A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Tino Stanković ◽  
Jochen Mueller ◽  
Paul Egan ◽  
Kristina Shea
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Lattice Structure ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Computational Optimization ◽  
Multiple Materials ◽  
Printed Materials ◽  
Displacement Constraints

Recent progress in additive manufacturing (AM) allows for printing customized products with multiple materials and complex geometries that could form the basis of multimaterial designs with high performance and novel functions. Effectively designing such complex products for optimal performance within the confines of AM constraints is challenging due to the need to consider fabrication constraints while searching for optimal designs with a large number of variables, which stem from new AM capabilities. In this study, fabrication constraints are addressed through empirically characterizing multiple printed materials' Young's modulus and density using a multimaterial inkjet-based 3D-printer. Data curves are modeled for the empirical data describing two base printing materials and 12 mixtures of them as inputs for a computational optimization process. An optimality criteria (OC) method is developed to search for solutions of multimaterial lattices with fixed topology and truss cross section sizes. Two representative optimization studies are presented and demonstrate higher performance with multimaterial approaches in comparison to using a single material. These include the optimization of a cubic lattice structure that must adhere to a fixed displacement constraint and a compliant beam lattice structure that must meet multiple fixed displacement constraints. Results demonstrate the feasibility of the approach as a general synthesis and optimization method for multimaterial, lightweight lattice structures that are large-scale and manufacturable on a commercial AM printer directly from the design optimization results.

Optimization of Additively Manufactured Multi-Material Lattice Structures Using Generalized Optimality Criteria

2015 ◽  
Author(s):  
Tino Stankovic ◽  
Jochen Mueller ◽  
Paul Egan ◽  
Kristina Shea
Keyword(s):  
Additive Manufacturing ◽  
Search Space ◽  
Optimality Criteria ◽  
Truss Structures ◽  
Lattice Structures ◽  
Computational Optimization ◽  
Optimality Criteria Method ◽  
Study Characteristics ◽  
Multiple Materials ◽  
Displacement Constraints

Recent progress in additive manufacturing allows for printing customized products with multiple materials and complex geometries. Effectively designing such complex products for optimal performance within the confines of additive manufacturing constraints is challenging, due to the large number of variables in the search space and uncertainties about how the manufacturing processes affect fabricated materials and structures. In this study, characteristics of materials, i.e. Young’s modulus (E), ultimate tensile strength (UTS) and density (ρ), for a multi-material inkjet-based 3D-printer are measured experimentally in order to generate data curves for a computational optimization process in configuring multimaterial lattice structures. An optimality criteria method is developed for computationally searching for optimal solutions of a multi-material lattice with fixed topology and truss cross-section sizes using the empirically obtained material measurements. Results demonstrate the feasibility of the approach for optimizing multi-material, lightweight truss structures subject to displacement constraints.

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.

scholarly journals Analysis of a Preliminary Design Approach for Conformal Lattice Structures

2021 ◽  
Vol 11 (23) ◽  
pp. 11449
Author(s):  
Pierandrea Dal Fabbro ◽  
Stefano Rosso ◽  
Alessandro Ceruti ◽  
Diego Boscolo Bozza ◽  
Roberto Meneghello ◽  
...  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Lattice Structure ◽  
Optimization Method ◽  
Free Form ◽  
Size Optimization ◽  
Lattice Structures ◽  
Finite Element Software ◽  
Beam Analysis ◽  
Prediction Of Mechanical Properties

An important issue when designing conformal lattice structures is the geometric modeling and prediction of mechanical properties. This paper presents suitable methods for obtaining optimized conformal lattice structures and validating them without the need for high computational power and time, enabling the designer to have quick feedback in the first design phases. A wireframe modeling method based on non-uniform rational basis spline (NURBS) free-form deformation (FFD) that allows conforming a regular lattice structure inside a design space is presented. Next, a previously proposed size optimization method is adopted for optimizing the cross-sections of lattice structures. Finally, two different commercial finite element software are involved for the validation of the results, based on Euler–Bernoulli and Timoshenko beam theories. The findings highlight the adaptability of the NURBS-FFD modeling approach and the reliability of the size optimization method, especially in stretching-dominated cell topologies and load conditions. At the same time, the limitation of the structural beam analysis when dealing with thick beams is noted. Moreover, the behavior of different kinds of lattices was investigated.

