Topology Optimization: Approaching the Material Distribution Problem using a Topological Function Description

2009 ◽  
Author(s):  
M.J. de Ruiter ◽  
F. van Keulen
Keyword(s):  
Topology Optimization ◽  
Material Distribution ◽  
Distribution Problem

A Method for Topology Optimization Results Estimation Based on the Analysis of Raster Images of the Material Distribution

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
P.A. Alekhin ◽  
A.O. Glebov ◽  
S.V. Karpov ◽  
S.V. Karpushkin
Keyword(s):  
Topology Optimization ◽  
Material Distribution

scholarly journals A Shape Optimization Method for Part Design Derived from the Buildability Restrictions of the Directed Energy Deposition Additive Manufacturing Process

Designs ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 19
Author(s):  
Andreas K. Lianos ◽  
Harry Bikas ◽  
Panagiotis Stavropoulos
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Energy Deposition ◽  
Design Method ◽  
Current Trend ◽  
Internal Stresses ◽  
Material Distribution ◽  
Load Case ◽  
Design Elements ◽  
Industrial Sectors

The design methodologies and part shape algorithms for additive manufacturing (AM) are rapidly growing fields, proven to be of critical importance for the uptake of additive manufacturing of parts with enhanced performance in all major industrial sectors. The current trend for part design is a computationally driven approach where the parts are algorithmically morphed to meet the functional requirements with optimized performance in terms of material distribution. However, the manufacturability restrictions of AM processes are not considered at the primary design phases but at a later post-morphed stage of the part’s design. This paper proposes an AM design method to ensure: (1) optimized material distribution based on the load case and (2) the part’s manufacturability. The buildability restrictions from the direct energy deposition (DED) AM technology were used as input to the AM shaping algorithm to grant high AM manufacturability. The first step of this work was to define the term of AM manufacturability, its effect on AM production, and to propose a framework to estimate the quantified value of AM manufacturability for the given part design. Moreover, an AM design method is proposed, based on the developed internal stresses of the build volume for the load case. Stress tensors are used for the determination of the build orientation and as input for the part morphing. A top-down mesoscale geometric optimization is used to realize the AM part design. The DED Design for Additive Manufacturing (DfAM) rules are used to delimitate the morphing of the part, representing at the same time the freeform mindset of the AM technology. The morphed shape of the part is optimized in terms of topology and AM manufacturability. The topology optimization and AM manufacturability indicator (TMI) is introduced to screen the percentage of design elements that serve topology optimization and the ones that serve AM manufacturability. In the end, a case study for proof of concept is realized.

Design of absorbing material distribution for sound barrier using topology optimization

2017 ◽  
Vol 56 (2) ◽  
pp. 315-329 ◽  
Author(s):  
Wenchang Zhao ◽  
Leilei Chen ◽  
Changjun Zheng ◽  
Cheng Liu ◽  
Haibo Chen
Keyword(s):  
Topology Optimization ◽  
Material Distribution ◽  
Sound Barrier ◽  
Absorbing Material

Investigation of Parameter Spaces for Topology Optimization With Three-Dimensional Orientation Fields for Multi-Axis Additive Manufacturing

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Joseph R. Kubalak ◽  
Alfred L. Wicks ◽  
Christopher B. Williams
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Design Space ◽  
Mechanical Performance ◽  
Unit Length ◽  
Three Dimensions ◽  
Layer By Layer ◽  
Material Distribution ◽  
Orientation Fields ◽  
Material Orientation

Abstract The layer-by-layer deposition process used in material extrusion (ME) additive manufacturing results in inter- and intra-layer bonds that reduce the mechanical performance of printed parts. Multi-axis (MA) ME techniques have shown potential for mitigating this issue by enabling tailored deposition directions based on loading conditions in three dimensions (3D). Planning deposition paths leveraging this capability remains a challenge, as an intelligent method for assigning these directions does not exist. Existing literature has introduced topology optimization (TO) methods that assign material orientations to discrete regions of a part by simultaneously optimizing material distribution and orientation. These methods are insufficient for MA–ME, as the process offers additional freedom in varying material orientation that is not accounted for in the orientation parameterizations used in those methods. Additionally, optimizing orientation design spaces is challenging due to their non-convexity, and this issue is amplified with increased flexibility; the chosen orientation parameterization heavily impacts the algorithm’s performance. Therefore, the authors (i) present a TO method to simultaneously optimize material distribution and orientation with considerations for 3D material orientation variation and (ii) establish a suitable parameterization of the orientation design space. Three parameterizations are explored in this work: Euler angles, explicit quaternions, and natural quaternions. The parameterizations are compared using two benchmark minimum compliance problems, a 2.5D Messerschmitt–Bölkow–Blohm beam and a 3D Wheel, and a multi-loaded structure undergoing (i) pure tension and (ii) three-point bending. For the Wheel, the presented algorithm demonstrated a 38% improvement in compliance over an algorithm that only allowed planar orientation variation. Additionally, natural quaternions maintain the well-shaped design space of explicit quaternions without the need for unit length constraints, which lowers computational costs. Finally, the authors present a path toward integrating optimized geometries and material orientation fields resulting from the presented algorithm with MA–ME processes.

