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1.
Validation of boundary element method for assessment of weld joints accounting for notch stress : magistrsko delo
Rok Skerbiš, 2022, master's thesis

Abstract: Robust, automated mesh generation on arbitrary weld joint geometries, using finite element method (FEM) is a problematic task. It was previously discovered, that an arbitrary weld joint geometry can be parameterized inside a CAD environment [1], however when it comes to domain discretization and boundary conditions assignment, the parameterized approach becomes too demanding inside FEM. This results in long FEM model preparation times and sometimes in problems with the parametric model itself, which leads to a need for an additional numerical method - boundary element method (BEM), which overcomes this issue and is beneficial in this case. BEM is a numerical method, that in addition to other applications finds a use in the elasto-mechanic problems, where the only concern is the boundary of the considered geometric domain. Since notch stress calculations of weld joints fall into this category, their calculation can be carried out with it. Since there is not much available information on whether or not such calculations are a suitable alternative for the currently used FEM, this thesis had to be confirmed through a structured and step by step procedure. First, a notch mesh quality study has been made, then other entities followed. It was discovered that BEM is applicable to the problem and capable of calculating results with sufficient quality. Furthermore, the parameter driven approach and automated calculation provide for additional advantageous potentials.
Keywords: weld joint, boundary element method, finite element method, spatial discretization, notch stress
Published in DKUM: 02.11.2022; Views: 397; Downloads: 0
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2.
Some basic difference equations of Schrodinger boundary value problems
Andreas Ruffing, Maria Meiler, Andrea Bruder, 2009, original scientific article

Abstract: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Keywords: differential equations, discretization, Schrödinger equations, value problems
Published in DKUM: 26.06.2017; Views: 1149; Downloads: 394
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3.
Oscillatory difference equations and moment problems
José M. Ferreira, Sandra Pinelas, Andreas Ruffing, 2014, original scientific article

Abstract: In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of theWess-Ruffing discretization.
Keywords: difference equations, Hermite polynomials, polynomials, discretization
Published in DKUM: 26.06.2017; Views: 1303; Downloads: 384
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4.
Difference-differential operators for basic adaptive discretizations and their central function systems
Lucia Birk, Sophia Roßkopf, Andreas Ruffing, 2012, original scientific article

Abstract: The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail.
Keywords: discretization, difference operator, Lie algebra, difference equations
Published in DKUM: 26.06.2017; Views: 1089; Downloads: 352
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5.
Symmetry preserving algorithm for large displacement frictionless contact by the pre-discretization penalty method
Dušan Gabriel, Jiři Plešek, Miran Ulbin, 2004, original scientific article

Abstract: A three-dimensional contact algorithm based on the pre-discretization penalty method is presented. Using the pre-discretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation ofthe problem and allows an easy incorporation of higher-order elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. Theproposed algorithm utilizes the BFGS method modified for constrained non-linear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders.
Keywords: mechanics, numerical methods, contacting surfaces, contact problems, 3D contact algorithm, discretization, higher order elements, finite element method, Gauss point search, pre-discretization penalty method
Published in DKUM: 01.06.2012; Views: 2349; Downloads: 86
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