Error analysis of fixed grid formulation for boundary based structural optimisation

Peter Dunning, H Alicia Kim, Glen Mullineux

Research output: Contribution to conferencePaper

Abstract

The fixed grid finite element approximation has become popular with boundary based topology optimization methods, due to its simplicity and speed in updating stiffness matrices. However, maximum errors occur on the boundary due to the homogenization of bi-material elements. This is of particular significance to boundary based optimization as sensitivity analysis along the boundary often drives the optimization. To date only a limited study of fixed grid errors exists, focusing on numerical examples. Errors in the fixed grid stiffness matrix approximation were identified as a possible source of errors observed in previous studies. This paper analytically investigates the errors in the fixed grid stiffness matrix approximation compared to classic finite element results. The analysis shows that generally errors increase as area ratio decreases and they are shape dependent. A simple example is used to investigate the global effect of the fixed grid approximation.
Original languageEnglish
Publication statusPublished - Jul 2008
Event7th ASMO UK / ISSMO conference on Engineering Design Optimization - Bath, UK United Kingdom
Duration: 7 Jul 20088 Jul 2008

Conference

Conference7th ASMO UK / ISSMO conference on Engineering Design Optimization
CountryUK United Kingdom
CityBath
Period7/07/088/07/08

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    Dunning, P., Kim, H. A., & Mullineux, G. (2008). Error analysis of fixed grid formulation for boundary based structural optimisation. Paper presented at 7th ASMO UK / ISSMO conference on Engineering Design Optimization, Bath, UK United Kingdom.