Numerical studies on CFRP strengthened steel columns under transverse impact

Strengthening of metallic structures using carbon fibre reinforced polymer (CFRP) has become a smart strengthening option over the conventional strengthening method. Transverse impact loading due to accidental vehicular collision can lead to the failure of existing steel hollow tubular columns. However, knowledge is very limited on the behaviour of CFRP strengthened steel members under dynamic impact loading condition. This paper deals with the numerical simulation of CFRP strengthened square hollow section (SHS) steel columns under transverse impact loading to predict the behaviour and failure modes. The transverse impact loading is simulated using finite element (FE) analysis based on numerical approach. The accuracy of the FE modelling is ensured by comparing the predicted results with available experimental tests. The effects of impact velocity, impact mass, support condition, axial loading and CFRP thickness are examined through detail parametric study. The impact simulation results indicate that the strengthening technique shows an improved impact resistance capacity by reducing lateral displacement of the strengthened column about 58% compared to the bare steel column. Axial loading plays an important role on the failure behaviour of tubular column.

Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller–Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥sqrt(2δ) in the F-KPP equation.

Numerical investigation of aerosol particle transport and deposition in realistic lung airway

Different human activities like combustion of fossil fuels, biomass burning, industrial and agricultural activities, emit a large amount of particulates into the atmosphere. As a consequence, the air we inhale contains significant amount of suspended particles, including organic and inorganic solids and liquids, as well as various microorganism, which are solely responsible for a number of pulmonary diseases. Developing a numerical model for transport and deposition of foreign particles in realistic lung geometry is very challenging due to the complex geometrical structure of the human lung. In this study, we have numerically investigated the airborne particle transport and its deposition in human lung surface. In order to obtain the appropriate results of particle transport and deposition in human lung, we have generated realistic lung geometry from the CT scan obtained from a local hospital. For a more accurate approach, we have also created a mucus layer inside the geometry, adjacent to the lung surface and added all apposite mucus layer properties to the wall surface. The Lagrangian particle tracking technique is employed by using ANSYS FLUENT solver to simulate the steady-state inspiratory flow. Various injection techniques have been introduced to release the foreign particles through the inlet of the geometry. In order to investigate the effects of particle size on deposition, numerical calculations are carried out for different sizes of particles ranging from 1 micron to 10 micron. The numerical results show that particle deposition pattern is completely dependent on its initial position and in case of realistic geometry; most of the particles are deposited on the rough wall surface of the lung geometry instead of carinal region.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.