Local Elastic and Geometric Stiffness Matrices for the Shell Element Applied in cFEM

In this paper local elastic and geometric stiffness matrices of ashell finite element are presented and discussed. The shell finiteelement is a rectangular plane element, specifically designedfor the so-called constrained finite element method. One of themost notable features of the proposed shell finite element isthat two perpendicular (in-plane) directions are distinguished,which is resulted in an unusual combination of otherwise classicshape functions. An important speciality of the derived stiffnessmatrices is that various options are considered, whichallows the user to decide how to consider the through-thicknessstress-strain distributions, as well as which second-order strainterms to consider from the Green-Lagrange strain matrix. Thederivations of the stiffness matrices are briefly summarizedthen numerical examples are provided. The numerical examplesillustrate the effect of the various options, as well as theyare used to prove the correctness of the proposed shell elementand of the completed derivations

Torsional Buckling of Thin-Walled Columns with Transverse Stiffeners: Analytical Studies

In this paper the pure torsional buckling of thin-walled column members is investigated, with a special focus on the effect of transverse plate elements, such as end-plates or transverse stiffeners. The linear buckling problem is aimed to solve analytically, therefore the necessary (differential) equations are first established. For some simple problems, namely doubly-symmetric I-sections with pinned-pinned or clamped-clamped supports and with rectangular stiffeners or end-plates, closed formulae are derived to calculate the critical force. It is shown that the transverse elements have two effects: the direct effect is due to the deformation of the transverse elements, while the indirect effect is that the transverse elements modify the longitudinal distribution of the member’s displacements. It is also shown how the stiffener-to-member connection influences the results. The analytical solutions are discussed by several numerical examples: the results from the derived formulae are compared to results from shell finite element buckling analyses

Constrained Finite Strip Method with Rigid Corner Element for the Buckling Analysis of Thin-Walled Members with Rounded Corners

In this paper modal decomposition of the deformations of thin-walled structural members are discussed. Modal decomposition is a process which separates the characteristic behavior modes. If applied in buckling analysis, modal decomposition makes it possible to analyze pure global or pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly useful in the design of thin-walled structural members, such as cold-formed steel beams or columns. Cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite element method and generalized beam theory fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. An extension to the constrained finite strip method is proposed and discussed. The proposal introduces rigid corner elements, which make it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled. The formulation of the proposal is summarized, then the rigid-corner approach is studied by an extended parametric study

Local stiffness matrices for the semi-analytical Finite Strip Method in case of various boundary conditions

In this paper the elastic and geometric stiffness matrices of the semi-analytical finite strip method (FSM) are discussed. The stiffness matrices are derived in various options. New derivations are presented for different longitudinal base functions, which corresponds to column/beam member with general boundary conditions. Numerical studies are performed to verify the new stiffness matrices as well as to illustrate the effect of the various options. It is shown that inconsistency is existing in the current implementations of FSM, which inconsistency has negligible effect in most of the practical cases, but might have non-negligible effect in certain specific cases

FEM-based approach for the stability design of thin-walled members by using cFSM base functions

This paper presents a new design approach for the stability design of thin-walled members. The proposed approach is based on the buckling modes and critical forces/moments determined by a linear buckling analysis performed on a regular shell finite element model. A fully automatic buckling mode identification technique is applied, by using the modal base functions of the newly proposed constrained finite strip method, where the various buckling types are separated by clearly defined mechanical criteria. The paper briefly summarizes the determination of modal base functions which then are used to approximate finite element displacement functions (i.e., buckling modes). The mode identification method provides the lowest critical values (forces or moments) to all the three characteristic buckling types: global, distortional and local, on the basis of which the buckling resistance can be calculated by using the design formulae of the direct strength method. The proposed new approach, which is potentially more general than any of the existing design approaches, is demonstrated on Z columns and beams with simple loading and boundary conditions. Critical values as well as resistances are calculated for some selected cases, the results are compared to those of another design method. The comparisons prove the applicability of the proposed procedure. Further research is necessary to extend the proposal for more general and more complex practical cases

A korszerű számítástechnikai eszközök hatékony alkalmazása vékonyfalú rúdszerkezetek stabilitási vizsgálataiban = Efficient application of today's computation technology in the stability analysis of thin-walled structures

