A transient topology optimization with time-varying deformation restriction via augmented Lagrange method

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

doi:10.1007/s10999-022-09598-6

Cited by 10 publications

(3 citation statements)

References 44 publications

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“…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]. A porous bone structure using local volume constraint generated by the AL method is displayed in Fig.…”

Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

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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.

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Section: Augmented Lagrangementioning

confidence: 99%

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Long,

Saeed,

Zhang

et al. 2024

CMES

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“…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

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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.

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“…Each method presents an inherent disadvantage, such that integral transformation techniques suffer at finding the inverse transformation; while numerical methods have high computational cost and limited accuracy. These disadvantages, especially loss of accuracy, mount up in applications where the solution must be further integrated, such as integral restrictions or integral objective functions in optimization, like in transient analysis and energy deformation analysis, [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A systematic approach to obtain the analytical solution for coupled linear second-order ordinary differential equations: Part II

Janczkowski Fogaça,

Lenz Cardoso

2024

J Braz. Soc. Mech. Sci. Eng.

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Coupled systems of second order ODEs are found in many areas, such as vibrations and electric circuits. Thus, accurate and efficient solutions are of great interest. This manuscript extends the concept of generalized integrating factor, recently introduced by the authors for one dimensional problems, to coupled n-dimensional systems of second order ODEs. The general formulation for time-varying coefficients is found and particularized to the constant coefficients. Closed-form integrating factors are obtained for the constant coefficient case under mild assumptions about the damping coefficient matrix. Analytical solutions for different types of continuous and discontinuous excitations are presented for problems with constant coefficients and proportional damping, disregarding the damping level. Examples are provided for each type of excitation studied in this manuscript. Results obtained with the proposed approach are compared to traditional numerical methods. Results show that the proposed procedure is accurate, not suffering with interpolation errors found in traditional numerical methods.

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A transient topology optimization with time-varying deformation restriction via augmented Lagrange method

Cited by 10 publications

References 44 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

A systematic approach to obtain the analytical solution for coupled linear second-order ordinary differential equations: Part II

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