Simplifications of the numerical model in the design of bar and diaphragm bracing systems

Molecular dynamics (MD) simulations are performed using adaptive intermolecular reactive bond order potential to analyze single-walled and double-walled carbon nanotubes. These carbon nanotubes were analyzed for buckling under compression and under torsion. The MD simulations create a comprehensive database for the critical buckling loads/strains and critical buckling torques/twist angles for armchair SWCNTs and DWCNTs of varying diameters and lengths. Using MD results as a computational benchmark, an equivalent thick shell model of CNT is proposed, which is amenable for analysis using a commercially available software ABAQUS. Based on our MD results, an empirical equation that describes the size-dependent Young's modulus for a single-walled carbon nanotube is established. Buckling analysis of CNT under compression and under torsion are performed with the equivalent shell model using size-dependent Young's modulus, Poisson's ratio = 0.19 and shell thickness h = 0.066 nm. We show that the equivalent shell model gives good estimate of critical buckling load/strain and critical buckling torque with respect to the MD results. Variation of critical twist angle with length of CNT, predicted by the shell model is in good qualitative agreement with MD simulation. However, the equivalent shell model underestimates the critical twist angle by 30% because the continuum shell model overestimates torsional stiffness of CNT compared to an atomistic model of CNT. The equivalent shell model is less computational intensive to implement as compared with MD. Its accuracy for predicting the buckling states for long carbon nanotubes allows it to be used for moderately long CNTs under compression/torsion, in-lieu of MD simulations.

Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. In this paper, an orthotropic elastic shell model with transverse shearing is developed to study the effects of transverse shearing on shell-like mechanics of microtubules. The study is based on a detailed comparison between four elastic beam and shell models with and without transverse shearing. It is shown that the length-dependent flexural rigidity of microtubules predicted by the present orthotropic shell model with transverse shearing is in good agreement with known experimental data and is consistently close to that given by the Timoshenko-beam model. Our results show that transverse shearing is essential for shell-like deformation of microtubules when the axial wave-length is not extremely long (compared to the diameter of microtubules which is ~25 nm) or the circumferential wave-number is larger than unity. In particular, transverse shearing is found to significantly lower the critical pressure for buckling of a long microtubule under radial pressure and leads to an even better agreement with recently observed experimental data. These results suggest that the 2D orthotropic shell model with transverse shearing is suitable to study the shell-like mechanics of microtubules for short axial wave-length and circumferential wave-number exceeding unity.

The paper presents the influence of sheet/purlin fasteners location (in reference to trapezoidal profile cross section) on shear flexibility of the cladding acting as a diaphragm. Analytical procedures were presented and their limitations were discussed. Next, selected schemes of fasteners location, known from engineering practice, but not included in European codes and recommendations, were analysed numerically in order to observe the differences in shear stiffness of the panel. The cantilevered diaphragm as a part of the roof of a single storey building was chosen for the analysis. The analysis was carried out for the valley-fixed trapezoidal sheeting with wide pans. Corrugated sheets were built by two types of models: full 3D shell model and equivalent orthotropic 2D shell model. Flexibility of fasteners and connections was included in the calculations using equivalent beam finite elements. The results were discussed from the stressed-skin design point of view.

Surface effect on buckling of microtubules in living cells using first-order shear deformation shell theory and standard linear solid model

An equivalent cylindrical shell model of vibration analysis based on simplified repeating unit cell for ring truss structure

Laminated shell model with second-order expansion of the reciprocals of Lamé coefficients Hα, Hβ and interlayer continuities fulfilment

3D shell model for the thermo-mechanical analysis of FGM structures via imposed and calculated temperature profiles

In the article three variants of roof bracing were considered: bar bracing, diaphragm bracing and the combination of bar and diaphragm bracing. Different analytical and numerical ways of taking into account the imperfections of the truss girder were compared. The entire 3D model of the roof (shell and beam elements with the eccentricities taken into account) was analysed numerically. Selected stressed-skin aspects were considered. Stabilizing forces in the purlins and forces in bracing elements (bar and/or diaphragm bracing, connections) were observed. The importance of the imperfection issues (e.g. shape of the imperfection, method of including imperfection, wind forces) was evaluated numerically to indicate the key points in the design procedure. The biggest forces in purlins occurred for “nonstandard” shape of the imperfection. On the other hand, in case of bracing elements, when wind forces were taken into consideration, “standard” approach of including the imperfection was safe approximation. Moreover, the diaphragm took over significant part of the bracing forces, however the distribution of the forces depended strongly on the flexibility of the bracing and purlin/truss connection.

Carbon nanotubes (CNTs) have potential applications in various fields of science and engineering due to their extremely high elasticity, strength, and thermal and electrical conductivity. Owing to their hollow and slender nature, these tubes are susceptible to buckling under a compressive axial load. As CNTs can undergo large, reversible post-buckling deformation, one may utilize this post-buckling response of CNT to manufacture mechanical energy storage devices at the nano-scale, or use it as a nano-knife or nano-pump. It is therefore important to understand the buckling behavior of CNTs under a compressive axial load. Experimental investigations on CNT buckling are very expensive and difficult to perform. As such, researchers often rely on molecular dynamics (MD) simulations, or continuum mechanics modeling to study their mechanical behaviors. In order to develop a good continuum mechanics model for buckling analysis of CNTs, one needs to possess adequate experimental or MD simulation data for its calibration. For “short” CNTs with small aspect ratios (≤10), researchers have reported different critical buckling loads/strains for the same CNTs based on MD simulations. Moreover, existing MD simulation data are not sufficiently comprehensive to allow rigorous benchmarking of continuum-based models. This chapter presents extensive sets of MD critical buckling loads/strains for armchair single-walled CNT (SWCNTs) and double-walled CNTs (DWCNTs), with various aspect ratios less than 10. These results serve to address the discrepancies found in the existing MD simulations, as well as to offer a comprehensive database for the critical buckling loads/strains for various armchair SWCNTs and DWCNTs. The Adaptive Intermolecular Reactive Bond Order (AIREBO) potential was adopted for MD simulations. Based on the MD results, the Young’s modulus, Poisson’s ratio and thickness for an equivalent continuum cylindrical shell model of CNTs are calibrated. The equivalent continuum shell model may be used to calculate the buckling loads of CNTs, in-lieu of MD simulations.

