Application of Geometrical and Material Nonlinear Analysis (GMNA) for evaluating the load-carrying capacity of compressed thin-walled steel members of class 4

The paper presents a study of the capacities of steel rack frames based on linear analysis (LA), geometric nonlinear analysis (GNA), and geometric and material nonlinear analysis (GMNIA). In the case of linear and geometric nonlinear analyses, the design is carried out to the Australian cold-formed steel structures AS/NZS4600. The study includes braced, unbraced, and semi-braced frames, and compact and noncompact cross sections. The paper shows axial force and bending moment paths for geometric and geometric and material nonlinear analyses, and explains the differences observed in the design capacities obtained using the different types of analysis based on these paths. The paper provides evidence to support the use of advanced GMNIA for the direct design of steel rack frames without the need for checking section or member capacities to a structural design standard.

A mixed element (3fME) for geometric and material nonlinear finite element analysis of plane skeletal structures is presented, which can reach any predefined accuracy with only one element per structural member. This element is based on the 3-field approach−an application of the Hu-Washizu principle−directly approximating the fields of displacements, strains and stresses. The presented formulation considers both (i) geometrically nonlinear behavior−by including the second-order term in the strain-displacement relations and establishing equilibrium in the deformed configuration−and (ii) materially nonlinear elastoplastic behavior, at the fibre level, automatically handling the axial-bending interaction. The illustrative examples include both compression- and tension-bending interaction, and compare the accuracy of the novel finite element with published results.

Sensitivity of plate response calculations to blast load definition

In recent years, high-strength steel has been used extensively for infrastructures because of its many advantages, such as its ductility and strain-hardening properties, which are inferior to those of ordinary structural steel, and the small dimensions of the structural elements, which lead to greater freedom and elegance in design, resulting in lighter structures. In practice, imperfections such as residual stresses due to the welding process and pre-buckling mode imperfections are inevitable in cylindrical structures made of high-strength steel. A small imperfection amplitude can lead to a disproportionate reduction in buckling strength. Therefore, imperfection sensitivity should be considered when studying the buckling behaviour of the shell. The influence of the combined residual stress and pre-buckling mode imperfection on the buckling behaviour of Q690 high strength steel cylindrical shell under global bending has not yet been investigated and described for all dimensions. In this paper, the combined imperfections influences on the buckling behaviour of high-strength steel cylindrical shell in global bending in the elastic-plastic range are investigated. Using the ABAQUS fine elements software, perfect cylinders with a constant length to thickness ratio equal to 7 and a radius to thickness ratio in the range 10≤ r/t ≤700 were considered to perform the linear bifurcation analysis (LBA) and the geometric nonlinear analysis (GNA). The non-linear analysis with imperfections (GNIA) and the geometric and material non-linear analysis with imperfections (GMNIA) were then performed considering imperfection amplitudes between 0.01 and 2 to derive the critical buckling loads known as bifurcation point for the models with different aspect ratio. The influences of the combined imperfections show that moderately and very thin cylinders are very sensitive to the increase of the pre-buckling mode imperfection amplitude and their buckling strength is insensitive to plasticity. For thick cylinders, the effect of plasticity is more consistent, while the buckling strength is not significantly affected by the increase in pre-buckling mode imperfection amplitude. The main objective is to predict the buckling sensitivity of cylinders under the influence of combined residual stress and pre-buckling mode imperfection. The obtained results, comments and conclusions intend to allow for safer.

Modeling with a combined geometric and material nonlinear analysis is described in this paper and applied to tensegrity rings representing the last generation of the tensegrity systems. The resulting algorithm model is new; it takes into account slackening and yielding of cables. The usual Newton–Raphson iterative method is used, but in an updated Lagrangian formulation. The response of an isolated and an assembly of several square-based ring cells subjected to different types of loads has been investigated by means of nodal displacements. It is shown that the tensegrity rings are less flexible as compared to the classical tensegrity systems. Special attention is paid to the influence of the slackening and yielding of cables on the total nonlinear behavior. It has been found that their combination in a nonlinear analysis model is important for a better understanding of the response of tensegrity rings.

