Checkerboard free topology optimization for compliance minimization applying the finite-volume theory

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

doi:10.1016/j.mechrescom.2020.103581

Cited by 12 publications

(8 citation statements)

References 26 publications

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“…For instance, the structure version of the finite-volume theory is incorporated into topology optimization code for compliance minimization of continuum linear elastic structures, cf. Araujo et al (2020). The multiphysics FVDAM with some modification is also suitable for incorporation into a structural analysis tool, such as Abaqus via the user material subroutine.…”

Section: Discussion and Future Workmentioning

confidence: 99%

Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture

Chen

2021

Journal of Intelligent Material Systems and Structures

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Electromechanical laminated composites with piezoelectric phases are increasingly being explored as multifunctional materials providing energy conversion between electric and mechanical energies. The current work explores thus-far undocumented combined microstructural effects of amplitude-to-wavelength ratio, volume fraction, poling direction of piezoelectric phases on both the homogenized properties and localized stress/electric field distributions in multilayered configurations under fully coupled electro-mechanical loading. In particular, the Multiphysics Finite-Volume Direct Averaging Micromechanics (FVDAM) and its counterpart, an in-house micromechanical multiphysics finite-element model, are utilized to investigate the homogenized and localized responses of wavy multilayered piezoelectric BaTiO3/PZT-7A architectures. These two methods generate highly agreeable results. Moreover, we critically examine the convergence of the finite-volume and finite element-based approaches via the Average Stress Theorem and Average Electric Displacement Theorem. The comparison shows the finite volume-based approach possesses a better numerical convergence. This study illustrates the FVDAM’s ability toward the analysis and design of engineered multilayered piezoelectric materials with wavy architecture.

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Section: Discussion and Future Workmentioning

confidence: 99%

Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture

Chen

2021

Journal of Intelligent Material Systems and Structures

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“…In general, the finite-volume theory employs the stress and displacement fields and imposes boundary and continuity conditions between adjacent subvolumes in an average-sense, which has guaranteed the checkerboard-free property discussed in Araujo et al (2020a).…”

Section: Finite-volume Theorymentioning

confidence: 99%

“…TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory 20 hours, 28 minutes, and 37 seconds in Araujo et al (2020a), while the same analysis employing the Top2DFVT algorithm took only 1 minute and 6 seconds, as shown in Table 1. For the RAMP approach, the penalty factor variable is adjusted to penal = 0:0.5:3, and the variable model is modified to 'RAMP'.…”

Section: Illustrative Examplesmentioning

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. In these earlier investigations, an efficient code was not provided. Furthermore, the Top2DFVT algorithm is based on the SIMP and RAMP material interpolation methods and employs sensitivity and density filters, leading to a more powerful tool. This algorithm is applied to some illustrative examples, demonstrating its effectiveness.

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“…Following Araujo et al (2020a), the local system of equations for a generic subvolume can be established as 𝒕 ̅ (𝑞) = 𝑲 (𝑞) 𝒖 ̅ (𝑞) , (4)…”

Section: Finite-volume Theorymentioning

confidence: 99%

“…Top2DFVT is an algorithm developed to obtain optimized topologies using the finitevolume theory for linear elastic continuum structures. The first use of this algorithm performed by Araujo et al (2020a) was based on the implementation suggested by the top99 code (Sigmund, 2001), where some operations, such as the filtering procedure and matrices assembly, dramatically increase the computational cost. Therefore, the main The proposed algorithm is a collection of Matlab functions written in 175 lines, disregarding the commented lines, that implement the design domain, material properties, finite-volume theory analysis, topology optimization, mesh-independency filters, and postprocessing.…”

Section: Software Descriptionmentioning

confidence: 99%

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

Araujo,

Júnior,

Filho

et al. 2024

Preprint

View full text Add to dashboard Cite

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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Checkerboard free topology optimization for compliance minimization applying the finite-volume theory

Cited by 12 publications

References 26 publications

Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture

Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture

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

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Checkerboard free topology optimization for compliance minimization applying the finite-volume theory

Cited by 12 publications

References 26 publications

Electromechanical response of multilayered piezoelectric BaTiO3/PZT-7A composites with wavy architecture

Electromechanical response of multilayered piezoelectric BaTiO3/PZT-7A composites with wavy architecture

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

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Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture

Electromechanical response of multilayered piezoelectric BaTiO₃/PZT-7A composites with wavy architecture