PWN ; Starosolski W., Komputerowe modelowanie betonowych ustrojów inżynierskich. Wybrane zagadnienia. Tom 1 i 2 Wydawnictwa Politechniki Śląskiej. Starosolski W.: Komputerowe modelowanie betonowych ustrojów inżynierskich, Sieczkowski J.: Podstawy komputerowego modelowania konstrukcji. P. Kossakowski, Inżynierski problem komputerowego modelowania pracy Komputerowe modelowanie betonowych ustrojów inżynierskich wybrane.

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Experimental and numerical investigations Discrete-based medium may be classified as a microstructured medium, and the microstructure can be related to the atomistic composition at a subscale, but also to the molecule, crystal, grain or truss organization betonoowych larger scales.

Historically, Lagrange during the XVIII-th century first obtained analytical results for the discrete string, which is reconsidered here as a paradigmatic structural model. The free vibrations equation of the microstructured string of length L is governed by a linear difference equation: It can be shown that the frequency equation of this discrete problem with the fixed-fixed boundary conditions w 0 w n 0 can be analytically solved and the exact frequencies are given by Lagrange [1]: The vibration frequency of the fixed-fixed nonlocal string is then modellowanie by introducing a sinusoidal mode shape in Eq.

The same reasoning may be followed for discrete beams or discrete plates. Hencky s model [] composed of rigid links connected by concentrated elastic springs can be considered as a discrete beam model, where the bending moment is related to the deflection as: M wi1 wi wi1 i EI 5 which may be approximated, after a continualization process, by the nonlocal constitutive law, whose differential format is of Eringen s type [5]: M 16 a e0 a M EI with w and e 0 6 These results may kompurerowe generalized to the in-plane and out-of-plane motion see Challamel [6, 7, 8]statics versus dynamics, one-dimensional versus two-dimensional plate media.

### Computer Methods in Structure Design (06 18 00)

Nonlocal structural mechanics is definitely an efficient engineering theory that may be able to capture the fundamental scale effects related to the microstructure of the discrete element.

A lot of applications may be found in the small-scale world but also for inyniesrkich scale structures in civil engineering such as truss structures for usrtojw. Applied Physics, Solids Structures, 51,. These factors concern local perturbations dominating over a spectrum of initial imperfections and external actions, non-uniform loading, discontinuities cuts, openingsnon-uniform loads application and non-uniform boundary conditions.

In this case the theoretical analysis of stability based on linear precritical and bifurcation models is insufficient.

An adequate approach to the real buckling process is a consecutive geometrically nonlinear analysis until the shell collapse.

Until recently, a successful carrying out of such analysis was unreal, but now due to modern computers and software based on finite element method FEMthis analysis appears quite possible. The article examines numerical imynierskich within ANSYS software beyonowych three groups of problems of deformation and buckling of axially compressed elastic circular cylindrical shells with essentially non-uniform precritical SSS.

Problems of the group 1 are devoted to the investigation of geometrically nonlinear behaviour of axially compressed shells under transversal kinematic local quasi-static actions LQA [1]. As LQA cause a strong non-uniform SSS of shells, the nature and conditions of load application influence on the features of shell behaviour. In this connection, geometrical and FE models of shells and also simulation models of five schemes of application and removal of an axial loading and LQA have been developed.

The axial loading is applied through rigid disks according to two types: The models of shells also consider three types of boundary conditions on the edges.

For two types the shell edges are hinged betonowhch rigid disks schemes Thus, for one type free out-of-plane ustrpjw are possible schemes 1,and for another one parallel edge displacements are supposed schemes 3, 4. For the third type of boundary conditions radial and tangent displacements are restricted on the edges, but out-of-plane edge displacements are allowed scheme 5. Numerical buckling simulations have been carried out by means of geometrically nonlinear analyses realized for step-by-step loading of a shell.

