After giving a brief background on the subject we introduce in section two the Phase-Integral Method of Fröman & Fröman in terms of the platform function of Yngve and Thidé. In section three we derive a different form of the radial Bohr-Sommerfeld condition in terms of the apsidal angle of the corresponding classical motion. Using the derived expression, we then show how easily one can calculate the exact energy eigenvalues of the hydrogen atom and the isotropic three-dimensional harmonic oscillator, we also derive an expression for higher order quantization condition. In section four we derive an expression for the angular frequencies of a restricted (0≤φ≤β) soap bubble and also give a proposition concerning the parameters l and m of the associated Legendre differential equation. / Vi använder Fröman & Frömans Fas-Integral Metod tillsammans med Yngve & Thidés plattformfunktion för att härleda kvantiseringsvilkoret för högre ordningar. I sektion tre skriver vi Bohr-Sommerfelds kvantiseringsvillkor på ett annorlunda sätt med hjälp av den så kallade apsidvinkeln (definierad i samma sektion) för motsvarande klassiska rörelse, vi visar också hur mycket detta underlättar beräkningar av energiegenvärden för väteatomen och den isotropa tredimensionella harmoniska oscillatorn. I sektion fyra tittar vi på en såpbubbla begränsad till området 0≤φ≤β för vilket vi härleder ett uttryck för dess (vinkel)egenfrekvenser. Här ger vi också en proposition angående parametrarna l och m tillhörande den associerade Legendreekvationen.

Comprehensive analysis of the ringcore method used for the determination of the residual stresses in mechanical components is presented in this thesis. Principles, advantages, disadvantages and applicability of this semidestructive experimental method are discussed too. At the same time the ringcore method is compared with the hole drilling method, which is used more frequently. All aspects of the ringcore method are analyzed by the finite element method. FE simulations, performed on the universal numerical model, verified principles of the integral method and the incremental strain method. FE simulations also provided basic information for the uncertainty analysis, which significantly affects the accuracy of the residual stress measurement. The main goal, which the present work deals with, is to create a global overview of all ringcore methods´ aspects elaborated in a clear and complex form.