keito Sekizawa ◽  
Asuka Suzuki ◽  
Naoki Takata ◽  
Makoto Kobashi ◽  
...  
Keyword(s):  
Strain Rate ◽  
Lattice Structure ◽  
Unit Cell ◽  
Lattice Structures ◽  
Powder Bed Fusion ◽  
Laser Powder Bed Fusion ◽  
Compressive Properties ◽  
Powder Bed ◽  
Unit Cells ◽  
Indentation Tests

In the present study, in order to elucidate geometrical features dominating deformation behaviors and their associated compressive properties of lattice structures, AlSi10Mg lattice structures with three different unit cells were fabricated by laser powder bed fusion. Compressive properties were examined by compression and indentation tests, micro X-ray computed tomography (CT), together with finite element analysis. The truncated octahedron- unit cell (TO) lattice structures exhibited highest stiffness and plateau stress among the studied lattice structures. The body centered cubic-unit cell (BCC) and TO lattice structures experienced the formation of shear bands with stress drops, while the hexagon-unit cell (Hexa) lattice structure behaved in a continuous deformation and flat plateau region. The Hexa lattice structure densified at a smaller strain than the BCC and TO lattice structures, due to high density of the struts in the compressive direction. Static and high-speed indentation tests revealed that the TO and Hexa exhibited slight strain rate dependence of the compressive strength, whereas the BCC lattice structure showed a large strain rate dependence. Among the lattice structures in the present study, the TO lattice exhibited the highest energy absorption capacity comparable to previously reported titanium alloy lattice structures.

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