This research also studies the influence of the sequence of the axial load and LQA application typical or initial LQA. For 5 komputterowe schemes in a wide range of axial loads, dependences of transversal reactions on typical lateral LQA are received. These dependences completely reflect main features of shells behaviour for desired axial load and LQA. For the schemes in the certain area of axial betonoych these dependences show an existence of the stable buckling mode of a shell with one local dent that corresponds to the experimental data and analytical solutions.

For the scheme 5 these dependences have a different character in comparison with other schemes. The visualisation results and comparisons of numerical In this case, the criterion of bifurcation points is a divergence of numerical solutions. Problems of the group concern the buckling behaviour of axially compressed shells with one transversal in the middle section or one longitudinal cut of various lengths [].

FE models reflect 5 mentioned loading schemes. Besides, numerical simulations repeat 60 own buckling tests of shells with cuts compressed according betonoeych the scheme betonowyc. Numerical problems consider three buckling analyses: The solution III provides the best correspondence to the experimental data for any cuts.

The main features of linear and geometrically nonlinear analyses of buckling problems are determined depending on loading schemes and on cut lengths.

A high efficiency of ANSYS software has been proved for numerical simulations of shells buckling taking into account a physical nonlinearity of material. Problems of the group 3 deal with numerical analyses [3] of deformation inyniwrskich stability of elastic circular cylindrical shells undergoing periodically non-uniform SSS of different nature: The study is focused on the effect of static resonance.

This effect consists in the increase of static lateral deformation of the shell and decrease of limit load in a case of non-uniform Beyonowych similar to the form of first Eigen vibration mode of a shell. The present ustrijw also contains an important number of comparisons of numerical solutions with experimental, analytical and other inynierakich researches. For all the groups of problems an excellent correspondence between the numerical results and known solutions confirms a good applicability of ANSYS software for the deformation and buckling problems of axially compressed cylindrical shells with essentially nonuniform SSS.

This work is supported by Alexander von Humboldt Foundation Institutional academic cooperation program, grant no. Theory and Applications, eds. Gorski, London, 3,pp [3] Krasovsky V.

### Proceedings of the STABILITY of STRUCTURES XIV-th SYMPOSIUM – PDF

Review and Current Trends in Stability of Structures, eds. The paper is devoted to post-buckling behaviour of selected elastic structures, in particular the shells of revolution with positive and negative Gaussian curvature, and also a seven-layer orthotropic cylindrical shell. The scheme of the Cassini ovaloidal shell and the equilibrium path The shells of revolution with positive and negative Gaussian curvature are distinguished by stable equilibrium paths.

The example of this shell is the Cassini ovaloidal shell Fig. The buckling and post-buckling behaviour of a family of these shells under external pressure were numerically FEM investigated by Malinowski et al [8]. The distinguishing mark of these shells are the stable equilibrium paths Fig. Scheme of the seven-layer cylindrical shell and the equilibrium paths The research was conducted within the framework of Statutory Activities in House of Poznan Univ. Science, 10, 4,pp Thompson J.

In the initial solutions, the flanges are made of flat plates, welded to the sinusoidal web sheet, requiring a specific welding technology. A new solution is proposed by the authors, in which the beam is composed by a web of trapezoidal cold-formed steel sheet and flanges of back-to-back lipped channel sections.

For connecting flanges to the web self-drilling screws are used. The paper summarizes the experimental and numerical investigations carried out at the CEMSIG Research Centre of the Politehnica University of Timisoara and, at the end, presents an investigation of sensitivity of webs to distortion of corrugations when the size of corrugations increases.

Five beams with corrugated webs CWB with a span of mm and a height of mm have been tested, considering different arrangements for self-drilling screws and shear panels. References [1] and [] show detailed information related to the behaviour of each tested specimen. Figure 1 shows, as an exemplification, the deformed shape of the CWB-5 beam at collapse and the distortion of the web corrugation in the region with the reduced number of screws.

Additional tests in order to determine the material properties and connections behaviour have been performed. Based on the conclusions of the second beam, of 16 m span with parallel flanges, on the following, the influence of the depth of corrugation on the global behaviour was studied.

