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Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

Full-field strain measurements are applied in studies of textile deformability during composite processing: (1) in testing of shear and tensile deformations of textiles (picture frame, bias and biaxial extension test) as an ''optical extensometer'', allowing accurate assessment of the sample deformation, which may differ significantly from the deformation applied by the testing device; (2) to study mechanisms of the textile deformation on the scale of the textile unit cell and of the individual yarns (meso-and micro-scale full-field strain measurements); (3) to measure the 3D-deformed shape and the distribution of local deformations (e.g., shear angles) of a textile reinforcement after draping, providing input data for the validation of material drape models and for the prediction of the consolidated part performance via structural finite element analysis. This paper discusses these three applications of the full-field strain measurements, providing examples of studies of deformability of woven (glass, glass/PP) and non-crimp (carbon) textile reinforcements. The authors conclude that optical full-field strain techniques are the preferable (sometimes the only) way of assuring correct deformation measurements during tensile or shear tests of textile.

The objective of this paper is to critically review the emerging non-probabilistic approaches for uncertainty treatment in finite element analysis. The paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis. First, the applicability of the non-probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint. The necessary conditions for a useful application of the non-probabilistic concepts are determined, and are proven to be complementary rather than competitive to the classical probabilistic approach. The second part of the paper focuses on numerical aspects of the interval finite element method. It describes two principal strategies for the implementation, i.e. the anti-optimisation and the interval arithmetic approach, and gives a state-of-the-art of the interval finite element algorithms available from literature. It is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output, and the main sources of this conservatism are identified. A numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built-up benchmark structure.

Three types of multibody models are presented for the investigation of the internal dynamics of a drive train in a wind turbine. The first approach is limited to the analysis of torsional vibrations only. Then a rigid multibody model is presented with special focus on the representation of the bearings and gears in the drive train. The generic model implementation can be used for parallel as well as planetary gear stages with both helical and spur gears. Examples for different gear stages describe the use of the presented formulations. Furthermore, the influence of the helix angle and the flexibility of the bearings on the results of eigenmode calculations are discussed. The eigenmodes of a planetary stage are classified as rotational, translational or out‐of‐plane modes. Thirdly, the extension to a flexible multibody model is presented as a method to include directly the drive train components' flexibilities. Finally, a comparison of two different modelling techniques is discussed for a wind turbine's drive train with a helical parallel gear stage and two planetary gear stages. In addition, the response calculation for a torque input at the generator demonstrates which eigenmodes can be excited through this path. Copyright © 2005 John Wiley & Sons, Ltd.