Topology Optimization of Hyperelastic Continua

2016 ◽  
Author(s):  
Trung Pham ◽  
Christopher Hoyle ◽  
Yue Zhang ◽  
Tam Nguyen
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Objective Function ◽  
Nonlinear Material ◽  
Material Distribution ◽  
Concentrated Force ◽  
Element Analysis ◽  
Hyperelastic Materials ◽  
Stiffness Matrices ◽  
Reference Domain

Topology optimization (TO) aims to find a material distribution within a reference domain, which optimizes objective function(s) and satisfies certain constraints. Topology optimization has various potential applications in early phases of structural design, e.g., reducing structural weight or maximizing structural stiffness. However, most research on TO has focused on linear elastic materials, which has severely restricted applications of TO to hyperelastic structures made of, e.g., rubber or elastomer. While there is some work in literature on TO of nonlinear continua, to the best knowledge of the authors there is no work which investigates the different models of hyperelastic material. Furthermore, topology optimized designs often possess complex geometries and intermediate densities making it difficult to manufacture such designs using conventional methods. Additive Manufacturing (AM) is capable of handling such complexities. Continuing advances in AM will allow for usage of rubber-like materials, which are modeled by hyperelastic constitutive laws, in producing complex structures designed by TO. The contribution of this paper is an investigation of different models of hyperelastic materials taking account of both geometrical and material nonlinearities, and their influences on the resulting topologies. Topology optimization of nonlinear continua is the main topic of few papers. This paper considers different isotropic hyperelastic models including the Ogden, Arruda–Boyce and Yeoh model under finite deformations, which have not yet been implemented in the context of topology optimization of continua. This paper proposes to start with a reference domain having known boundary and loading conditions. Material parameters of different models that fill the domain are also known. Maximizing the stiffness of the structure subject to a volume constraint is used as the design objective. The domain is then meshed into a large number of finite elements, and each element is assigned a density between 0 and 1, which becomes design variable of the optimization problem. These densities are further penalized to make intermediate densities (i.e., not 0 or 1) less favorable. Optimized material distribution will be constructed from optimized values of design variables. Because of the penalization factors that make the problem nonlinear, the Method of Moving Asymptotes (MMA) is utilized to update it iteratively. At each iteration the nonlinear finite element problem is solved using the Finite Element Analysis Program (FEAP), which has been modified to accept penalized densities on element stiffness matrices and internal nodal forces, and a filtering scheme is applied on the sensitivities of objective function to guarantee the existence of solution. The proposed method is tested on several numerical examples. The first two examples are common benchmark models, which are a simply supported beam , and a beam fixed at two ends. Both models are subjected to a concentrated force at midpoints of their edges. The effects of linear and nonlinear material behaviors are compared with regards to resulting designs. The third example is a foremost attempt to reflect on TO in design of airless tire through a simple model, which demonstrates capability of the method in solving real-world design problems.

Topology and Free Size Optimization With Manufacturing Constraints for Light Weight Die Cast Automotive Backrest Frame

2009 ◽  
Author(s):  
Sreeram Polavarapu ◽  
Lonny L. Thompson ◽  
Mica Grujicic
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Design Space ◽  
Size Optimization ◽  
Manufacturing Constraints ◽  
Material Distribution ◽  
Front Seat ◽  
Die Cast ◽  
Stiffening Ribs ◽  
Multiple Load

Finite element analysis, together with topology and free-size optimization is used to design a lightweight die cast automotive front seat backrest frame when subjected to loads prescribed by ECE R17 European government regulations and additional loads which are predicted in an event of crash. In particular, an effort is made here to study the characteristics of a die cast automotive front seat backrest frame and develop a method for predicting the optimized material and support rib distribution which provides a lightweight seat which satisfies both strength and deflection requirements in a design space which includes the action of multiple load cases. An existing commercially available die cast backrest frame serves as the reference design space. Both 3D surface and solid models are created for representation as shell and solid finite element models for analysis. The objective function for topology optimization of the 3D solid model is to minimize mass of the component subject to stress and deflection constraints and is used as a guide in determining optimal geometric distribution of stiffening ribs. When the shell model of the reference seat is subjected to free-size optimization with this same constraint and objective given, an optimized material distribution measured by shell element thicknesses is obtained. For the topology optimization, manufacturing constraints of preferred draw direction and symmetry are applied in order to obtain an optimized material distribution which can be manufactured in the die-cast process. The procedure followed in this work generated an optimal material distribution and stiffening ribs in a lightweight die cast automotive seat backrest frame when subjected to multiple load cases. An overall reduction in weight of 13% is achieved over a reference commercially available die cast backrest frame component.

scholarly journals Design and Development of a Compliant Clutch Fork using Topology Optimization

2019 ◽  
Vol 8 (11) ◽  
pp. 3625-3629
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Automotive Application ◽  
Material Distribution ◽  
Optimum Size ◽  
Elastic Continuum ◽  
Active Research ◽  
Design Experiments ◽  
Topology Optimization Method

Compliant mechanisms and its systems are the focus of the active research. It describes a single elastic continuum used to transfer the motion and force mechanically. Their flexibility and stabilities are significant. Topology optimization Method is taken for designing the compliant mechanisms. It is a Material distribution approach for finding the optimum size and shape of the structure. The Author focused mainly on automotive application of Compliant Mechanism.i.e Design and implement of compliant clutch fork using topology optimization. Dimensional data is gathered in order to model the actual clutch fork. Compliant clutch fork designs are developed by reducing the weights compare to actual clutch fork with the help of topology optimization to get optimal compliant design. Experiments are directed to confirm the functionality of compliant clutch fork.

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