In this sense, three different depths for the corrugated web have been chosen, i. For this analyses the case with transversal translational and rotational springs at the top 1. Also, it should be mention that in case of screws, the optimized solution used for beam CWB-5 was adopted, i. Plotting all three curves on the same graph, it is easy to see that curve for corrugation A85 has a reduced stiffness compared to the other two due to the fact the depth of the corrugations is more sensible to the end distortion of the corrugations.

More, after reaching the maximum load the curve drop suddenly and a stable path can be seen due to the buckling coming from in-plane loading of the web. The curves for corrugation A30 and A45 have the same stiffness, but the maximum force is lower in case of A45 and a plateau can be seen.

Another aspect is related to the optimisation of screws used both as seam fasteners and for connecting the web to the flanges.

Force-displacement curve for the three different depths of corrugated web On the aim of optimizing the technical solution for a mass production of such beams, the further investigations will focus on these aspects.

YORK Aerospace Sciences, School of Engineering, University of Glasgow James Watt South Building, Glasgow G1 8QQ, UK Loughlan [3] reminded us that the structural design engineer who is unaware of the degrading influence of Bending Twisting coupling on buckling response may choose a lay-up configuration for which a simple orthotropic analysis approach leads to a significant overestimate of the critical shear stress, i.

This degrading influence applies equally to the critical compressive stress, yet recent studies [1] illustrate that the exact closed form solution for othotropic laminates continues to be incorrectly applied to Bending Twisting coupled designs.

For laminated plates that have a fixed number of constant-thickness plies, Loughlan [3] demonstrated, by a finite strip approach, that, for a given degree of material anisotropy, the stacking sequence of the plies significantly alters the degree of Bending Twisting coupling in the laminate and hence the shear buckling performance.

Composite plates that have the same dimensions and are of the same weight behave very differently as a result of lay-up configuration. It should also be noted that these effects are direction dependent, i. The current article serves to provide more clarity on this subject by identifying laminates with matching stiffness properties, which differ only by their coupling terms D 16, D 6thus offering a clearer understanding on their isolated influence on buckling performance.

The non-dimensional bounds on both compression k x, and shear k xy, buckling strength have previously been assessed using closed form solutions, applied to a definitive listings of Bending Twisting coupled laminates [7]: However, subsequent comparisons of these approximate closed form solutions, against an exact infinite strip method, has revealed that whilst high level inaccuracy is obtained for certain anisotropy characteristics, there are significant errors on the unsafe side, for others.

Compression buckling assessments were found to be within 0. Shear buckling assessments revealed a rather more random distribution with much larger inaccuracies. These inaccuracies will be addressed in this article and the applicability of the revised closed form buckling solutions to fibre-metal laminates FML will be demonstrated.

That combination provides many benefits such as higher bearing strength and huge impact resistance comparing pure metallic material. Connection with fibre reinforced material also guarantees better fatigue characteristics as well as high strength and stiffness of the structure.

FMLs are also characterized by relatively high corrosion and fire resistance which increase significantly its durability [1].

Furthermore, Fibre Metal Laminate composites can be designed to be strong in a specific direction which gives engineers a lot of possibilities for specific industrial application. Another great advantage of FMLs over conventional material is a low density of the material which results in lower mass of entire structure.

## The impact of the use of building information modeling on its durability

For the purpose of this study, the 3- FML profiles of Z-section were designed by appropriate composite layers arrangement. To obtain accurate profile geometry and properties samples were manufactured in the pressure chamber of the autoclave system. Performing curing cycle of that system at a specific heating rate and pressures allowed to obtain high-quality composite structures [5].

Simply support boundary conditions were defined by blocking kinematic degrees of freedom of loaded edges [4]. Specific nodes were coupled to guarantee the equal displacement and uniform compression in axial direction. Numerical analyses of the structure stability were performed in two stages.