Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Lin Cheng ◽  
Xuan Liang ◽  
Eric Belski ◽  
Xue Wang ◽  
Jennifer M. Sietins ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Density Distribution ◽  
Lattice Structure ◽  
Design Method ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Variable Density ◽  
Structure Theory ◽  
Mapping Technique ◽  
Optimal Density

Additive manufacturing (AM) is now capable of fabricating geometrically complex geometries such as a variable-density lattice structure. This ability to handle geometric complexity provides the designer an opportunity to rethink the design method. In this work, a novel topology optimization algorithm is proposed to design variable-density lattice infill to maximize the first eigenfrequency of the structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization (AH), and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the AH method is employed to calculate the effective mechanical properties of a predefined lattice structure as a function of its relative densities. Once the optimal density distribution is obtained, a continuous mapping technique is used to convert the optimal density distribution into variable-density lattice structured design. Two three-dimensional (3D) examples are used to validate the proposed method, where the designs are printed by the EOS direct metal laser sintering (DMLS) process in Ti6Al4V. Experimental results obtained from dynamical testing of the printed samples and detailed simulation results are in good agreement with the homogenized model results, which demonstrates the accuracy and efficiency of the proposed method.

Epitaxial Ni nanoparticles on CaF2(001), (110) and (111) surfaces studied by three-dimensional RHEED, GIXD and GISAXS reciprocal-space mapping techniques

2017 ◽  
Vol 50 (3) ◽  
pp. 830-839 ◽  
Author(s):  
S. M. Suturin ◽  
V. V. Fedorov ◽  
A. M. Korovin ◽  
N. S. Sokolov ◽  
A. V. Nashchekin ◽  
...  
Keyword(s):  
Lattice Structure ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
High Energy ◽  
Reciprocal Space ◽  
Mapping Technique ◽  
Face Centered Cubic ◽  
X Ray ◽  
Cubic Lattice ◽  
Face Centered

The development of growth techniques aimed at the fabrication of nanoscale heterostructures with layers of ferroic 3dmetals on semiconductor substrates is very important for their potential usage in magnetic media recording applications. A structural study is presented of single-crystal nickel island ensembles grown epitaxially on top of CaF2/Si insulator-on-semiconductor heteroepitaxial substrates with (111), (110) and (001) fluorite surface orientations. The CaF2buffer layer in the studied multilayer system prevents the formation of nickel silicide, guides the nucleation of nickel islands and serves as an insulating layer in a potential tunneling spin injection device. The present study, employing both direct-space and reciprocal-space techniques, is a continuation of earlier research on ferromagnetic 3dtransition metals grown epitaxially on non-magnetic and magnetically ordered fluorides. It is demonstrated that arrays of stand-alone faceted nickel islands with a face-centered cubic lattice can be grown controllably on CaF2surfaces of (111), (110) and (001) orientations. The proposed two-stage nickel growth technique employs deposition of a thin seeding layer at low temperature followed by formation of the islands at high temperature. The application of an advanced three-dimensional mapping technique exploiting reflection high-energy electron diffraction (RHEED) has proved that the nickel islands tend to inherit the lattice orientation of the underlying fluorite layer, though they exhibit a certain amount of {111} twinning. As shown by scanning electron microscopy, grazing-incidence X-ray diffraction (GIXD) and grazing-incidence small-angle X-ray scattering (GISAXS), the islands are of similar shape, being faceted with {111} and {100} planes. The results obtained are compared with those from earlier studies of Co/CaF2epitaxial nanoparticles, with special attention paid to the peculiarities related to the differences in lattice structure of the deposited metals: the dual-phase hexagonal close-packed/face-centered cubic lattice structure of cobalt as opposed to the single-phase face-centered cubic lattice structure of nickel.