In this paper, an equivalent thick cylindrical shell model is proposed for the buckling analysis of short single-walled carbon nanotubes (SWCNTs) with allowance for different chiral angles. Extensive, molecular dynamics (MD) simulations are first performed using the adaptive intermolecular reactive bond order potential to determine the critical buckling loads/strains. The MD simulations buckling results are then used as reference solutions to calibrate the properties of the thick cylindrical shell model. Central to this development is the establishment of an empirical expression for the Young's modulus that is a function of both the diameter and the chiral angle of the SWCNT. For the shell model, we have assumed that the Poisson ratio ν = 0.19 and the shell thickness h = 0.066 nm . It will be shown that the proposed shell model furnishes good estimates of the critical buckling loads for SWCNTs with different chiral angles. The critical buckling strains are also evaluated from the critical buckling load with the aid of the stress–strain relation of SWCNTs.

The article analyses the impact of wind suction on roof coverings glued with polyurethane adhesives to flat roofs, i.e., roofs with an up to 20% slope. The impact of the cyclical wind was simulated in fatigue tests, gradually increasing the test pressure in repeated sequences until the first delamination occurred. The tests were carried out for eight test sets, with concrete and trapezoidal sheets used as a construction substrate, on whose surface thermal insulation layers were glued with polyurethane adhesive; the thermal insulation layers were EPS (expanded polystyrene) and PIR (polymer mainly of polyisocyanurate groups), respectively, followed by flexible sheets, i.e., a laminated PVC membrane (polyvinylchloride) and an EPDM (terpolymer of ethylene, propylene and a diene with a residual unsaturated portion of diene in the side chain)-type rubber-based membrane. The test results were compared with the functional requirements determined with computational simulation methods for the maximum wind load values on the example of wind loads for Poland. The tests confirmed that some polyurethane adhesives could ensure the operation of flexible sheets used as flat roof coverings that are failure-free from the point of view of resistance to wind suction.

The purpose of the paper is to perform a static analysis of a thin-wall cold-rolled steel cross-section of a trapezoidal sheet by means of a mathematical model developed in ANSYS, commercially available software applications. The trapezoidal sheets are used typically as an external cladding which covers the structures of steel halls. Investigating into behaviour of the trapezoidal sheets subjected to extreme loads represents an urgent issue in wind engineering. A physical tension test has been performed in order to verify and confirm the mathematical model. Experiments have been performed to prove results of the static analysis into the behaviour of a load-carrying structure formed by a thin-wall cross-section.

For most plants the mathematical model is not known exactly or it is too complicated for the controller design (for example it may be nonlinear). The usual procedure is to design the controller with a simplified model and nominal values of the plant parameters. An important design goal is therefore to reduce the influence of parameter uncertainty, neglected dynamics, and nonlinearity on the dynamics of the closed loop. A survey on the origin of uncertainty in modelling and model simplifications and on design of robust, adaptive and intelligent control systems is given in [85.1].

Within the past few years remarkable progress has been achieved on the nonlinear analysis of so termed flexible shells, mainly influenced by the fundamental results of Reissner, John and Koiter [1–4]. A novel approach to the displacement formulation of general and constrained geometrically nonlinear shell equations has been given in recent years by Pietraszkiewicz [5–7]. In particular, based on polar decomposition of shell strains and rotations it was suggested to classify small strain shell models according to the magnitude of the rotation angle of the material elements. It is known from the literature that most of the engineering shell problems may be tackled accurately enough with the help of moderate rotation shell theories [5–12]. Numerical applications of corresponding shell equations may be found e.g. in [12–14], There are, however, various one- and two-dimensional shell problems to which large rotation shell models with nonlinear membran and bending strains should be applied. In these situations the rotational part of deformation dominates. Several shell theories with nonlinear change of curvature expressions have been already given (see [15–17] and literature cited therein). It turned out, however, that most of the corresponding field equations are very complicated and virtually useless for numerical applications. On the other hand we have shown recently [16] that various approaches used in engineering practice may lead to inconsistent shell equations.

Aeroelastic vibration, influenced by wind load effects, is relevant to the structural design of tall buildings. In the framework of performance-based design of wind load–sensitive structures, the effects induced by variability in the loading estimation, often relying on the results of a wind tunnel test, must be evaluated. This research is a continuation of a recent study by the author on the stochastic dynamics of tall buildings, contaminated by experimental errors, wind load uncertainty, and modeling simplifications. A number of reduced-order models are described and discussed. Among these models, a recently developed one that couples the along-wind dynamic response with intervention costs due to nonstructural damage on the external façade is considered. Even though the models assume a linear structural response dominated by the primary vibration modes and vortex shedding effects are not directly considered, they are sufficiently accurate for the purpose of evaluating, in a semianalytical form, the probability density function of the generalized dynamic response. The study examines the use of the reduced Fokker–Planck equation in high dimensions to derive the probability function of stationary wind response, depending on the mean wind speed and standard deviation of a parametric along-wind loading error term.