Stability calculation is the main objective during the analysis of domes. To investigate the effects of the initial defect, geometric nonlinearity, and material nonlinearity on the stability performance of different dome structures, 60 m numerical models were built and optimized by an iterative force-finding APDL program. Then, linear buckling analysis, geometric nonlinear stability analysis, geometric nonlinear stability analysis with initial defects, and dual nonlinear analysis with initial defects were discussed to compare the stability performance of ridge-beam cable domes (RCDs), suspen-domes, and conventional cable domes via finite element analysis. The results show that the buckling loads all follow the order of initial defect + dual nonlinear analysis < initial defect + geometric nonlinear analysis < geometric nonlinear analysis < linear buckling. The addition of ridge beams improves the overall stability and transforms the instability modes from local concave instability to overall torsional buckling. The ultimate load amplification coefficients of the RCD are close to those of the suspen-dome, while the vertical displacements of the RCD are more than those of the conventional cable dome, so the RCD has sufficient stiffness to reduce local displacement. Under 2–3 load combinations, internal ridge beams change from a tensile-bending state to a compressive-bending state, causing the entire instability of the RCD afterwards.

KEYWORD: Bridge; Cable-stayed; Nonlinear analysis; Prestressed concrete; Under-deck ABSTRACT: Under-deck cable-stayed bridges have recently emerged as one of promising bridge forms due to their remarkable advantages such as high structural efficiency, easy construction, econ- omy and elegant appearance. The stayed cables provide supports on the prestressed concrete deck. The cables are located under the deck and deviated through struts, which introduces cable deviation forces on th e deck. In the design of this type of bridges, both the ultimate load and ductility should be examined, which requires the estimation of full-range behaviour. An analytical beam model and its correspond- ing beam finite element model for geometric and material nonlinear analysis are developed for this type of bridges. The model accounts for the interaction between the axial and flexural deformations of the deck, and uses the actual stress-strain curves of materials considering their stress path- dependence. In the structural system, the deck interacts with the stayed cables. With a nonlinear ki- nematical theory, complete description of the nonlinear interaction between the stay cables and the deck is obtained.

Reliability based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections

Determination of the patch loading resistance of girders with corrugated webs using nonlinear finite element analysis

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Numerical investigations

Concrete bridges with corrugated steel webs and prestressed by both internal and external tendons have emerged as one of the promising bridge forms. In view of the different behaviour of components and the large shear deformation of webs with negligible flexural stiffness, the assumption that plane sections remain plane may no longer be valid, and therefore the classical Euler-Bernoulli and Timoshenko beam models may not be applicable. In the design of this type of bridges, both the ultimate load and ductility should be examined, which requires the estimation of full-range behaviour. An analytical sandwich beam model and its corresponding beam finite element model for geometric and material nonlinear analysis are developed for this type of bridges considering the diaphragm effects. Different rotations are assigned to the flanges and corrugated steel webs to describe the displacements. The model accounts for the interaction between the axial and flexural deformations of the beam, and uses the actual stress-strain curves of materials considering their stress path-dependence. With a nonlinear kinematical theory, complete description of the nonlinear interaction between the external tendons and the beam is obtained. The numerical model proposed is verified by experiments.

Provisions leading to the assessment of the buckling resistance of pressurised spherical shells are available since 2008 when they were published first time as the European Design Recommendations (EDR) (cf. Rotter and Schmidt in Buckling of Steel Shells: European Design Recommendations. ECCS, 2008 [13], Rotter and Schmidt in Buckling of Steel Shells: European Design Recommendations. ECCS, 2013 [14]). This collection of recommendations comprises rules which refer to the buckling resistance of steel shells of different shapes. In the first step of the general procedure, the calculation of two reference quantities: the elastic critical buckling reference pRcr and the plastic reference resistance pRpl is required. These quantities should be determined in the linear buckling analysis (LBA) and in the materially nonlinear analysis (MNA) respectively. Only in the case of spherical shells the existing procedure has exceptional character. It is based on the geometrically nonlinear analysis (GNA) and on the geometrically and materially nonlinear analysis (GMNA), respectively. From this reason, in this particular case there was a need to change the existing provisions. The first version of a new procedure was presented in the work of Blazejewski and Marcinowski (Buckling capacity curves for pressurized spherical shells. Taylor & Francis Group, London, pp. 401–406, 2016 [4]). All steps of the procedure leading to the assessment of buckling resistance of pressurized steel, spherical shells were presented in that work. The elaborated procedure is consistent with provisions of Eurocode EN1993-1-6 (cf. Blazejewski and Marcinowski in The worst geometrical imperfections of steel spherical shells, pp. 219–226, 2014 [3]) and with general recommendations inserted in Europeans Design Recommendations. In the present work the proposed capacity curves were compared with the existing provisions of ECCS for three different fabrication quality classes predicted. Comparisons of the author’s proposal with some experimental results obtained by other authors are presented as well. They have confirmed that the proposed procedure is less conservative than the existing one but it is still safe.

