It is important to account for inherent variability in the material properties in the design and analysis of engineering structures. These properties are typically not homogeneous, but vary across the spatial coordinates within a structure, as well as from specimen to specimen. This form of uncertainty is commonly modelled using random fields within the Stochastic Finite Element Method. Simulation within this framework can be complicated by the dependence of a random field's correlation function upon the geometry of the domain over which it is defined. In this paper, a new method is proposed for simulating random fields over a general two-dimension curved surface, represented as a finite element mesh. The covariance function is parametrised using the geodesic distance, evaluated using the solution to the 'discrete geodesic problem,' and a point discretisation approach is subsequently applied in order to sample the random field at the nodes of the model. The major contribution of the present work is the development of a methodology for simulating random fields over curved surfaces of arbitrary geometry, with a focus upon non-intrusive application to industrial finite element models using 'off the shelf' commercial software. In order to demonstrate the potential impact of the the proposed approach, the algorithm is applied in an uncertainty quantification case study concerning vibration and buckling of an industrial composite aircraft wing model.
This paper presents a multi-level aeroelastic tailoring framework for the optimisation of composite aircraft wings. The framework is capable of structural sizing and produces detailed composite ply configurations through robust and reliability-based design optimisation, and is demonstrated on a representative regional jet airliner finite element wing box model. The optimisation procedure is divided into two levels. The first level optimises the wing structure for minimum weight subject to multiple constraints including strain, buckling, aeroelastic stability and gust response. These first level solutions are then fed into the second level to be further optimised for robustness or reliability by considering uncertainties in material properties at ply level. Both the principles of robust and reliability-based design optimisation can also be used in combination to ensure a balance between the robustness and reliability of the structural performance. In order to keep computations to an acceptable cost, the second level optimisation employs the Polynomial Chaos Expansion method to approximate the effect of probabilistic uncertainty on structural performance. In comparison to the original benchmark wing, the framework produces an overall weight reduction of 32.1%, despite a 1.5% increase from the first to the second level optimisation that accounts for stochastic design variations.
In the present work, a higher-order beam model able to characterize correctly the three-dimensional strain and stress fields with minimum computational efforts is proposed. One-dimensional models are formulated by employing the Carrera Unified Formulation (CUF), according to which the generic 3D displacement field is expressed as the expansion of the primary mechanical variables. In such a way, by employing a recursive index notation, the governing equations and the related finite element arrays of arbitrarily refined beam models can be written in a very compact and unified manner. A Component-Wise (CW) approach is developed in this work by using Lagrange polynomials as expanding cross-sectional functions. By using the principle of virtual work and CUF, free vibration and linearized buckling analyses of composite aerospace structures are investigated. The capabilities of the proposed methodology and the advantages over the classical methods and state-of-the-art tools are widely demonstrated by numerical results.
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