Javaslatot tettünk vékonyfalú szelvények stabilitásvesztési módjainak új, mechanikai alapon történő definiálásra. Kidolgoztuk a cFSM (constrained Finite Strip Method) eljárást. A cFSM-mel tetszőleges nyitott keresztmetszetű két-csuklós prizmatikus rúd rugalmas stabilitásvizsgálata elvégezhető: tetszőleges tiszta vagy interakciós módhoz tartozó kritikus erő/nyomaték számítható. Megmutattuk, hogy a cFSM alkalmas tetszőleges végessávos sajátalak mód-identifikációjára, azaz számszerűsíthető a stabilitásvesztési típusok jelenléte egy adott stabilitásvesztési módban. Javaslatot tettünk az identifikációhoz szükséges ortonormálás opcióira. A cFSM módszert összehasonlítottuk a GBT (Generalized Beam Theory) módszerrel, rámutattunk a lényeges hasonlóságokra és különbségekre. Kidolgoztunk egy eljárást, melynek segítségével végeselemes módszerrel meghatározott sajátalakok mód-identifikációja is elvégezhető közelítően. Analitikus megoldottuk síkbeli és tisztán elcsavarodó kihajláshoz tartozó kritikus erő számítását, a rudat felületelemekkel modellezve, a lemez- és tárcsaelmélet feltevéseit használva. A megoldás magyarázatot ad a cFSM és más módszerek között a kihajlási/kifordulási kritikus értékben adódó különbségekre. Paraméteres vizsgálatokat hajtottunk végre a cFSM és a fél-analitikus végessávos módszer (VSM) közötti eltérésekre. Vizsgáltuk a VSM-be jelentkező interakció hatását, valamint a hidegen hengerelt szelvények esetén jelenlévő saroklekerekítések hatását. | We have proposed new, mechanics-based definitions for the various buckling types of thin-walled members. We have worked out the constrained Finte Stip Method (cFSM). cFSM is able to perform elastic stability analysis for uniform two-hinged members with arbitrary thin-walled cross-section: critical force/moment can be calculated to any clear or interacted buckling modes. We have shown that cFSM is able to identify arbitrary buckling mode calculated by a regular finite strip analysis, i.e., to determine the contribution of the buckling types to a given buckled shape. Options have been proposed for the orthonormalization, necessary for the identification. We have compared cFSM and the Generalized Beam Theory, important similarities and differences have been identified. We have proposed an approximate method for the identification of buckling modes calculated by finite element method. We have given analytical solution for the critical force to flexural and pure torsional buckling of columns. The solution is based on shell model in which the member is modelled by surface elements. The solution explains the differences of critical forces/moments for global member buckling, calculated by cFSM and other methods. We have performed parametric studies to analyze the differences between cFSM and semi-analytical finite strip method (FSM). We have investigated the interaction effect in FSM, as well as the effect of rounded corners typical for cold-formed members

Is the Definition of Roma an Important Matter? The Parallel Application of Self and External Classification of Ethnicity in a Population-Based Health Interview Survey

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Data to genetic risk assessment on high-density cholesterol level associated polymorphisms in Hungarian general and Roma populations

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A Visco-hypoplastic Constitutive Model for Rolled Asphalt

Experience has shown that the durability of “high-modulus” asphalts made with modified bitumen is unsatisfactory. The misdirected “development” forced in recent decades necessitates a more accurate understanding of the mechanical behavior of rolled asphalts, i.e., constitutive formulation of a numerical asphalt model. The authors elaborate a numerical procedure to model the visco-hypoplastic constitutive behavior of the rolled asphalts by the appropriate composition of the hypoplastic theory of soil mechanics and, taking into account the existing asphalt models. This proposal is justified because rolled asphalt is nothing more than an aggregate skeleton of mineral origin, the voids of which are filled with high-viscosity bitumen. The model allows to quantify the interaction of the two components, such as the formation of ruts due to pressure on the bitumen, the formation of cracks due to cooling-induced tensile stresses, and the viscous behavior of asphalt. Validity of this complex numerical model can already be considered proven theoretically, but it still needs to be experimentally verified for the viscous behavior. This new constitutive model has important theoretical and practical consequences such as a new visco-hypoplastic model of rolled asphalt as partially saturated granular material with cooling-induced isotropic residual stresses