Three-field floating projection topology optimization of continuum structures

Huang, Xiaodong; Li, Weibai

doi:10.1016/j.cma.2022.115444

Cited by 33 publications

(19 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the relaxed topology optimization problem using the linear material interpolation scheme can not guarantee a clear topology, 0/1 constraints of the design variables must be considered. To simulate a large number of 0/1 constraints, the implicit filtering and floating projection constraints are imposed on the design variables in the three-field FPTO method [17]. The implicit filter constraint has the same expression as the substitution filtering scheme in eqn.…”

Section: Topology Optimization Formulationmentioning

confidence: 99%

“…The boundary-based topology optimization methods include the level-set (LS) method [2][3][4], moving morphable components (MMC) method [5,6], the feature-driven optimization method [7], and other LS variants [8,9]. The element-based topology optimization methods include the solid isotropic material penalization (SIMP) method [1,10,11], the bi-directional evolutionary structural optimization (BESO) method [12][13][14], and the recently proposed floating projection topology optimization (FPTO) method [15][16][17]. Different from the boundary-based topology optimization methods using local boundary design variables, the element-based topology optimization methods define the design variables over the whole design domain, and therefore freely dig new holes or create new members by switching the values of the design variables between 0 and 1.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Matlab code of topology optimization by imposing the implicit floating projection constraint

Huang

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents a Matlab code to implement the three-field floating projection topology optimization (FPTO) method using the linear material interpolation scheme. The material penalization scheme in the traditional element-based topology optimization approaches makes an optimal solution being close to 0/1 to avoid handling a large number of 0/1 constraints of the design variables. Instead, the implicit floating projection constraint in the FPTO method numerically simulates 0/1 constraints of the design variables so that even a linear material interpolation scheme can be employed. By gradually tightening 0/1 constraints, more and more design variables are pushed to 0/1 until an optimized element-based design with a clear topology is accurately represented by a smooth design. The implicit floating projection constraint provides a numerical engine for topology optimization, which is fundamentally different from the physical engine by material penalization. The Matlab code in this paper will focus on the numerical implementation of such an implicit constraint integrated with the common-used optimizer, e.g., optimality criteria (OC) or the method of moving asymptotes (MMA), as well as the extraction and evaluation of the smooth design. The Matlab code of the three-field FPTO method is also extended to other topology optimization problems. The provided Matlab code enables the readers to understand the FPTO method better and test this newly-developed topology optimization method for their own topology optimization problems.

show abstract

Section: Topology Optimization Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Matlab code of topology optimization by imposing the implicit floating projection constraint

Huang

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…(Roque et al, 2021) Topology optimization is a mathematical method that optimizes the layout of materials within a given design space, for a set of loads, boundary conditions, and constraints with the aim of maximizing system performance. The optimization topology method is directly extended to a robust formulation to achieve an eroded, intermediate, and widened design topology so that the design is resistant to possible manufacturing errors (Huang & Li, 2022). Topology optimization is also a shape optimization method that determines the optimal structure in the design domain for high structural efficiency (Kim, 2020).…”

Section: Topology Optimizationmentioning

confidence: 99%

Optimization of the Underframe of the Sultan Wind Turbine V5 Using the Optimization Topology Method

Ghifari¹,

Erwin²,

Wiyono³

2022

JIIT

View full text Add to dashboard Cite

Sultan wind turbine is one of the products of the New Renewable Energy Engineering Lab, Faculty of Engineering Untirta which has developed from year to year until now. To keep up with industrial developments in today's era, renewal is needed to improve and update the technology contained in the sultan wind turbine. In particular, today's optimization topologies are seen as providing the possibility to realize truly manufacturing-optimized designs through topology optimization. A topological optimization is an approach that is considered powerful in design because it contributes to designs that can save energy, materials ,and time that cannot be achieved economically using other manufacturing processes. A topological optimization, as it is often called, computer configuration of the best material over 3D space, usually represented as a grid, to satisfy or optimize physical parameters. Designers using these automated systems often seek to understand the interaction of physical constraints with the final design and their implications for other physical characteristics. Such understanding is a challenge to using a visualization approach to explore the design solution space. The essence of our new approach is to summarize an ensemble of solutions by automatically selecting a set of examples and parameterizing a design space.

show abstract

“…Structural topology optimization can be traced back to the work by Cheng and Olhoff [3] and has been widely investigated since the pioneering paper regarding the homogenization method by Bendsøe and Kikuchie [4]. Some representative algorithms were developed, including the solid isotropic material with penalization (SIMP) [5,6], evolutionary structural optimization (ESO) [7], bi-directional evolutionary structural optimization (BESO) [8], level-set method [9], moving morphable component (MMC)-based method [10], and floating projection topology optimization (FPTO) algorithm [11][12][13]. These algorithms are widely used in solving different optimization problems, including large-scale problems [14,15], fluid and heat transfer problems [16,17], energy problems [18], frequency problems [19,20], thermoelastic problems [21], multi-material problems [22,23], failure problems [24], and design for additive manufacturing (DfAM) [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…The use of the material penalization scheme increases the non-linearity and non-convexity of the objective functional or constraint function, causing that the algorithm easily runs into a local optimum [62]. The material penalization scheme could cause the overestimation of structural stiffness in density-based methods [63], and in terms of new optimization problems, the physical meaning of the material penalization model needs to be investigated and explained, especially for the multi-material structure design [13,64]. When removing the material penalization scheme from the algorithm, improved solutions can be expected.…”

Section: Introductionmentioning

confidence: 99%

On Non-Penalization SEMDOT Using Discrete Variable Sensitivities

Long

Rolfe

2022

Preprint

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

Three-field floating projection topology optimization of continuum structures

Cited by 33 publications

References 52 publications

A Matlab code of topology optimization by imposing the implicit floating projection constraint

A Matlab code of topology optimization by imposing the implicit floating projection constraint

Optimization of the Underframe of the Sultan Wind Turbine V5 Using the Optimization Topology Method

On Non-Penalization SEMDOT Using Discrete Variable Sensitivities

Contact Info

Product

Resources

About