Topology optimization with manufacturing constraints: A unified projection-based approach

Vatanabe, Sandro L.; Lippi, Tiago N.; Lima, Cícero R. de; Paulino, Gláucio H.; Silva, Emilío Carlos Nelli

doi:10.1016/j.advengsoft.2016.07.002

Cited by 152 publications

(67 citation statements)

References 24 publications

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“…As mentioned in Section 2.2, minimum length scale control is necessary to ensure the material in surface layer region varies with an anticipated manner. There are many methods that can be used to control the length scale of structure . However, these methods have to construct extra constraints or projection process, while the robust formulation based on erosion, intermediate, and dilation projections can be easily implemented with small change in the proposed method and has also proved its effectiveness in controlling the minimum length scale .…”

Section: Topology Optimization Of Structures With Graded Surfacesmentioning

confidence: 99%

“…Density filtering is a classical projection‐based approach to obtain structural topology with desirable features, such as checkerboard‐free solutions and black‐white designs . The projection schemes are also utilized to control length scales on structural members generated by topology optimization . In addition, Gaynor and Guest proposed a projection‐based topology optimization method to design self‐supporting additive manufacturing structures where all features rise at an angle that is larger than the minimum allowable self‐supporting angle.…”

Section: Introductionmentioning

confidence: 99%

“…[42][43][44] The projection schemes are also utilized to control length scales on structural members generated by topology optimization. 42,45,46 In addition, Gaynor and Guest 47 proposed a projection-based topology optimization method to design self-supporting additive manufacturing structures where all features rise at an angle that is larger than the minimum allowable self-supporting angle. Zhang et al 48 presented a projection-based topology optimization approach to obtain optimal structures made of curved plates with fixed thickness.…”

Section: Introductionmentioning

confidence: 99%

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A projection‐based method for topology optimization of structures with graded surfaces

Luo

Liu

2019

Numerical Meth Engineering

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Summary Graded surfaces widely exist in natural structures and inspire engineers to apply functionally graded (FG) materials to cover structural surfaces for performance improvement, protection, or other special functionalities. However, how to design such structures with FG surfaces by topology optimization is a quite challenging problem due to the difficulty for determining material properties of structural surfaces with prescribed variation rule. This paper presents a novel projection‐based method for topology optimization of this class of FG structures. Firstly, a projection process is proposed for ensuring the material properties of the surfaces vary with a prescribed function. A criterion of determining the values of parameters in projection process is given by a strict theoretical derivation, and then, a new interpolation function is established, which is capable of simultaneously obtaining clear substrate topologies and realizable FG surfaces. Though such structures are actually multimaterial gradient structures, only the design variables of single‐material topology optimization problem are needed. In the current research, the classical compliance minimization problem with a mass constraint is considered and the robust formulation is used to control the length scale of substrates. Several 2D and 3D numerical examples illustrate the validity and applicability of the proposed method.

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Section: Topology Optimization Of Structures With Graded Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A projection‐based method for topology optimization of structures with graded surfaces

Luo

Liu

2019

Numerical Meth Engineering

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“…Initially, length-scale control was part of methods devised to solve numerical issues, such as mesh dependent solutions and checker-board patterns (Sigmund and Petersson 1998), and to avoid thin or single node hinges in compliant mechanism design problems (Luo et al 2008b;Sigmund 2009). Researchers have also applied length-scale control methods to obtain manufacturable designs (Liu et al 2015;Allaire et al 2016;Vatanabe et al 2016;Lazarov et al 2016). Another potential benefit of minimum length-scale control is the implicit improvement in stress and buckling performance.…”

Section: Introductionmentioning

confidence: 99%

Minimum length-scale constraints for parameterized implicit function based topology optimization

Dunning

2018

Struct Multidisc Optim

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This paper introduces explicit minimum length-scale constraint functions suitable for parameterized implicit function based topology optimization methods. Length-scale control in topology optimization has many potential benefits, such as removing numerical artifacts, mesh independent solutions, avoiding thin, or single node hinges in compliant mechanism design and meeting manufacturing constraints. Several methods have been developed to control length-scale when using density-based or signed-distance-based level-set methods. In this paper a method is introduced to control length-scale for parameterized implicit function based topology optimization. Explicit constraint functions to control the minimum length in the structure and void regions are proposed and implementation issues explored in detail. Several examples are presented to show the efficacy of the proposed method. The examples demonstrate that the method can simultaneously control minimum structure and void length-scale, design hinge free compliant mechanisms and control minimum length-scale for three dimensional structures.

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“…A symmetry and pattern constraint method was developed as a tool for use in the continuous topology optimization by mapping the design variables. 11 Vatanabe et al 12 presented manufacturing constraint techniques based on a domain of design variables projected approach, which illustrate the ability of the method can efficiently control the optimization solution. Nodal variables are implemented as the design variables to control over the thickness of structural members in topology optimization problems, which is achieved through the use of mesh independent.…”

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confidence: 99%

An engineering constraint method for continuum structural topology optimization

Zhu

Chen

2017

Advances in Mechanical Engineering

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Manufacturing and machining property are the most important features of structures. The product with good processing property is not only to decrease its costs but also to increase its efficiency. It is very difficult to design and machine because of the complicated results of topology optimization. This study introduces a heuristic approach using an engineering constraint in topology optimization sensitivity process. With this special method, the result of topology optimization can meet the structural design requirement. Several numerical examples were provided to show that the positive influence of new engineering constraint method on the reasonable results of topology optimization was significant. It was a good way to control the material distribution of continuum structural topology optimization using this method. KeywordsEngineering constraint, topology optimization, manufacturing and machining property, sensitivity Since early research by Bendsøe and Kikuchi, 1 topology optimization is recognized as an important technique to figure out the optimal structure layout within the given design domain. Recently, this technique has been recognized as a most efficient method in searching for optimum structure.2 The application of topology optimization in structure design can be used in many fields, such as automobile and aerospace industries. However, practical structure optimization work does not take engineering constraint into account, which becomes an obstacle to process designing and manufacturing. 3,4 To solve industry applications, many numerical methods have been proposed to make the results of topology optimization more feasible. The singular value decomposition (SVD) 5 was successfully applied in the model reduction. Topology optimization with sensitivity filter developed by Sigmund 6 can provide meshindependent, checkerboard-free results and minima size control; besides, the slope and perimeter constraint technique 7,8 can also solve this problem. A maximum length control approach was presented by Guest 9 and was applied to restrict the size of material distribution in the topology optimization design domain. However, even if the minimum/maximum size control and instability problem are solved very successfully, there are still many difficulties about the transformation of the results of optimization to reality structure design, for example, to design the rib of wheel structure with rotational symmetry feature using topology optimization is still another great challenge.Symmetry and repetitive feature is an important characteristic of the structure, whose function is to

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Topology optimization with manufacturing constraints: A unified projection-based approach

Cited by 152 publications

References 24 publications

A projection‐based method for topology optimization of structures with graded surfaces

A projection‐based method for topology optimization of structures with graded surfaces

Minimum length-scale constraints for parameterized implicit function based topology optimization

An engineering constraint method for continuum structural topology optimization

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