Multiphase Thermomechanical Topology Optimization of Functionally Graded Lattice Injection Molds

2016 ◽  
Author(s):  
Tong Wu ◽  
Kai Liu ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Mechanical Performance ◽  
Lattice Structure ◽  
Functionally Graded ◽  
Unit Cell ◽  
Design Approach ◽  
Stiffness Reduction ◽  
Lattice Unit ◽  
Graded Lattice

This work presents a design methodology of lightweight, thermally efficient injection molds with functionally graded lattice structure using multiphase thermomechanical topology optimization. The aim of this methodology is to increase or maintain thermal and mechanical performance as well as to lower the cost of thermomechanical components such as injection molds when these are fabricated using additive manufacturing technologies. The proposed design approach makes use of thermal and mechanical finite element analyses to evaluate the components stiffness and heat conduction in two length scales: mesoscale and macroscale. The mesoscale contains the structural features of the lattice unit cell. Mesoscale homogenized properties are implemented in the macroscale model, which contains the components boundary conditions including the external mechanical loads as well as the heat sources and heat sinks. The macroscale design problem addressed in this work is to find the optimal distribution of given number of lattice unit cell phases within the component so its mass is minimized, while satisfying stiffness and heat conduction constraints of the overall component and the specific regions. This problem is solved through two steps: conceptual design generation and multiphase material distribution. In the first step, the mass is minimized subject to constraints of mechanical compliance and thermal cost function. In the second step, a given number of lattice material are optimally distributed subjected to nonlinear thermal and mechanical constraints, e.g., maximum nodal temperature, maximum nodal displacement. The proposed design approach is demonstrated through 2D and 3D examples including the optimal design of the core of an injection mold. The results demonstrate that a small reduction in mechanical and thermal performance allows for significant mass savings: the second example shows that 3.5% heat conduction reduction and 8.7% stiffness reduction results in 30.3% mass reduction.

scholarly journals Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1528
Author(s):  
Khaled G. Mostafa ◽  
Guilherme A. Momesso ◽  
Xiuhui Li ◽  
David S. Nobes ◽  
Ahmed J. Qureshi
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Lattice Structure ◽  
Cell Types ◽  
Functionally Graded ◽  
Unit Cell ◽  
Lattice Structures ◽  
Unit Cells ◽  
Mechanical Properties Characterization ◽  
Graded Lattice

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.

scholarly journals Compressive Properties of Additively Manufactured Functionally Graded Kagome Lattice Structure

Metals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 517 ◽  
Author(s):  
Rinoj Gautam ◽  
Sridhar Idapalapati
Keyword(s):  
Energy Absorption ◽  
Fused Deposition Modeling ◽  
Mechanical Performance ◽  
Lattice Structure ◽  
Peak Load ◽  
Functionally Graded ◽  
Uniform Density ◽  
Compressive Properties ◽  
Fused Deposition ◽  
Number Of Layers

Cellular lattice structures have important applications in aerospace, automobile and defense industries due to their high specific strength, modulus and energy absorption. Additive manufacturing provides the design freedom to fabricate complex cellular structures. This study investigates the compressive properties and deformation behavior of a Ti-6Al-4V unit Kagome structure fabricated by selective laser melting. Further, the mechanical performance of multi-unit and multi-layer Kagome structure of acrylonitrile butadiene styrene (ABS) ABS-M30™ manufactured by fused deposition modeling is explored. The effect of a number of layers of Kagome structure on the compressive properties is investigated. This paper also explores the mechanical properties of functionally graded and uniform density Kagome structure. The stiffness of the structure decreased with the increase in the number of layers whereas no change in peak load was observed. The functionally graded Kagome structure provided 35% more energy absorption than the uniform density structure.

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.

Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

2019 ◽  
Author(s):  
Jenmy Zimi Zhang ◽  
Conner Sharpe ◽  
Carolyn Conner Seepersad
Keyword(s):  
Three Dimensional ◽  
Surrogate Models ◽  
Functionally Graded ◽  
Unit Cell ◽  
Cell Stiffness ◽  
Stress Constraint ◽  
Compact Representation ◽  
Lattice Structures ◽  
Worst Case ◽  
Graded Lattice

Abstract This paper presents a computationally tractable approach for designing lattice structures for stiffness and strength. Yielding in the mesostructure is determined by a worst-case stress analysis of the homogenization simulation data. This provides a physically meaningful, generalizable, and conservative way to estimate structural failure in three-dimensional functionally graded lattice structures composed of any unit cell architectures. Computational efficiency of the design framework is ensured by developing surrogate models for the unit cell stiffness and strength as a function of density. The surrogate models are then used in the coarse-scale analysis and synthesis. The proposed methodology further uses a compact representation of the material distribution via B-splines, which reduces the size of the design parameter space while ensuring a smooth density variation that is desirable for manufacturing. The proposed method is demonstrated in compliance minimization studies using two types of unit cells with distinct mechanical properties. The effects of B-spline mesh refinement and the presence of a stress constraint on the optimization results are also investigated.

scholarly journals Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Jenmy Zimi Zhang ◽  
Conner Sharpe ◽  
Carolyn Conner Seepersad
Keyword(s):  
Three Dimensional ◽  
Surrogate Models ◽  
Functionally Graded ◽  
Unit Cell ◽  
Cell Stiffness ◽  
Stress Constraint ◽  
Compact Representation ◽  
Lattice Structures ◽  
Worst Case ◽  
Graded Lattice

Abstract This paper presents a computationally tractable approach for designing lattice structures for stiffness and strength. Yielding in the mesostructure is determined by a worst-case stress analysis of the homogenization simulation data. This provides a physically meaningful, generalizable, and conservative way to estimate structural failure in three-dimensional functionally graded lattice structures composed of any unit cell architectures. Computational efficiency of the design framework is ensured by developing surrogate models for the unit cell stiffness and strength as a function of density. The surrogate models are then used in the coarse-scale analysis and synthesis. The proposed methodology further uses a compact representation of the material distribution via B-splines, which reduces the size of the design parameter space while ensuring a smooth density variation that is desirable for manufacturing. The proposed method is demonstrated in compliance with minimization studies using two types of unit cells with distinct mechanical properties. The effects of B-spline mesh refinement and the presence of a stress constraint on the optimization results are also 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.

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