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.

Optimization for Anisotropy in Additively Manufactured Lattice Structures

2016 ◽  
Author(s):  
Tino Stanković ◽  
Jochen Mueller ◽  
Kristina Shea
Keyword(s):  
Lattice Structure ◽  
Optimality Criteria ◽  
Influential Factors ◽  
Lattice Structures ◽  
Factors Affecting ◽  
Anisotropic Models ◽  
Build Orientation ◽  
Euler Buckling ◽  
Buckling Constraints ◽  
Single Material

The build orientation of fabricated parts is one the most influential factors affecting material properties in many Additive Manufacturing (AM) processes. Applications such as the optimization of lattice structures for AM, are particularly affected as knowledge of the anisotropy model of the material is crucial. The investigation in this paper shows the influence of material anisotropy and build orientation on the optimized lattice structure designs. First, a material property characterization study for both compression and tension states of a single material is carried out for the example of inkjet 3D printing. Then, a generalized optimality criteria method is extended for the optimal sizing of single material and fixed topology lattice structures with respect to displacement, stress and Euler buckling constraints. The stress and Euler buckling constraints are formulated as side constraints that are handled in combination with fully-stressed design recursion. The results demonstrate the effect of anisotropy on the optimized designs caused by individual struts’ build orientation. This demonstrates the need to include anisotropic models in the optimization in order to produce solutions that can be fabricated and tested.

scholarly journals Toward the integration of lattice structure-based topology optimization and additive manufacturing for the design of turbomachinery components

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401985978
Author(s):  
Enrico Boccini ◽  
Rocco Furferi ◽  
Lapo Governi ◽  
Enrico Meli ◽  
Alessandro Ridolfi ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Lattice Structure ◽  
Three Dimensional ◽  
Optimization Method ◽  
Lattice Structures ◽  
Stiffness Properties ◽  
Maximum Stiffness ◽  
Layer Manufacturing ◽  
Innovative Materials

Used in several industrial fields to create innovative designs, topology optimization is a method to design a structure characterized by maximum stiffness properties and reduced weights. By integrating topology optimization with additive layer manufacturing and, at the same time, by using innovative materials such as lattice structures, it is possible to realize complex three-dimensional geometries unthinkable using traditional subtractive techniques. Surprisingly, the extraordinary potential of topology optimization method (especially when coupled with additive manufacturing and lattice structures) has not yet been extensively developed to study rotating machines. Based on the above considerations, the applicability of topology optimization, additive manufacturing, and lattice structures to the fields of turbomachinery and rotordynamics is here explored. Such techniques are applied to a turbine disk to optimize its performance in terms of resonance and mass reduction. The obtained results are quite encouraging since this approach allows improving existing turbomachinery components’ performance when compared with traditional one.

scholarly journals Memory-Efficient Modeling and Slicing of Large-Scale Adaptive Lattice Structures

2021 ◽  
pp. 1-16
Author(s):  
Shengjun Liu ◽  
Tao Liu ◽  
Qiang Zou ◽  
Weiming Wang ◽  
Eugeni L. Doubrovski ◽  
...  
Keyword(s):  
Large Scale ◽  
Lattice Structure ◽  
Weighted Graph ◽  
Lattice Structures ◽  
Computational Framework ◽  
Density Distributions ◽  
Graded Material ◽  
Convolution Surfaces ◽  
Supporting Structures ◽  
Memory Efficient

Abstract Lattice structures have been widely used in various applications of additive manufacturing due to its superior physical properties. If modeled by triangular meshes, a lattice structure with huge number of struts would consume massive memory. This hinders the use of lattice structures in large-scale applications (e.g., to design the interior structure of a solid with spatially graded material properties). To solve this issue, we propose a memory-efficient method for the modeling and slicing of adaptive lattice structures. A lattice structure is represented by a weighted graph where the edge weights store the struts' radii. When slicing the structure, its solid model is locally evaluated through convolution surfaces and in a streaming manner. As such, only limited memory is needed to generate the toolpaths of fabrication. Also, the use of convolution surfaces leads to natural blending at intersections of struts, which can avoid the stress concentration at these regions. We also present a computational framework for optimizing supporting structures and adapting lattice structures with prescribed density distributions. The presented methods have been validated by a series of case studies with large number (up to 100M) of struts to demonstrate its applicability to large-scale lattice structures.

