## Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings – Annual report year: 2009 › Research › peer-review

### Standard

**Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation.** / Lazarov, Boyan Stefanov; Sigmund, Ole.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings – Annual report year: 2009 › Research › peer-review

### Harvard

*WCSMO-8 8th World Congress on Structural and Multidisciplinary Optimization - 8, 2009, LNEC, Lisbon, Portugal.*8th World Congress on Structural and Multidisciplinary Optimization, Lisbon, Portugal, 01/06/2009.

### APA

*WCSMO-8 8th World Congress on Structural and Multidisciplinary Optimization - 8, 2009, LNEC, Lisbon, Portugal*

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### MLA

*WCSMO-8 8th World Congress on Structural and Multidisciplinary Optimization - 8, 2009, LNEC, Lisbon, Portugal.*2009.

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### Bibtex

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### RIS

TY - GEN

T1 - Sensitivity Filters In Topology Optimisation As A Solution To Helmholtz Type Differential Equation

AU - Lazarov, Boyan Stefanov

AU - Sigmund, Ole

PY - 2009

Y1 - 2009

N2 - The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology information about the neighbour cells, which is difficult to obtain when the mesh program is separated from the computational code, especially for irregular meshes. The problem becomes even tougher in parallel environments, where the domain is decomposed into multiple non-overlapping partitions. Obtaining information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers.

AB - The focus of the study in this article is on the use of a Helmholtz type differential equation as a filter for topology optimisation problems. Until now various filtering schemes have been utilised in order to impose mesh independence in this type of problems. The usual techniques require topology information about the neighbour cells, which is difficult to obtain when the mesh program is separated from the computational code, especially for irregular meshes. The problem becomes even tougher in parallel environments, where the domain is decomposed into multiple non-overlapping partitions. Obtaining information about the neighbour sub-domains is an expensive operation. The proposed filtering technique requires only mesh information necessary for the finite element discretisation of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz type differential equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimisation problems in linear elasticity, solved on sequential and parallel computers.

M3 - Article in proceedings

BT - WCSMO-8 8th World Congress on Structural and Multidisciplinary Optimization - 8, 2009, LNEC, Lisbon, Portugal

ER -