Optimization of anisotropic composite panels with T-shaped stiffeners including transverse shear effects and out-of-plane loading

A two-step method to optimize anisotropic composite panels with T-shaped stiffeners, including a new formulation of the transverse shear properties and an approximation of the ply contiguity (blocking) constraints as functions of the lamination parameters is provided. At the first step, a representative element of the stiffened panel (superstiffener) is optimized using mathematical programming and lamination parameters subjected to combined loading (in-plane and out-of-plane) under strength (laminate or ply failure), buckling and practical design constraints. Ply blocking constraints are imposed at this step to improve convergence towards practical laminates. At the second step, the actual superstiffener’s laminates are obtained by using a genetic algorithm. Results, for the case considered, show that the inclusion of transverse shear effects has an associated 2.5% mass penalty and that neglecting its effects might invoke earlier buckling failure. In addition, the influence of designing for failure strength at laminate or ply level is assessed.     

Distributed parameter model updating using the Karhunen–Loève expansion

Discrepancies between experimentally measured data and computational predictions are unavoidable for complex engineering dynamical systems. To reduce this gap, model updating methods have been developed over the past three decades. Current methods for model updating often use discrete parameters, such as thickness or joint stiffness, for model updating. However, there are many parameters in a numerical model which are spatially distributed in nature. Such parameters include, but are not limited to, thickness, Poisson's ratio, Young's modulus, density and damping. In this paper a novel approach is proposed which takes account of the distributed nature of the parameters to be updated, by expressing the parameters as spatially correlated random fields. Based on this assumption, the random fields corresponding to the parameters to be updated have been expanded in a spectral decomposition known as the Karhunen–Loève (KL) expansion. Using the KL expansion, the mass and stiffness matrices are expanded in series in terms of discrete parameters. These parameters in turn are obtained using a sensitivity based optimization approach. A numerical example involving a beam with distributed updating parameters is used to illustrate this new idea.     

Regularization in model updating

This paper presents the theory of sensitivity‐based model updating with a special focus on the properties of the solution that result from the combination of optimization of the response prediction with a priori information about the uncertain parameters. Model updating, together with the additional regularization criterion, is an optimization with two objective functions, and must be linearized to obtain the solution. Structured solutions are obtained, based on the generalized singular value decomposition (GSVD), and specific features of the parameter and response paths as the regularization parameter varies are explored. The four different types of spaces that arise in the solution are discussed together with the characteristics of the regularized solution families. These concepts are demonstrated on a simulated discrete example and on an experimental case study. Copyright © 2007 John Wiley & Sons, Ltd.     

Model-based identification of rotating machines

Over the decades, vibration-based condition monitoring has become well accepted and widely used to identify faults in rotating machines. However, the quantification of faults may require a significant number of tests to be carried out which may be time consuming and costly, if not impossible, by experiments alone. In the recent past, it has been observed that model-based identification has played a significant role in the rapid resolution and quantification of faults. The paper seeks to give an overview of the recent developments in this field which has considerable practical importance.     

Quantitative experimental measurements of matrix cracking and delamination using acoustic emission

Quantitative measurements of the amplitude and angular variation of acoustic emission (AE) events due to matrix cracking and delamination in large quasi-isotropic composite plate specimens are reported. A procedure for determining the minimum specimen size necessary to make quantitative measurements is presented. The amplitude of AE events is quoted as the absolute surface displacement of different guided wave modes and can therefore be used as the input to forward models of the AE process. Matrix cracking events are found to be dominated by the S₀ guided wave mode and have a pronounced amplitude variation with angle. Events due to delamination growth are dominated by the A₀ guided wave mode and have no clear angular dependence.     

Random matrix eigenvalue problems in structural dynamics

Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean‐centred perturbation‐based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is ‘best’ in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed‐form expression is derived for a general rth‐order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi‐square distribution. Both approaches result in simple closed‐form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the ‘small randomness’ assumption usually employed in mean‐centred‐perturbation‐based methods can be relaxed considerably using these methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Stochastic model updating: Part 2—application to a set of physical structures

The application of a stochastic model updating technique using Monte-Carlo inverse propagation and multivariate multiple regression to converge a set of analytical models with randomised updating parameters upon a set of nominally identical physical structures is considered. The structure in question is a short beam manufactured from two components, one of folded steel and the other flat. The two are connected by two rows of spot-welds. The main uncertainty in the model is concerned with the spot-weld but there is also considerable manufacturing variability, principally in the radii of the folds.     

The stochastic aeroelastic response analysis of helicopter rotors using deep and shallow machine learning

Neural Computing and Applications - This paper addresses the influence of manufacturing variability of a helicopter rotor blade on its aeroelastic responses. An aeroelastic analysis using finite...     

Initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners

This paper provides an approach to perform initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners. The method divides the optimisation problem into two steps. At the first step, composite optimisation is performed using mathematical programming, where the skin and the stiffeners are modelled using lamination parameters accounting for their anisotropy. Skin and stiffener laminates are assumed to be symmetric, or mid-plane symmetric laminates with 0°, 90°, 45°, or −45° ply angles. The stiffened panel is subjected to a combined loading under strength, buckling and practical design constraints. Buckling constraints are computed using closed form solutions and an energy method (Rayleigh-Ritz). Conservatism is partially removed in the buckling analysis by considering the skin-stiffener flange interaction and decreasing the effective width of the skin. Furthermore, the manufacture of the stiffener is embedded within the design variables. At the second step, the actual skin and stiffener lay-ups are obtained using genetic algorithms, accounting for manufacturability and design practices. This two step approach permits the separation of the structural analysis (strength, buckling, etc.), which is performed at the first step, from the laminate stacking sequence combinatorial problem, which is dealt efficiently with genetic algorithms at the second step.     

Perturbation methods for the estimation of parameter variability in stochastic model updating

The problem of model updating in the presence of test-structure variability is addressed. Model updating equations are developed using the sensitivity method and presented in a stochastic form with terms that each consist of a deterministic part and a random variable. Two perturbation methods are then developed for the estimation of the first and second statistical moments of randomised updating parameters from measured variability in modal responses (e.g. natural frequencies and mode shapes). A particular aspect of the stochastic model updating problem is the requirement for large amounts of computing time, which may be reduced by making various assumptions and simplifications. It is shown that when the correlation between the updating parameters and the measurements is omitted, then the requirement to calculate the second-order sensitivities is no longer necessary, yet there is no significant deterioration in the estimated parameter distributions. Numerical simulations and a physical experiment are used to illustrate the stochastic model updating procedure.