Solving equilibrium equations for stress and deflection functions in a thin elastic shallow shell

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dc.contributor.authorOkelo, Jeconia Abonyo
dc.date.accessioned2012-02-02T12:37:36Z
dc.date.available2012-02-02T12:37:36Z
dc.date.issued2012-02-02
dc.descriptionThe QA 935.O38en_US
dc.description.abstractA problem connected with the study of thin elastic shallow shells in the theory of non-linear elasticity is considered. The equilibrium equations are in the form V4 B1 (x, y) + Eh n4 B2 (x,y)=0 DV 4 B2 (x,y) - n 4 B1 (x,y) = S(x,y) The entire domain of the shell n bounded in R3 4 is the biharmonic operator  4 (---)= ( + 2 4 +  4) ( x4  x2  y2  y4) 4 is the pucher 's operator 4 (----)=  2 fd 2 - 2 2 f +  2 + 2 f2  x2  y2  x  y  x  y  x2 ( y2 E: Young's modulus of elasticity of the material  h: the uniform thickness of the shell  D= Eh 3 (I- u2)-1 is the flexural rigidity of the material 12 µ=Poisson's ratio i (x,y) is the stress function 2(x,y) is the deflection function S(x,y) is the external force on the projection of the shell  on xy plane The entire boundary of the shell in the form dn is assumed clamped so that the deflection and slopes are zero boundaries The entire domain of the shell l  is bounded in R3 having middle surface in Monge's form Z= f (x ,y ). Galerkin's orthogonality conditions are applied to solve the equilibrium equations for stress and deflections. Appropriate forms of orhonormal Fourier's double series are formulated for1 (x, y) and 2(x, y) to satisfy the boundary conditions. Finally the existence and the uniqueness of the solutions are established.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/2558
dc.language.isoenen_US
dc.subjectNonlinear control theory//Nonlinear difference equations//Elestic plates shellsen_US
dc.titleSolving equilibrium equations for stress and deflection functions in a thin elastic shallow shellen_US
dc.typeThesisen_US
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