Wind uplift strength of trapezoidal steel cladding with closely spaced ribs

When crest-fixed thin trapezoidal steel cladding with closely spaced ribs is subjected to wind uplift/suction forces, local dimpling or pull-through failures occur prematurely at their screw connections because of the large stress concentrations in the cladding under the screw heads. Currently, the design of crest-fixed profiled steel cladding is mainly based on time consuming and expensive laboratory tests due to the lack of adequate design rules. In this research, a shell finite element model of crest-fixed trapezoidal steel cladding with closely spaced ribs was developed and validated using experimental results. The finite element model included a recently developed splitting criterion and other advanced features including geometric imperfections, buckling effects, contact modelling and hyperelastic behaviour of neoprene washers, and was used in a detailed parametric study to develop suitable design formulae for local failures. This paper presents the details of the finite element analyses, large scale experiments and their results including the new wind uplift design strength formulae for trapezoidal steel cladding with closely spaced ribs. The new design formulae can be used to achieve both safe and optimised solutions.

Steady natural convection of non-Newtonian power-law fluid in a trapezoidal enclosure

Numerically investigation of free convection heat transfer in a differentially heated trapezoidal cavity filled with non-Newtonian Power-law fluid has been performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is maintained as uniformly cooled. The top and bottom surfaces are kept adiabatic with initially quiescent fluid inside the enclosure. Finite volume based commercial software FLUENT 14.5 is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 10^5 to 10^7, Prandtl number, Pr of 100 to 10,000 and power index, n of 0.6 to 1.4. Outcomes have been reported in terms of isotherms, streamline, and local Nusselt number for various Ra, Pr, n and inclined angles. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Onset of transition in mixed convection of a lid-driven trapezoidal enclosure filled with water-Al2O3 nanofluid

A numerical study is carried out to investigate the transition from laminar to chaos in mixed convection heat transfer inside a lid-driven trapezoidal enclosure. In this study, the top wall is considered as isothermal cold surface, which is moving in its own plane at a constant speed, and a constant high temperature is provided at the bottom surface. The enclosure is assumed to be filled with water-Al2O3 nanofluid. The governing Navier–Stokes and thermal energy equations are expressed in non-dimensional forms and are solved using Galerkin finite element method. Attention is paid in the present study on the pure mixed convection regime at Richandson number, Ri = 1. The numerical simulations are carried out over a wide range of Reynolds (0.1 ≤ Re ≤ 103) and Grashof (0.01 ≤ Gr ≤ 106) numbers. Effects of the presence of nanofluid on the characteristics of mixed convection heat transfer are also explored. The average Nusselt numbers of the heated wall are computed to demonstrate the influence of flow parameter variations on heat transfer. The corresponding change of flow and thermal fields is visualized from the streamline and the isotherm contour plots.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Natural balancing of flying capacitor voltages in multicell inverter under PD carrier-based PWM

The flying capacitor multicell inverter (FCMI) possesses natural balancing property. With the phase-shifted (PS) carrier-based scheme, natural balancing can be achieved in a straightforward manner. However, to achieve natural balancing with the harmonically optimal phase-disposition (PD) carrierbased scheme, the conventional approaches require (n-1) x (n-1) trapezoidal carrier signals for an n-level inverter, which is (n-1) x (n-2) times more than that in the standard PD scheme. This paper proposes two improved natural balancing strategies for FMI under PD scheme, which use the same (n-1) carrier signals as used in the standard PD scheme. In the first scheme, on-line detection is performed of the band in which the modulation signal is located, corresponding period number of the carrier, and rising or falling half cycle of the carrier waveform to generate the switching signals based on certain rules. In the second strategy, the output voltage level selection is first processed and the switching signals are then generated according to a rule based on preferential cell selection algorithm. These methods are easy to use and can be simply implemented as compared to the other available methods. Simulation and experimental results are presented for a five-level inverter to verify these proposed schemes.

Effect of overload cycles on thin steel roof claddings during cyclonic winds

During an investigation on thin steel roof claddings under simulated cyclonic wind loading, it was found that trapezoidal roof claddings behaved quite differently to corrugated (arc and tangent type) roof claddings due to the presence of overload cycles. The overload cycles caused a reduction in fatigue life for corrugated roofing whereas the reverse occurred for trapezoidal roofing. This contrasting behavior of the two crest-fixed roof claddings was investigated using small scale roofing models instead of the commonly used large scale two-span roof claddings. It was found that overload cycles formed a weaker locally dimpled mechanism around the fastener holes of corrugated roofing and thus accelerated the fatigue-caused pull-through failure. In contrast, a stronger deformed shape was formed in trapezoidal roofing which delayed the pull-through failure. Both laboratory testing and finite element analysis of small scale models were used to study the contrasting behavior of roof claddings.

Shear strength and stiffness of crest-fixed steel claddings

Diaphragm action of crest-fixed profiled steel claddings is present in low-rise buildings whether the designer acknowledges it or not. For the designers to take advantage of the diaphragm strength of the crest-fixed steel claddings in the design of low-rise buildings in a similar manner to valley-fixed claddings, and to design the buildings based on the true behaviour rather than the assumed behaviour, shear/racking behaviour of the three trapezoidal and corrugated steel claddings commonly used at present was investigated using large scale experiments. Crest-fixed claddings (up to a maximum size of 6 x 6.2m) with different aspect ratio and fastening systems were tested to failure, based on which suitable shear strength and stiffness values have been proposed for these claddings as they are used at present. A simple analytical model combined with basic connection data from small scale experiments was used to predict the shear strength of tested panels. Currently attempts are being made to develop general design formulae to determine shear strength and stiffness of crest-fixed steel claddings...

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.