Analysis of a Preliminary Design Approach for Conformal Lattice Structures

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.

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Lattice Structure Design for Additive Manufacturing: Unit Cell Topology Optimization

Volume 2A: 45th Design Automation Conference ◽

10.1115/detc2019-97863 ◽

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.

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

Advances in Mechanical Engineering ◽

10.1177/1687814019859789 ◽

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.

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Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing

Materials ◽

10.3390/ma11112073 ◽

2018 ◽

Vol 11 (11) ◽

pp. 2073 ◽

Cited By ~ 13

Author(s):

Wenjiong Chen ◽

Xiaonan Zheng ◽

Shutian Liu

Keyword(s):

Finite Element ◽

Lattice Structure ◽

Experimental Testing ◽

Modeling Method ◽

Finite Element Mesh ◽

Size Optimization ◽

Lattice Structures ◽

Uniform Lattice ◽

Element Mesh ◽

Unit Cells

A parameterization modeling method based on finite element mesh to create complex large-scale lattice structures for AM is presented, and a corresponding approach for size optimization of lattice structures is also developed. In the modeling method, meshing technique is employed to obtain the meshes and nodes of lattice structures for a given geometry. Then, a parametric description of lattice unit cells based on the element type, element nodes and their connecting relationships is developed. Once the unit cell design is selected, the initial lattice structure can be assembled by the unit cells in each finite element. Furthermore, modification of lattice structures can be operated by moving mesh nodes and changing cross-sectional areas of bars. The graded and non-uniform lattice structures can be constructed easily based on the proposed modeling method. Moreover, a size optimization algorithm based on moving iso-surface threshold (MIST) method is proposed to optimize lattice structures for enhancing the mechanical performance. To demonstrate the effectiveness of the proposed method, numerical examples and experimental testing are presented, and experimental testing shows 11% improved stiffness of the optimized non-uniform lattice structure than uniform one.

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Optimization Approaches in Design for Additive Manufacturing

Proceedings of the Design Society: International Conference on Engineering Design ◽

10.1017/dsi.2019.85 ◽

2019 ◽

Vol 1 (1) ◽

pp. 809-818

Author(s):

Stefano Rosso ◽

Gianpaolo Savio ◽

Federico Uriati ◽

Roberto Meneghello ◽

Gianmaria Concheri

Keyword(s):

Topology Optimization ◽

Additive Manufacturing ◽

Geometric Modeling ◽

Lattice Structure ◽

Software Tool ◽

Lattice Structures ◽

Commercial Software ◽

Lightweight Structure ◽

Sharp Edges ◽

Manufacturing Technologies

AbstractNowadays, topology optimization and lattice structures are being re-discovered thanks to Additive Manufacturing technologies, that allow to easily produce parts with complex geometries.The primary aim of this work is to provide an original contribution for geometric modeling of conformal lattice structures for both wireframe and mesh models, improving previously presented methods. The secondary aim is to compare the proposed approaches with commercial software solutions on a piston rod as a case study.The central part of the rod undergoes size optimization of conformal lattice structure beams diameters using the proposed methods, and topology optimization using commercial software tool. The optimized lattice is modeled with a NURBS approach and with the novel mesh approach, while the topologically optimized part is manually remodeled to obtain a proper geometry. Results show that the lattice mesh modelling approach has the best performance, resulting in a lightweight structure with smooth surfaces and without sharp edges at nodes, enhancing mechanical properties and fatigue life.

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

Journal of Mechanical Design ◽

10.1115/1.4030995 ◽

2015 ◽

Vol 137 (11) ◽

Cited By ~ 45

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.

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Geometric modeling of lattice structures for additive manufacturing

Rapid Prototyping Journal ◽

10.1108/rpj-07-2016-0122 ◽

2018 ◽

Vol 24 (2) ◽

pp. 351-360 ◽

Cited By ~ 20

Author(s):

Gianpaolo Savio ◽

Roberto Meneghello ◽

Gianmaria Concheri

Keyword(s):

Additive Manufacturing ◽

Computer Aided Design ◽

Geometric Modeling ◽

Lattice Structure ◽

Subdivision Surfaces ◽

Lattice Structures ◽

Content Type ◽

Critical Issues ◽

Surface Subdivision ◽

Manufacturing Technologies

Purpose This paper aims to propose a consistent approach to geometric modeling of optimized lattice structures for additive manufacturing technologies. Design/methodology/approach The proposed method applies subdivision surfaces schemes to an automatically defined initial mesh model of an arbitrarily complex lattice structure. The approach has been developed for cubic cells. Considering different aspects, five subdivision schemes have been studied: Mid-Edge, an original scheme proposed by the authors, Doo–Sabin, Catmull–Clark and Bi-Quartic. A generalization to other types of cell has also been proposed. Findings The proposed approach allows to obtain consistent and smooth geometric models of optimized lattice structures, overcoming critical issues on complex models highlighted in literature, such as scalability, robustness and automation. Moreover, no sharp edge is obtained, and consequently, stress concentration is reduced, improving static and fatigue resistance of the whole structure. Originality/value An original and robust method for modeling optimized lattice structures was proposed, allowing to obtain mesh models suitable for additive manufacturing technologies. The method opens new perspectives in the development of specific computer-aided design tools for additive manufacturing, based on mesh modeling and surface subdivision. These approaches and slicing tools are suitable for parallel computation, therefore allowing the implementation of algorithms dedicated to graphics cards.

