An approach for reliability-based robust design optimisation of angle-ply composites

Variations of manufacturing process parameters and environmental aspects may affect the quality and performance of composite materials, which consequently affects their structural behaviour. Reliability-based design optimisation (RBDO) and robust design optimisation (RDO) searches for safe structural systems with minimal variability of response when subjected to uncertainties in material design parameters. An approach that simultaneously considers reliability and robustness is proposed in this paper. Depending on a given reliability index imposed on composite structures, a trade-off is established between the performance targets and robustness. Robustness is expressed in terms of the coefficient of variation of the constrained structural response weighted by its nominal value. The Pareto normed front is built and the nearest point to the origin is estimated as the best solution of the bi-objective optimisation problem.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.