An Aggregation-Free Local Volume Fraction Formulation for Topological Design of Porous Structure

Long, Kai; Chen, Zhuo; Zhang, Chengwan; Yang, Xiaoyu; Saeed, Nouman

doi:10.3390/ma14195726

Cited by 14 publications

(5 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later, Giraldo-Londono et al generalized the AL technique for the transient topology optimization issue by including stress constraints at each time step [128]. An aggregation-free local volume proportion formulation for porous structure was presented by Long et al [129], which was subsequently developed into a multimaterial porous structure [130]. The AL method is also performed to the topology optimization under constraints of multiple nodal displacements, maximum transient responses problem, and fatigueresistance issue [131][132][133].…”

Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

View full text Add to dashboard Cite

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures. These structures, commonly encountered in engineering applications, often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables. As a result, sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges. Over the past several decades, topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds. In comparison to the large-scale equation solution, sensitivity analysis, graphics post-processing, etc., the progress of the sequential approximation functions and their corresponding optimizers make sluggish progress. Researchers, particularly novices, pay special attention to their difficulties with a particular problem. Thus, this paper provides an overview of sequential approximation functions, related literature on topology optimization methods, and their applications. Starting from optimality criteria and sequential linear programming, the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables. In addition, recent advancements have led to the emergence of approaches such as Augmented Lagrange, sequential approximate integer, and non-gradient approximation are also introduced. By highlighting real-world applications and case studies, the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area. Furthermore, to provide a comprehensive overview, this paper offers several novel developments that aim to illuminate potential directions for future research.

show abstract

Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

View full text Add to dashboard Cite

show abstract

“…Dou [33] imposed implicit control over local volume proportion via morphology transformation mode, which was extended to the thermo-mechanical buckling problem [34]. Long et al [35,36] recently suggested a cluster-free formulation for the local volume constraints to verify that the upper bounds can be satisfied precisely. Hu et al [37] introduced the block-wise similarity constraints into the generative design by mimicking textures.…”

Section: Topology Optimization On Porous Structuresmentioning

confidence: 99%

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

Zhang,

Long,

Chen

et al. 2024

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials. The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass, as well as the local volume fraction of all phases. The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function, avoiding the parameter dependence in the conventional aggregation process. Furthermore, the local volume percentage can be precisely satisfied. The effects including the global mass bound, the influence radius and local volume percentage on final designs are exploited through numerical examples. The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance. All results, including those for irregular structures and multiple volume fraction constraints, demonstrate that the proposed method can provide an efficient solution for multiple material infill structures.

show abstract

“…Therefore, the penalty parameter p should be greater than 1 (p > 1) in penalized SEMDOT for convergency and reasonable topologies. The porous structure design problem is a suitable test case to evaluate the capability of SEMDOT in the aspect of forming smooth boundaries as numerous holes will be formed in this case [72,73]. Here, the porous structure constraint proposed by Wu et al [72] is incorporated into Equation ( 26), which is formulated by…”

Section: Compliance Minimization Casementioning

confidence: 99%

On Non-Penalization SEMDOT Using Discrete Variable Sensitivities

Long

Rolfe

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Density-based topology optimization algorithms, such as solid isotropic material with penalization (SIMP), pursue solid/void solutions to yield distinct topologies, however blurry or zigzag boundaries are unavoidable. By contrast, newly developed elemental volume fraction based algorithms pursue solid/void grid points, and the intermediate elements, consisting of both solid and void grid points, are artificially defined as boundary elements through which smooth boundaries can be formed. Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm is a typical elemental volume fraction based method developed based on the SIMP framework. However, the current version of SEMDOT needs to use the material penalization scheme in SIMP to facilitate the distinction of solid, void, and boundary elements. This framework restriction has motivated the development of the non-penalized SEMDOT algorithm to establish the physically meaningful relation between the elemental volume fraction and its material property. This study adopts discrete variable sensitivities for solid, void and assumed boundary elements instead of continuous variable sensitivities to eliminate the material penalization scheme and obtain efficient smooth topological layouts. The efficiency, effectiveness, and general applicability of the proposed non-penalized SEMDOT algorithm are demonstrated in three case studies containing compliance minimization, compliant mechanism design, and heat conduction problems, as well as thorough comparisons with penalized SEMDOT. The numerical results show that the convergency of non-penalized SEMDOT is stronger than penalized SEMDOT, and improved results can be obtained by non-penalized SEMDOT.

show abstract

An Aggregation-Free Local Volume Fraction Formulation for Topological Design of Porous Structure

Cited by 14 publications

References 58 publications

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

On Non-Penalization SEMDOT Using Discrete Variable Sensitivities

Contact Info

Product

Resources

About