Variational based analysis and modelling using B-splines

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dc.contributor.advisor Thompson, Chris en_UK Sherar, P. A. en_UK 2005-11-23T14:33:07Z 2005-11-23T14:33:07Z 2004 en_UK
dc.description.abstract The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions. We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes. The algorithms developed can be applied to other fields where a variational form of the problem exists and where such tensor product B-spline functions can be specified as potential solutions. en_UK
dc.format.extent 1883 bytes
dc.format.extent 6218993 bytes
dc.format.mimetype text/plain
dc.format.mimetype application/pdf
dc.language.iso en_UK en_UK
dc.publisher Cranfield University en_UK
dc.subject.other Geometric smoothing en_UK
dc.subject.other Finite element analysis en_UK
dc.subject.other Rayleigh-Ritz method en_UK
dc.subject.other Tensor notation en_UK
dc.title Variational based analysis and modelling using B-splines en_UK
dc.type Thesis or dissertation en_UK
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD
dc.publisher.department School of Mechanical Engineering; Applied Mathematics and Computing Group

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