scholarly journals Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

2019 ◽  
Vol 25 (9) ◽  
pp. 1482-1492
Author(s):  
Tong Wu ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Mechanical Performance ◽  
Mechanical Load ◽  
Design Method ◽  
Three Dimensional ◽  
Optimization Method ◽  
Cellular Structures ◽  
Injection Mold ◽  
Computationally Efficient ◽  
Content Type

Purpose This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM). Design/methodology/approach The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied. Findings A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze. Originality/value By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance. Practical implications This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

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 Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices

2017 ◽  
Author(s):  
Botao Zhang ◽  
Kunal Mhapsekar ◽  
Sam Anand
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Volume Fraction ◽  
Complex Geometry ◽  
Lattice Structure ◽  
Variable Density ◽  
Light Weight ◽  
Lattice Structures ◽  
Density Mapping ◽  
Usage Cost

Additive manufacturing (AM) processes enable the creation of lattice structures having complex geometry which offer great potential for designing light weight parts. The combination of AM and cellular lattice structures provide promising design solutions in terms of material usage, cost and part weight. However, the geometric complexity of the structures calls for a robust methodology to incorporate the lattices in parts designs and create optimum light weight designs. This paper proposes a novel method for designing light weight variable-density lattice structures using gyroids. The parametric 3D implicit function of gyroids has been used to control the shape and volume fraction of the lattice. The proposed method is then combined with the density distribution information from topology optimization algorithm. A density mapping and interpolation approach is proposed to map the output of topology optimization into the parametric gyroids structures which results in an optimum lightweight lattice structure with uniformly varying densities across the design space. The proposed methodology has been validated with two test cases.

Lattice structure optimization and homogenization through finite element analyses

2020 ◽  
Vol 234 (12) ◽  
pp. 1490-1502 ◽  
Author(s):  
Florian Vlădulescu ◽  
Dan Mihai Constantinescu
Keyword(s):  
Fundamental Frequency ◽  
Lattice Structure ◽  
Geometric Model ◽  
Three Dimensional ◽  
Variable Density ◽  
Second Stage ◽  
Lattice Cell ◽  
Lattice Density ◽  
Homogenized Model

Lattice topology optimization can stimulate the design of new materials with spatially dependent properties with composite parts or three-dimensional printed components. The present work considers a mounting bracket for an industrial robotic arm as a case study, having as the main objective the increase of the fundamental frequency and secondly its mass reduction. Two design approaches were considered by using the ANSYS software: the first stage optimized the orthotropic lattice material by establishing an optimal variable cubic cell lattice density distribution in the geometric model; the second stage used a homogenized model based on the lattice optimization resulted from the previous stage and considered different volume fractions and variable density for four different types of cells. Homogenization increased the stiffness of the bracket by using the same cubic lattice cell and the fundamental frequency increased from 1227 Hz obtained with lattice optimization to 1366 Hz after homogenization. For the unoptimized bracket the fundamental frequency was only 839 Hz. The mass was reduced to more than half. The most effective proved to be the midpoint lattice cell as by homogenization the mass was reduced from 45.5 kg to 18.22 kg.

scholarly journals Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hongling Ye ◽  
Ning Chen ◽  
Yunkang Sui ◽  
Jun Tie
Keyword(s):  
Topology Optimization ◽  
Exponential Function ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Taylor Series Expansion ◽  
Optimal Model ◽  
Filter Function ◽  
Frequency Constraints ◽  
Design Variables ◽  
Dynamic Topology

The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM) design variable fields. The composite exponential function (CEF) is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP) algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

Topology Tailoring Method of TWB Autobody Parts Based on HyperWorks

2011 ◽  
Vol 697-698 ◽  
pp. 631-635
Author(s):  
An Ping Xu ◽  
Y.S. Liu ◽  
H. Wang ◽  
Y. Liu ◽  
Y.N. Fu
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Working Condition ◽  
Design Method ◽  
Lightweight Design ◽  
Variable Density ◽  
Side Impact ◽  
Impact Simulation ◽  
Tailor Welded Blanks ◽  
Specific Working

In the paper, a lightweight design method for tailor-welded blanks (TWBs), termed as Topology Tailoring Method (TTM), is proposed, which is based on topology optimization philosophy and in which the variable density method is employed so as to reach the goal of the smallest structure strain energy. By using this method, a TWB autodoor subjected to a specific working condition is topologically optimized in HyperWorks, thus obtaining the more lightweight autodoor. At last, a side impact simulation of the autodoor is demonstrated, thus showing the effectiveness of the method.

