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.
|Title of host publication||7th ASMO UK/ISSMO conference on Engineering Design Optimization|
|Place of Publication||Leeds|
|Number of pages||10|
|ISBN (Electronic)||9780853162728, 0853162727|
|Publication status||Published - 8 Jul 2008|
Dunning, P., Kim, H. A., & Mullineux, G. (2008). Error analysis of fixed grid formulation for boundary based structural optimisation. In V. Toropov (Ed.), 7th ASMO UK/ISSMO conference on Engineering Design Optimization ASMO-UK. http://people.bath.ac.uk/enshak/pdfs/ASMO08_FGanalysis.pdf