Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Numerical methods in multibody system dynamics

"Series: Solid mechanics and its applications, vol. 226"

Experimental and numerical approaches for structural assessment in new footbridge designs (SFRSCC–GFPR hybrid structure)

Within the civil engineering field, the use of the Finite Element Method has acquired a significant importance, since numerical simulations have been employed in a broad field, which encloses the design, analysis and prediction of the structural behaviour of constructions and infrastructures. Nevertheless, these mathematical simulations can only be useful if all the mechanical properties of the materials, boundary conditions and damages are properly modelled. Therefore, it is required not only experimental data (static and/or dynamic tests) to provide references parameters, but also robust calibration methods able to model damage or other special structural conditions. The present paper addresses the model calibration of a footbridge bridge tested with static loads and ambient vibrations. Damage assessment was also carried out based on a hybrid numerical procedure, which combines discrete damage functions with sets of piecewise linear damage functions. Results from the model calibration shows that the model reproduces with good accuracy the experimental behaviour of the bridge.

Evaluation of seismic vulnerability assessment parameters for portuguese vernacular constructions with nonlinear numerical analysis

Considering that vernacular architecture may bear important lessons on hazard mitigation and that well-constructed examples showing traditional seismic resistant features can present far less vulnerability than expected, this study aims at understanding the resisting mechanisms and seismic behavior of vernacular buildings through detailed finite element modeling and nonlinear static (pushover) analysis. This paper focuses specifically on a type of vernacular rammed earth constructions found in the Portuguese region of Alentejo. Several rammed earth constructions found in the region were selected and studied in terms of dimensions, architectural layout, structural solutions, construction materials and detailing and, as a result, a reference model was built, which intends to be a simplified representative example of these constructions, gathering the most common characteristics. Different parameters that may affect the seismic response of this type of vernacular constructions have been identified and a numerical parametric study was defined aiming at evaluating and quantifying their influence in the seismic behavior of this type of vernacular buildings. This paper is part of an ongoing research which includes the development of a simplified methodology for assessing the seismic vulnerability of vernacular buildings, based on vulnerability index evaluation methods.

A spectrum-driven damage Identification technique : application and validation through the numerical simulation of the Z24 Bridge

The present paper focuses on a damage identification method based on the use of the second order spectral properties of the nodal response processes. The explicit dependence on the frequency content of the outputs power spectral densities makes them suitable for damage detection and localization. The well-known case study of the Z24 Bridge in Switzerland is chosen to apply and further investigate this technique with the aim of validating its reliability. Numerical simulations of the dynamic response of the structure subjected to different types of excitation are carried out to assess the variability of the spectrum-driven method with respect to both type and position of the excitation sources. The simulated data obtained from random vibrations, impulse, ramp and shaking forces, allowed to build the power spectrum matrix from which the main eigenparameters of reference and damage scenarios are extracted. Afterwards, complex eigenvectors and real eigenvalues are properly weighed and combined and a damage index based on the difference between spectral modes is computed to pinpoint the damage. Finally, a group of vibration-based damage identification methods are selected from the literature to compare the results obtained and to evaluate the performance of the spectral index.

Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method.

Integration methods in dynamic analysis

"Series title: Springerbriefs in applied sciences and technology, ISSN 2191-530X"