Existing provisions leading to the assessment of the buckling resistance of pressurised spherical shells were published in the European Design Recommendations (EDR) [1]. This book comprises rules which refer to the stability of steel shells of different shapes. In the first step of the general procedure they require calculation of two reference quantities: the elastic critical buckling reference <i>p</i><sub>Rcr</sub> and the plastic reference resistance <i>p</i><sub>Rpl</sub>. These quantities should be determined in the linear buckling analysis (LBA) and in the materially nonlinear analysis (MNA) respectively. Only in the case of spherical shells the existing procedure has exceptional character. It is based on the geometrically nonlinear analysis (GNA) and on the geometrically and materially nonlinear analysis (GMNA), respectively. From this reason, in this particular case there was a need to change the existing approach. The new procedure was presented in the work of Błażejewski & Marcinowski in 2016 (comp. [2]). All steps of the procedure leading to the assessment of buckling resistance of pressurized steel, spherical shells were presented in this work. The elaborated procedure is consistent with provisions of Eurocode EN1993-1-6 (comp. [3]) and with recommendations inserted in Europeans Design Recommendations [1]. The proposed capacity curves were compared with existing proposal published in [1] for three different fabrication quality classes predicted in [3]. In this work also comparisons of author’s proposals with experimental results obtained by other authors were presented.

The objective of this paper is to demonstrate how simple bar-spring models can illustrate elementary and advanced structural behavior, including stability, imperfection sensitivity, and plastic collapse. In addition, the same bar-spring models also provide a ready means for assessing structural reliability. Bar-spring models for a column (both post-buckling stable and unstable), a frame, and a plate are all developed. For each model the influence of geometric imperfections are explicitly introduced and the ultimate strength considering plastic collapse of the supporting springs derived. The developed expressions are compared to material and geometric nonlinear finite element analysis models of analogous continuous systems, using yield surface based plastic hinge beam elements (in MASTAN) for the column and frame and shell elements (in ABAQUS) for the plate. The results show excellent qualitative agreement, and surprisingly good quantitative agreement. The developed bar-spring models are used in Monte Carlo simulations and in the development of first order Taylor Series approximations to provide the statistics of the ultimate strength as used in structural reliability calculations. Good agreement between conventional first order second moment assumptions and the Monte Carlo simulations of the bar-spring models is demonstrated. It is intended that the developed models provide a useful illustration of basic concepts central to structural stability and structural reliability.

PurposeStainless steel has different advantages when compared to conventional carbon steel. The corrosion resistance and aesthetic appearance are the most known; however, its better behaviour under elevated temperatures can also be important in buildings design. In spite of the initial cost, stainless-steel application as a structural material has been increasing. Elliptical hollow sections integrate the architectural attributes of the circular hollow sections and the structural advantages of the rectangular hollow sections (RHSs). Hence, the application of stainless-steel material combined with elliptical hollow profiles stands as an interesting design option. The purpose of the paper is to better understand the resistance of stainless-steel-beam columns in case of fireDesign/methodology/approachThe research presents a numerical study on the behaviour of stainless-steel members with slender elliptical hollow section (EHS) subjected to axial compression and bending about the strong axis at elevated temperatures. A parametric numerical study is presented here considering with and without out-of-plane buckling different stainless-steel grades, cross-section and member slenderness, bending moment diagrams and elevated temperatures.FindingsThe tested design methodologies proved to be inadequate for the EHS members being in some situations too conservative.Originality/valueThe safety and accuracy of Eurocode 3 (EC3) design methodology and of a recent design proposal developed for I-sections and cold-formed RHSs are analysed applying material and geometric non-linear analysis considering imperfections with the finite element software SAFIR.