حل مسائل مكانيك جامدات با استفاده از توابع پايه هموار به شكل بدون شبكه محلي

چكيده انگليسي :

Solution of solid mechanics problems using smooth basis functions in a meshless local form Ehsan Soleimanifar e soleimanifar@cv iut ac ir Date of Submission September 19 2011 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Prof Bijan Boroomand boromand@cc iut ac ir AbstractIn this dissertation solution of partial differential equations PDEs with constant coefficients has beeninvestigated using smooth basis functions in a meshless local form These PDEs have a wide range ofapplications in engineering and scientific fields First a local meshless method based on previous researcheshas been described and the properties of the method are investigated through solving some numericalexamples In this method the solution domain is discretized using a set of points The main deficiency of thismethod is the lack of accuracy in problems with an irregular distribution of nodes A simple workaround hasbeen devised to address a wide class of such problems Also a new meshless local method has been developed for solution of PDEs with constant coefficients In thismethod the procedure of solution begins by discretizing the solution domain using nodal points A cloud consisting of a set of adjacent nodes is associated with each of these nodes Solution of the differentialequation in each cloud is divided into homogeneous and particular parts Each of these parts is constructed asa series of exponential basis functions EBFs with constant coefficients Basis functions of the homogeneoussolution are calculated such that the homogeneous differential equation is exactly satisfied in the domain Aset of intermediate points are distributed in the domain and on the boundaries in order to constitute thesystem of equations The equations inside the domain must be formed such that the continuity between thesolutions of adjacent clouds is provided A residual value is constructed at each intermediate point in thedomain to guarantee the continuity between clouds For imposing the boundary conditions a similar approachhas been used This approach has a good capability for satisfaction of the boundary conditions and conformsto the formulation used inside the domain Selection of the homogeneous basis functions is one of the mostimportant parameters affecting the quality of the solution Suitable selection of these functions plays animportant role in reducing the computational error and reaching appropriate accuracy in the final resuts Inthe present research these basis functions are selected such that the sampling theorems conditions aresatisfied By using the sampling theorems the maximum frequency of the basis functions is limited Finallythe formulation of the proposed method has been applied to some important and useful PDEs in solidmechanics problems including Helmholtz Poisson elasticity and elastic wave equations in 2D domains Several benchmark examples have been solved in each category of problems The results of solved numericalexamples show that the proposed method is capable for solving problems on domains with arbitrary shapesand boundary conditions and is not sensitive due to irregularity of the nodal points The ability to solve theproblems with rather high frequencies and problems with singular points near the boundary of the domain aresome of the other features of this method Although the proposed method of this dissertation has been usedfor solving some classes of important solid mechanics problems it can be extended for solving many otherPDEs with constant coefficients Keywordsdifferential equations exponential basis functions meshless method sampling theorems solid mechanics

سليماني فر، احسان

حل مسائل مكانيك جامدات با استفاده از توابع پايه هموار به شكل بدون شبكه محلي

معادلات ديفرانسيل , توابع پايه نمايي , قضاياي نمونه برداري