Complex variable methods for shape sensitivity of finite element models

Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series...

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Vydané v:	Finite elements in analysis and design Ročník 47; číslo 10; s. 1146 - 1156
Hlavní autori:	Voorhees, Andrew, Millwater, Harry, Bagley, Ronald
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.10.2011 Elsevier
Predmet:	Complex Taylor series expansion (CTSE) Complex variables Computer programs Design sensitivities Error detection Exact sciences and technology Finite differencing Finite element method Fourier differentiation Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Optimization Physics Sciences and techniques of general use Sensitivity analysis Sensitivity methods Software Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Design sensitivities Complex Taylor series expansion (CTSE) Fourier differentiation Finite differencing Sensitivity methods Optimization Geometrical shape Sensitivity analysis Displacement(deformation) Taylor series Modeling Complex variable method Finite element method Complex method Linear elasticity Series expansion Structure modification Potential method Differentiation Mesh generation Structural analysis
ISSN:	0168-874X, 1872-6925
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Popis
Shrnutí:	Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series expansion method (CTSE), the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. That is, the real valued coordinates of the mesh are unaltered and no other modifications to the software are required. Fourier differentiation (FD) provides higher order sensitivities by conducting an FFT analysis of multiple complex variable analyses around a sampling radius in the complex plane. Implementation of complex variable sensitivity methods requires complex variable finite element software such that complex nodal coordinates can be used to implement a perturbation in the shape of interest in the complex domain. All resulting finite element outputs such as displacements, strains and stresses become complex and accurate derivatives of all finite element outputs with respect to the shape parameter of interest are available. The methodologies are demonstrated using two-dimensional finite element models of linear elasticity problems with known analytical solutions. It is found that the error in the sensitivities is primarily defined by the error in the finite element solution not the error in the sensitivity method. Hence, more accurate sensitivities can be obtained through mesh refinement.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0168-874X 1872-6925
DOI:	10.1016/j.finel.2011.05.003