Checkerboard-free topology optimization for compliance minimization of continuum elastic structures based on the generalized finite-volume theory

Araujo, Marcelo Vitor Oliveira; Lages, Eduardo Nobre; Cavalcante, Marcio A. A.

doi:10.1590/1679-78256053

Cited by 7 publications

(3 citation statements)

References 38 publications

(38 reference statements)

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“…As discussed by Araujo et al (2020b), the topology optimization problem based on the finite-volume theory is a checkerboard-free approach; however, it is observed the occurrence of the mesh-dependency numerical issue. As a result, for topology problems employing the finite-volume theory, filtering techniques are employed to circumvent the mesh dependence issue.…”

Section: Mesh-independent Filtersmentioning

confidence: 99%

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

Araujo,

Júnior,

Filho

et al. 2024

Preprint

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The finite-volume theory has shown to be numerically efficient and stable for topology optimization of continuum elastic structures. The significant features of this numerical technique are the local satisfaction of equilibrium equations and the employment of compatibility conditions along edges in a surface-averaged sense. These are essential properties to adequately mitigate some numerical instabilities in the gradient version of topology optimization algorithms, such as checkerboard, mesh dependence, and local minima issues. Several computational tools have been proposed for topology optimization employing analysis domains discretized with essential features for finite-element approaches. However, this is the first contribution to offer a platform to generate optimized topologies by employing a Matlab code based on the finite-volume theory for compliance minimization problems. The Top2DFVT provides a platform to perform 2D topology optimization of structures in Matlab, from domain initialization for structured meshes to data post-processing. This contribution represents a significant advancement over earlier publications on topology optimization based on the finite-volume theory, which needed more efficient computational tools. Moreover, the Top2DFVT algorithm incorporates SIMP and RAMP material interpolation schemes alongside sensitivity and density filtering techniques, culminating in a notably enhanced optimization tool. The application of this algorithm to various illustrative cases confirms its efficacy and underscores its potential for advancing the field of structural optimization.

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Section: Mesh-independent Filtersmentioning

confidence: 99%

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

Araujo,

Júnior,

Filho

et al. 2024

Preprint

Self Cite

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“…Nevertheless, whatever SIMP (solid isotropic material penalty) or RAMP (rational approximation of material properties) is used, topology optimization is often accompanied by some numerical instability phenomena, mainly including mesh dependence, checkerboard pattern, and too many gray-scale elements [5]. In order to solve these problems, Araujo et al [6] used a topology optimization algorithm derived from generalized finite-volume theory, which is implemented via applying mesh independent filter, to avoid mesh dependency. Cui et al [7] presented the modified optimality criterion (OC) method related to the density filtering based on tanh-function to solve the SIMP model, so as to suppress the generation of intermediate density elements as well as improve the computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Modified proportional topology optimization algorithm for multiple optimization problems

RAO,

DU,

CHENG

et al. 2024

mech

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Three modified proportional topology optimization (MPTO) algorithms are presented in this paper, which are named MPTOc, MPTOs and MPTOm, respectively. MPTOc aims to address the minimum compliance problem with volume constraint, MPTOs aims to solve the minimum volume fraction problem under stress constraint, and MPTOm aims to tackle the minimum volume fraction problem under compliance and stress constraints. In order to get rid of the shortcomings of the original proportional topology optimization (PTO) algorithm and improve the comprehensive performance of the PTO algorithm, the proposed algorithms modify the material interpolation scheme and introduce the Heaviside threshold function based on the PTO algorithm. To confirm the effectiveness and superiority of the presented algorithms, multiple optimization problems for the classical MBB beam are solved, and the original PTO algorithm is compared with the new algorithms. Numerical examples show that MPTOc, MPTOs and MPTOm enjoy distinct advantages over the PTO algorithm in the matter of convergence efficiency and the ability to obtain distinct topology structure without redundancy. Moreover, MPTOc has the fastest convergence speed among these algorithms and can acquire the smallest (best) compliance value. In addition, the new algorithms are also superior to PTO concerning suppressing gray-scale elements.

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“…Araujo et al [10] discussed topology optimization applied to continuum elastic structures. The primary purpose of the research is to demonstrate the checkerboard-free property of the generalized finite-volume theory.…”

mentioning

confidence: 99%

7th International Symposium on Solid Mechanics - Special Issue

Tita

Fantuzzi

2020

Lat. Am. j. solids struct.

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This shows the high level of the event in terms of the presentations and the works published in the Procedures of MECSOL 2019. This Special Issue publishes improved and enlarged versions of 10 (ten) articles presented at MECSOL 2019, which covered different topics such as Fatigue and Failure Analyses; Composite Materials and Structures; Elasticity, Plasticity, Damage and Fracture Mechanics: Models, Experiments and Applications; Viscoelasticity and Viscoplasticity: Models, Experiments and Applications; Impact Engineering; Structural Reliability Methods and Reliability-Based Design Optimization; Optimization of Materials, Fluids and Structures; Numerical Methods: FEM, XFEM, GFEM, BEM and others methods; Nonlinear Analyses: Buckling, Post-Buckling and Contact Analyses. In other words, this Special Issue is devoted to scientists and engineers, who are investigating recent developments in analysis and state-of-the-art techniques on Solid Mechanics.Lima et al.[1] described an analysis of the dynamic response of coupled soil-pile-foundation systems. This work presents the influence of three issues on the vertical dynamic foundation response. The analysis presented in the article allows an in-depth understanding of the dynamic response of coupled soil-pile-foundation systems.Pellizzer et al.[2] discussed the time-dependent reliability of reinforced concrete considering the boundary element method. Corrosion of reinforcing bars caused by chloride ions is one of the main pathological manifestations. Therefore, the time-variant reliability problem is solved using Monte Carlo simulation with several applications.The exact solution for the buckling problem of cylindrical panels have been presented by Soares et al. [3]. These structures have frames attached to the circular edges. The boundary conditions differ from the classical simply supported ones, often assumed for design purposes, in the sense that the torsion resisted by the frames are also taken into account. Results are reported for valuable benchmarks in future studies.Anisotropic damage propagation has been presented by Petrini et al.[4] using a thermodynamically consistent phase field framework. In particular the present approach is adapted to include the effect of preferential cleavage planes 7th International Symposium on Solid Mechanics -Special Issue V. Tita et al.

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Checkerboard-free topology optimization for compliance minimization of continuum elastic structures based on the generalized finite-volume theory

Cited by 7 publications

References 38 publications

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

Modified proportional topology optimization algorithm for multiple optimization problems

7th International Symposium on Solid Mechanics - Special Issue

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