Topology optimization of cracked structures using peridynamics

Kefal, Adnan; Sohouli, Abdolrasoul; Öterkuş, Erkan; Yıldız, Mehmet; Suleman, Afzal

doi:10.1007/s00161-019-00830-x

Cited by 55 publications

(22 citation statements)

References 81 publications

(95 reference statements)

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“…Peridynamics can be applicable for both elastic and plastic materials [6][7][8][9][10], composite and polycrystalline materials [11][12][13][14][15][16], multiphysics [17][18][19], large deformation problems [20], topology optimization [21] and multiscale modeling [22,23]. Peridynamics can also be suitable for structural idealization to analyze slender structures by using PD beam models [24][25][26][27] or thin wall structures by using PD plate and shell models [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

Nguyen

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics-based machine learning model for one-and twodimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a preexisting crack, a two-dimensional representation of a three-point bending test and a plate subjected to dynamic load are simulated.

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Section: Introductionmentioning

confidence: 99%

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

Nguyen

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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“…K is symmetric matrix that includes all the stiffness contributions of the particles in their horizon. For explicit mathematical definition, reader can refer to recent study of Kefal et al [49].…”

Section: Peridynamicmentioning

confidence: 99%

“…There are very few studies included direct utilization of PD for TO of cracked structures. The first study in literature was performed by Kefal et al [49], who integrated bond-based PD with BESO optimization scheme to perform TO of structures with discontinuities. Bond-based PD can be considered as a non-local method accommodating symmetric interactions between particles.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of authors' knowledge, there is no research study on the extensive comparison of PD-TO capabilities for topology optimization of cracked structures with respect to FEM-TO. In fact, the available studies ( [49,50]) only make consecutive comparison between FEM and PD for performing topology optimization of structures without cracks. However, there is a need for justifying why TO algorithms should substitute peridynamics for conventional FEM approach in topology optimization of cracked structures.…”

Section: Introductionmentioning

confidence: 99%

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Comparative Study of Peridynamics and Finite Element Method for Practical Modeling of Cracks in Topology Optimization

Motlagh

Kefal

2021

Symmetry

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Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization.

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“…This aspect carries huge potential to advance the modeling of materials and the application of PD has therefore expanded to fields outside of damage modeling. Exemplary areas of application are multiphysics [46][47][48], multiscale modeling [49][50][51], topology optimization [52,53] and biological systems [54,55]. An extensive overview of recent publications on PD can be found in [56].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

2021

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Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.

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Topology optimization of cracked structures using peridynamics

Cited by 55 publications

References 81 publications

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

A peridynamic-based machine learning model for one-dimensional and two-dimensional structures

Comparative Study of Peridynamics and Finite Element Method for Practical Modeling of Cracks in Topology Optimization

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

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