Design Tool for Topology Optimization of Self Supporting Variable Density Lattice Structures for Additive Manufacturing

2021 ◽  
pp. 1-36
Author(s):  
Matthew McConaha ◽  
Vysakh Venugopal ◽  
Sam Anand
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Lattice Structure ◽  
Variable Density ◽  
Design Tool ◽  
Lattice Structures ◽  
Interpolation Scheme ◽  
Void Space ◽  
Lattice Density ◽  
Optimization Methodology

Abstract Additive manufacturing (AM) allows for the inclusion of complicated geometric features that are impractical or impossible to manufacture by other means. Among such features is the collection of intricate and periodic strut-like geometries known as lattice structures. Lattice structures are desirable for their ability to provide stiffness through a large number of supporting members while employing void space within the geometry as a means to reduce part material volume. Strut thicknesses of every lattice in a part are generally not well optimized in order to maximize part stiffness, and often every lattice unit cell is identical throughout the part. This work presents a lattice density optimization methodology able to find the optimal graded lattice density distribution for maximizing the part stiffness and also improving the additive manufacturability of the part. The material property interpolation scheme used in SIMP optimization is replaced by a representative volume element (RVE)-based interpolation scheme that more accurately captures the material properties of the prescribed lattice structure at an arbitrary density. A filter has been developed that allows for the trimming of unnecessary lattices while simultaneously ensuring that the geometry remains self-supporting during the AM build process. This filter is incorporated seamlessly within the topology optimization routine. This increases the optimality of the resulting design compared to full-domain lattice filling and increases the viability of the design from a manufacturing standpoint compared to unconstrained lattice trimming.

A Novel Design Method for Nonuniform Lattice Structures Based on Topology Optimization

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Yafeng Han ◽  
Wen Feng Lu
Keyword(s):  
Mechanical Properties ◽  
Topology Optimization ◽  
Relative Density ◽  
Common Ground ◽  
Lattice Structure ◽  
Design Method ◽  
Lattice Structures ◽  
Structural Wall ◽  
Unit Cells ◽  
The Common

Lattice structures are broadly used in lightweight structure designs and multifunctional applications. Especially, with the unprecedented capabilities of additive manufacturing (AM) technologies and computational optimization methods, design of nonuniform lattice structures has recently attracted great research interests. To eliminate constraints of the common “ground structure approaches” (GSAs), a novel topology optimization-based method is proposed in this paper. Particularly, the structural wall thickness in the proposed design method was set as uniform for better manufacturability. As a solution to carry out the optimized material distribution for the lattice structure, geometrical size of each unit cell was set as design variable. The relative density model, which can be obtained from the solid isotropic microstructure with penalization (SIMP)-based topology optimization method, was mapped into a nonuniform lattice structure with different size cells. Finite element analysis (FEA)-based homogenization method was applied to obtain the mechanical properties of these different size gradient unit cells. With similar mechanical properties, elements with different “relative density” were translated into unit cells with different size. Consequently, the common topology optimization result can be mapped into a nonuniform lattice structure. This proposed method was computationally and experimentally validated by two different load-support design cases. Taking advantage of the changeable surface-to-volume ratio through manipulating the cell size, this method was also applied to design a heat sink with optimum heat dissipation efficiency. Most importantly, this design method provides a new perspective to design nonuniform lattice structures with enhanced functionality and manufacturability.

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