scholarly journals A Topology Optimization Method for Stochastic Lattice Structures

2021 ◽  
pp. 235-240
Author(s):  
Filippo Cucinotta ◽  
Marcello Raffaele ◽  
Fabio Salmeri
Keyword(s):  
Topology Optimization ◽  
3D Printing ◽  
Structural Optimization ◽  
High Performance ◽  
Three Dimensional ◽  
Optimization Method ◽  
Lattice Structures ◽  
Low Weight ◽  
Topology Optimization Method

AbstractStochastic lattice structures are very powerful solutions for filling three-dimensional spaces using a generative algorithm. They are suitable for 3D printing and are well appropriate to structural optimization and mass distribution, allowing for high-performance and low-weight structures. The paper shows a method, developed in the Rhino-Grasshopper environment, to distribute lattice structures until a goal is achieved, e.g. the reduction of the weight, the harmonization of the stresses or the limitation of the strain. As case study, a cantilever beam made of Titan alloy, by means of SLS technology has been optimized. The results of the work show the potentiality of the methodology, with a very performing structure and low computational efforts.

A fuzzy optimization method for octet-truss lattices

2019 ◽  
Vol 25 (9) ◽  
pp. 1525-1535
Author(s):  
Yunhui Yang ◽  
Libin Zhao ◽  
Dexuan Qi ◽  
Meijuan Shan ◽  
Jianyu Zhang
Keyword(s):  
Mechanical Properties ◽  
Lattice Structure ◽  
Fuzzy Optimization ◽  
Material Model ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Content Type ◽  
Unit Cells ◽  
Octet Truss

Purpose This paper aims to present a multiscale fuzzy optimization (FO) method to optimize both the density distribution and macrotopology of a uniform octet-truss lattice structure. Design/methodology/approach The design formulae for the strut radii are presented based on the effective mechanical properties obtained from the representative volume element. The proposed basic lattice material is applied in a normalization process to determine the material model with penalization. The solid isotropic material with penalization (SIMP) method is extended to solve the minimum compliance problem using the optimality criteria. The evolutionary deletion process is proposed to delete elements corresponding to thin-strut unit cells and to obtain the optimal macrotopology. Findings Both numerical cases indicate that the FO results significantly improved in structural performance compared with the results of the conventional SIMP. The deleting threshold controls the macrotopology of the graded-density lattice structures with negligible effects on the mechanical properties. Originality/value This paper presents one of the first multiscale optimization methods to optimize both the relative density and macrotopology of uniform octet-truss lattices. The material model and corresponding optimality criteria of octet-truss lattices are proposed and implemented in the optimization.

Diketopyrrolopyrrole (DPP) pigments

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Christie ◽  
Adrian Abel
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Lattice Structure ◽  
Special Importance ◽  
Synthetic Process ◽  
Organic Pigments ◽  
Technical Performance ◽  
Retrosynthetic Analysis ◽  
Crystal Structural ◽  
Large Scale Manufacture

Abstract Since their industrial introduction in the 1980s, DPP pigments now constitute a highly important group of high-performance carbonyl pigments. The DPP system was first discovered by accident in 1974, and was subsequently re-investigated by Ciba Geigy who recognized its potential to provide commercial organic pigments. DPP pigments exhibit strong similarities compared with quinacridone pigments, in terms of their molecular and crystal structures and their properties, including low solubility and excellent fastness properties. X-ray crystal structural analysis has demonstrated that their technical performance is the result of intermolecular hydrogen bonding and π–π stacking interactions in the crystal lattice structure. Based on a simple retrosynthetic analysis, an efficient synthetic process was developed by Ciba Geigy for their large-scale manufacture. DPP pigments currently provide orange through to reddish violet shades and have become of special importance in providing brilliant saturated red shades with the outstanding durability required for applications such as automotive paints.

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