Topology optimization of binary structures using Integer Linear Programming

Sivapuram, Raghavendra; Picelli, Renato

doi:10.1016/j.finel.2017.10.006

Cited by 92 publications

(57 citation statements)

References 46 publications

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“…Picelli et al (2015) proposed a BESO approach where binary solid-void design variables are used along with the process of fluid flooding which allows the fluid and structure to be modeled during optimization with separate domains. Sivapuram and Picelli (2017) recently created the topology optimization of binary structure (TOBS) method and applied a similar approach to solve for a design-dependent fluid pressure problem. However, the piecewise constant discrete nature of BESO often yield the boundaries to be represented by finite elements' jagged edges.…”

Section: Introductionmentioning

confidence: 99%

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

Neofytou

Picelli

Huang

et al. 2020

Struct Multidisc Optim

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This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young's modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young's modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.

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Section: Introductionmentioning

confidence: 99%

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

Neofytou

Picelli

Huang

et al. 2020

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…The sequence by Picelli et al (2015aPicelli et al ( , b, 2017a Vicente et al (2015) extended the bi-directional evolutionary structural optimization (BESO) method to address design-dependent hydrostatic pressure, acoustic-, and fluid-structure interaction problems with binary {0, 1} design variables by completely switching fluid and solid elements. Recently, Sivapuram and Picelli (2018) created the topology optimization of binary structures (TOBS) method that benefits from {0, 1} variables and formal mathematical programming, including the solution for a design-dependent fluid pressure problem. While the SIMP method lacks of explicit fluid-structure interfaces, the BESO and TOBS methods have jaggered boundaries.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization for design-dependent hydrostatic pressure loading via the level-set method

Picelli

Neofytou

Kim

2019

Struct Multidisc Optim

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A few level-set topology optimization (LSTO) methods have been proposed to address complex fluid-structure interaction. Most of them did not explore benchmark fluid pressure loading problems and some of their solutions are inconsistent with those obtained via density-based and binary topology optimization methods. This paper presents a LSTO strategy for designdependent pressure. It employs a fluid field governed by Laplace's equation to compute hydrostatic fluid pressure fields that are loading linear elastic structures. Compliance minimization of these structures is carried out considering the designdependency of the pressure load with moving boundaries. The Ersatz material approach with fixed grid is applied together with work equivalent load integration. Shape sensitivities are used. Numerical results show smooth convergence and good agreement with the solutions obtained by other topology optimization methods.

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“…Nevertheless, the main drawbacks of the continuation method are that it can still result in the appearance of grey material in the final structure and that the convergence of the algorithm is significantly slowed compared to SIMP without continuation. The former leads to optimal solutions without explicitly defined structural boundaries, challenging the development of these methods in problems where it is imperative that the structural boundaries be explicitly defined …”

Section: Introductionmentioning

confidence: 99%

“…However, this method requires one to solve the problem initially on a coarse mesh and then use the obtained solution to construct a starting point for the same problem on a refined mesh. Sivapuram and Picelli extended on this idea, however implement a mesh‐independent BESO filter to smooth out the sensitivity numbers such that the gradual mesh refinement is not required. This article builds on this work by limiting the amount the objective and constraint functions can change, based on a neighborhood constraint, and developing a convergence criterion that depends on the convergence of the neighborhood constraint to size zero.…”

Section: Introductionmentioning

confidence: 99%

“…The former leads to optimal solutions without explicitly defined structural boundaries, challenging the development of these methods in problems where it is imperative that the structural boundaries be explicitly defined. 9,10 In the literature, there exists a small variety of methods that treat the topology optimization of continuum structures as a discrete problem. One group is made up of boundary-description-based methods, such as level-set methods (LSMs).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

Munk

2018

Numerical Meth Engineering

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Summary A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first‐order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing‐box, showing that topology optimization for mass minimization of real‐world structures can be considered using the proposed methodology.

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Topology optimization of binary structures using Integer Linear Programming

Cited by 92 publications

References 46 publications

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

Topology optimization for design-dependent hydrostatic pressure loading via the level-set method

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

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