Constrained Finite Element Method: Demonstrative Examples on the Global Modes of Thin-Walled Members

In this paper a novel method is presented for the modal decomposition of thin-walled members. The proposed method follows the logic of the constrained finite strip method (cFSM), however, polynomial longitudinal shape functions are applied together with a longitudinal discretization. Thus, strips are transformed into multiple shell finite elements. The longitudinal shape functions are selected in such a way that modal decomposition similar to cFSM can be realized, therefore, the new method can conveniently be described as constrained finite element method (cFEM), possessing all the modal features of cFSM, but with significantly more flexible applicability. The method is briefly presented and illustrated by global buckling problems

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

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

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

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

Stability Analysis of Thin-Walled Members with Curved Cross-Section Parts: Inelastic Behavior

In this paper the buckling behavior of thin-walled members with cross-sections with curved parts is investigated. Due to the curved parts, shell-like buckling is a potential mode of failure. The objective of the research is to understand whether shell-like buckling behavior might be governing in practical cold-formed steel members. For this aim, numerical studies have been carried out, involving linear buckling analysis as well as nonlinear analysis with imperfections, by considering various cross-sections. Based on the results it is concluded that shell-like behavior might be critical in certain 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

Investigation of the relationship of general and digital health literacy with various health-related outcomes

BackgroundDespite the growing number of health literacy surveys, we know little about the combined effect of the different dimensions of health literacy on various health-related outcomes.ObjectiveThus, our study aimed to examine the impacts of general and digital health literacy on health behaviour, confidence in vaccination, self-perceived health, and health care utilization.MethodsOur research was part of the Health Literacy Population Survey 2019–2021, which was an international, multicentre, cross-sectional study. The data were collected via computer-assisted telephone interview in December 2020 in Hungary. Multiple multinomial logistic and multivariate linear regression models were used to analyse the separately effects of general and digital health literacy on the studied outcomes. Moreover, the combined effect of general and digital health literacy was also analysed via sensitivity analyses. In the last step, the interactions between general and digital health literacy were examined using the Johnson-Neyman procedure.ResultsThe results did not reveal any associations between health literacy and health behaviour. Health care use was only affected by digital health literacy; however, this effect was inconsistent. Both dimensions of health literacy were positively associated with self-perceived health and vaccination confidence.ConclusionOur results suggest that increasing health literacy could promote health and vaccination confidence, while the potential effect of higher digital health literacy on more conscious use of the health care system should be investigated further