Continuous density-based topology optimization of cracked structures using peridynamics

Sohouli, Abdolrasoul; Kefal, Adnan; Abdelhamid, Ahmed; Yıldız, Mehmet; Suleman, Afzal

doi:10.1007/s00158-020-02608-1

Cited by 25 publications

(8 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

2021

View full text Add to dashboard Cite

show abstract

“…Bond-based PD can be considered as a non-local method accommodating symmetric interactions between particles. Later, peridynamics based topology optimization (PD-TO) approach was extended to [50] gradient-based optimization algorithms for complex engineering problems involving cracks. Most recently, the PD-TO algorithm was also utilized for multi material topology optimization [51].…”

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%

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

Motlagh

Kefal

2021

Symmetry

View full text Add to dashboard Cite

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.

show abstract

“…is technique explains metamorphosis of the model layout, iterative aspect, and slow transformation in every new upcoming layout that renovates keen on the dense, outdated, and also immoderate-performance shape. Density-based technique for topology optimization [3] have been developed to such an extent that the structures for numerous engineering categories are implemented using advanced computational means, especially in favor of aerospace and automotive to achieve optimal weight, stiffness, strength, and frequency with the help of design objectives. It is known that the density fundamental variables lie in the range of 1 and 0 [4].…”

Section: Introductionmentioning

confidence: 99%

Improved Efficient Projection Density Function Based on Topology Optimization

Saeed

Long

Ansari

et al. 2021

Journal of Mathematics

View full text Add to dashboard Cite

Topology optimization is a powerful tool having capability of generating new solution to engineering design problems, while these designs enhance manufacturability and reduce manufacturing costs in a computational setting. Mesh-independent convergence and other techniques have been widely used as topology optimization technique, but they produce gray transition regions which is not a favorable condition for any material. In this article, a modified topology optimization formulation using a new function has been proposed. The suggested scheme makes use of the Heaviside Projection Method (HPM) to continuum topology optimization. Such technique is helpful to obtain the minimum length scale influence on void and solid phases. Application of this proposed approach is implemented to obtain the minimum compliance for macrostructures. Numerical remarkable examples illustrate the noteworthy value of the proposed approach.

show abstract

Continuous density-based topology optimization of cracked structures using peridynamics

Cited by 25 publications

References 48 publications

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

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

Improved Efficient Projection Density Function Based on Topology Optimization

Contact Info

Product

Resources

About