Felszíni és felszín alatti áramlások számításának új eszköze: a hálónélküli véges elem módszer = A new tool for the computation of surface and subsurface flows: the meshless finite element method

A kutatásban a témavezető által korábban kidolgozott multi-elliptikus interpolációs módszeren alapuló hálónélküli módszereket konstruáltunk elliptikus parciális differenciálegyenletek megoldására. Ezek jellegzetessége, hogy a megoldási tartományt nem kell sem ráccsal vagy végeselemes hálóval diszkretizálni, ehelyett elég azokon egy struktúra nélküli ponthalmazt megadni. A struktúranélküliség ellenére lehetséges jól közelítő módszereket definiálni, melyek még többszintű, gyors megoldási technikákkal is kombinálhatók. A partikuláris megoldások elvét alkalmazva, az eredeti probléma visszavezethető homogén probléma megoldására. Ehhez elegendő volt egy speciális perem típusú interpolációt konstruálni, mely numerikusan kevés műveletigényű és ugyanakkor stabil módszer. A technikát általánosítottuk nemkonstans együtthatós elliptikus problémákra is, és ez a megközelítés lett az alapja a peremrekonstrukció módszerének és a regularizált alapmegoldás-módszernek is. Még általánosabban alkalmazhatónak bizonyultak a radiális bázisfüggvényeken alapuló lokális hálónélküli sémák, és különösen a multi-elliptikus interpolációra alapozott újraglobalizált sémák, melyeket az utóbbi évben fejlesztettünk ki. Ezeket sikerrel alkalmaztuk a Stokes-probléma megoldására is. A témavezető nagyrészben ezekre a kutatási eredményekre alapozva 2007 februárjában MTA-doktori értekezést adott be, melyet szakmai jelentésként fájlban csatoltunk. | In the present project, meshless methods based on the multi-elliptic interpolation proposed earlier by the project leader were constructed in order to solve elliptic partial differential equations. Their main feature is that there is no need to discretize the domain by either a grid or a finite element mesh. In spite of the lack of the structure, it is possible to define meshless methods with good approximation properties, moreover, they can be combined with fast, multi-level solution techniques. Applying the idea of the particular solutions, the problem can be converted to the solution of a homogeneous problem. To this end, it is sufficient to construct a special boundary interpolation, which requires low computational cost and remains numerically stable. The technique was generalized to elliptic problems with nonconstant coefficients, moreover, this approach became the basis of the boundary reconstruction method as well as the regularized method of fundamental solutions. The local meshless schemes based on the radial basis functions and especially the re-globalized schemes based on the multi-elliptic interpolation have proved even more generally applicable. These methods were developed in the last year and they were succesfully applied to the Stokes problem. Based mainly on these research results, the project leader submitted his Doctoral Theses to the Hungarian Academy of Sciences in February, 2007, which is attached as a research report in a separated file

Measurement of Velocity and Concentration Profiles of Pneumatically Conveyed Particles in a Square-Shaped Pipe Using Electrostatic Sensor Arrays

Cross-sectional measurement of particle velocity and concentration in a pneumatic conveying pipe is desirable for the characterisation of particle flow dynamics and determination of particle mass flow rate. In this study, an inner-inserted electrostatic sensor array consisting of nine pairs of electrodes is implemented to measure the cross-sectional velocity and concentration profiling of particles over the whole cross section in a square-shaped pipe. Experimental tests were conducted on both vertical and horizontal pipe sections on a test rig under dilute conditions with different air velocities and particle mass flow rates. Test results show that the slope-shaped particle concentration profile changes to an arch-shaped one when the particles flow from a horizontal pipe to a vertical one. The particle velocity profile is arch-shaped in both vertical and horizontal pipes. A comparative study of cross-sectional mean particle velocity and concentration measured by the developed electrostatic sensor arrays is conducted

Measurement of plastic strain and plastic strain rate during orthogonal cutting for Ti-6Al-4V

Finite Element Modelling used to predict machining outcomes needs to be supplied with the appropriate material thermomechanical properties which are obtained by specific testing devices and methodologies. However, these tests are usually not representative of the extreme conditions achieved in machining processes and the obtained material law may not be suitable enough. Inverse identification could address this problem by obtaining material thermomechanical properties directly from machining outcomes such as cutting forces, temperatures, strain or strain rates. Nevertheless, this technique needs to be supplied with accurate machining outcomes. However, some of them such as strain or strain rate are difficult to be properly measured. The aim of this paper is to present a methodology to measure plastic strain and strain rate during orthogonal machining under plane strain conditions. The main idea is to create a physical microgrid in a workpiece and to analyze the distortion suffered by this grid. The novelty of the method consists on its capability of measuring strain and strain rate fields in a very localized area (primary shear zone) using a single image. The methodology was applied in orthogonal cutting of Ti-6Al-4V under cutting conditions that are representative of the broaching process. Experimental results were compared with DIC measurements, analytical results based on unequal division shear zone model, literature results and with numerical fields obtained from an AdvantEdge-2D model

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Operator-adapted finite element wavelets : theory and applications to a posteriori error estimation and adaptive computational modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2005.Includes bibliographical references (leaves 166-171).We propose a simple and unified approach for a posteriori error estimation and adaptive mesh refinement in finite element analysis using multiresolution signal processing principles. Given a sequence of nested discretizations of a domain we begin by constructing approximation spaces at each level of discretization spanned by conforming finite element interpolation functions. The solution to the virtual work equation can then be expressed as a telescopic sum consisting of the solution on the coarsest mesh along with a sequence of error terms denoted as two-level errors. These error terms are the projections of the solution onto complementary spaces that are scale-orthogonal with respect to the inner product induced by the weak-form of the governing differential operator. The problem of generating a compact, yet accurate representation of the solution then reduces to that of generating a compact, yet accurate representation of each of these error components. This problem is solved in three steps: (a) we first efficiently construct a set of scale-orthogonal wavelets that form a Riesz stable basis (in the energy-norm) for the complementary spaces; (b) we then efficiently estimate the contribution of each wavelet to the two-level error and finally (c) we select a subset of the wavelets at each level to preserve and solve exactly for the corresponding coefficients. Our approach has several advantages over a posteriori error estimation and adaptive refinement techniques in vogue in finite element analysis. First, in contrast to the true error, the two-level errors can be estimated very accurately even on coarse meshes. Second, mesh refinement is carried out by the addition of wavelets rather than element subdivision.(cont.) This implies that the technique does not have to directly deal with the handling of irregular vertices. Third, the error estimation and adaptive refinement steps use the same basis. Therefore, the estimates accurately predict how much the error will reduce upon mesh refinement. Finally, the proposed approach naturally and easily accommodates error estimation and adaptive refinement based on both the energy norm as well any bounded linear functional of interest (i.e., goal-oriented error estimation and adaptivity). We demonstrate the application of our approach to the adaptive solution of second and fourth- order problems such as heat transfer, linear elasticity and deformation of thin plates.by Raghunathan Sudarshan.Ph.D