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dc.contributor.advisorIlanko, Sinniahen_NZ
dc.contributor.authorMonterrubio Salazar, Luis Emilioen_NZ
dc.date.accessioned2013-01-14T20:33:06Z
dc.date.available2013-05-22T03:47:00Z
dc.date.issued2009en_NZ
dc.identifier.citationMonterrubio Salazar, L. E. (2009). The use of positive and negative penalty functions in solving constrained optimization problems and partial differential equations (Thesis, Doctor of Philosophy (PhD)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/7050en
dc.identifier.urihttps://hdl.handle.net/10289/7050
dc.description.abstractThe Rayleigh-Ritz Method together with the Penalty Function Method is used to investigate the use of different types of penalty parameters. The use of artificial springs as penalty parameters is a very well established procedure to model constraints in the Rayleigh-Ritz Method, the Finite Element Method and other numerical methods. Historically, large positive values were used to define the stiffness coefficient of artificial springs, until recent publications demonstrated that it is possible to use negative values to define the stiffness coefficients of the springs. Furthermore, recent publications show that constraints can be enforced using positive and negative mass or inertia in vibration problems and in a more generic sense using eigenpenalty parameters which are penalty parameters in the matrix associated with the eigenvalue. Before the commencement of this thesis, solutions using artificial inertia were published only for beams and simple spring-mass systems. In this thesis the use of all possible types of penalty parameters are investigated in vibration problems of Euler-Bernoulli beams, thin plates and shallow shells and in elastic stability analysis of Euler-Bernoulli beams, including penalty parameters associated with the geometrical stiffness matrix. The study includes the use of penalty parameters for both enforcing support boundary conditions and continuity conditions along structural joints. This investigation started with the selection of the set of admissible functions that would: (a) allow modelling of beams, plates and shells in completely free boundary conditions; (b) not present any limitation in the number of functions that can be used in the solution. This gives the possibility to converge to the constraint solution and to model any type of boundary conditions. The procedure proposed in this work combines several advantages: accuracy of the results, relative fast convergence, simplicity of the set of admissible functions and flexibility to define boundary conditions. While there are other procedures that may give better accuracy for specific cases, the proposed method is more widely applicable. The procedure used in this work also includes a way to check for round-off errors and ill-conditioning in the results; as well as a way to bracket the exact solution with upper and lower-bound results.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherThe University of Waikatoen_NZ
dc.rightsAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.en_NZ
dc.subjectRayleigh-Ritz Methoden_NZ
dc.subjectPenalty functionsen_NZ
dc.subjectVibrationen_NZ
dc.subjectBucklingen_NZ
dc.titleThe use of positive and negative penalty functions in solving constrained optimization problems and partial differential equationsen_NZ
dc.typeThesisen_NZ
thesis.degree.disciplineEngineeringen_NZ
thesis.degree.grantorUniversity of Waikatoen_NZ
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (PhD)en_NZ
uow.identifier.adthttp://adt.waikato.ac.nz/uploads/adt-uow20090624.142615
pubs.place-of-publicationHamilton, New Zealanden_NZ


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