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The Design of Optimal Lattice Structures Manufactured by Maypole Braiding

Journal of Mechanical Design ◽

10.1115/1.4031122 ◽

2015 ◽

Vol 137 (10) ◽

Cited By ~ 10

Author(s):

Austin Gurley ◽

David Beale ◽

Royall Broughton ◽

David Branscomb

Keyword(s):

Carbon Fiber ◽

Full Advantage ◽

Cross Sections ◽

Design Methodology ◽

Lattice Structure ◽

Axial Stiffness ◽

Lattice Structures ◽

Braided Composite ◽

Composite Lattice ◽

Round Cross

Beginning with the maypole braiding process and its inherent constraints, we develop a design methodology for the realization of optimal braided composite lattice structures. This process requires novel geometric, mechanical, and optimization procedures for comprehensive design-ability, while taking full advantage of the capabilities of maypole braiding. The composite lattice structures are braided using yarns comprised of multiple prepreg carbon fiber (CF) tows that are themselves consolidated in a thin braided jacket to maintain round cross sections. Results show that optimal lattice-structure tubes provide significant improvement over smooth-walled CF tubes and nonoptimal lattices in torsion and bending, while maintaining comparable axial stiffness (AE).

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Anisotropy of a Selective Laser-Melted Ti–6Al–4V Lattice Structure

10.21203/rs.3.rs-1018975/v1 ◽

2021 ◽

Author(s):

Dingye YAO ◽

Weixing ZHOU ◽

Yuli MA ◽

Bo He

Keyword(s):

Mechanical Properties ◽

Cross Section ◽

Cross Sections ◽

Lattice Structure ◽

Physical Models ◽

Image Correlation ◽

Isotropic Hardening ◽

Lattice Structures ◽

Compression Tests ◽

Small Cross Section

Abstract Selective laser melting (SLM) is a widely adopted additive manufacturing process for the preparation of metallic lattice structures. However, it causes a build-direction-dependent anisotropy of morphologies, microstructures, and mechanical properties, making it difficult to predict the behavior and performance of lattice structures. In this study, tensile samples with different cross-sections and build directions (BDs) were fabricated by SLM. The anisotropic morphology, microstructure, and tensile properties were observed and measured using optical microscopy, scanning electron microscopy, and three-dimensional digital image correlation to determine the effects of the size and BD of SLMed materials. The extracted data were sequentially used to modify the geometric and physical models of the lattice. Body-centered cubic lattice structures were fabricated by SLM, and compression tests were performed to verify the modified compression model. In addition to the BD-related grains, the cross-sectional area of the SLMed sample affects its mechanical properties. The small cross-section makes the microstructure finer because the proportion of the contour path that uses higher power is no longer negligible. The sample with small cross-section has more anisotropy because of the lack of tolerance to heterogeneity and macro defects like roughness. In this study, by analyzing samples with small cross-sections, a model consisting of an isotropic hardening law and Hill’s anisotropic yield function is established to describe the yield and plasticity behavior of the as-built SLMed Ti–6Al–4V lattice. The simulated and experimental data fit very well, verifying the methodology employed in this study.

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Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

Advances in Difference Equations ◽

10.1186/s13662-021-03234-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Mehwish Bari ◽

Ghulam Mustafa ◽

Abdul Ghaffar ◽

Kottakkaran Sooppy Nisar ◽

Dumitru Baleanu

Keyword(s):

Computer Graphics ◽

Geometric Modeling ◽

Tension Control ◽

Free Form ◽

Subdivision Surfaces ◽

Smooth Curves ◽

Practical Applications ◽

Tension Parameter ◽

Exact Reproduction ◽

Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

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Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

Volume 2: 31st Design Automation Conference, Parts A and B ◽

10.1115/detc2005-85176 ◽

2005 ◽

Author(s):

Akihiro Takezawa ◽

Shinji Nishiwaki ◽

Kazuhiro Izui ◽

Masataka Yoshimura

Keyword(s):

Topology Optimization ◽

Cross Sections ◽

Strain Energy ◽

Optimization Procedure ◽

Optimization Method ◽

Structural Topology ◽

Energy Concept ◽

Conceptual Design Phase ◽

Complementary Strain ◽

Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

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