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Numerical methods for limit and shakedown analysis. Deterministic and probabilistic problems.
(2003)
Solar sails are propelled in space by reflecting solar photons off large mirroring surfaces, thereby transforming the momentum of the photons into a propulsive force. This innovative concept for low-thrust space propulsion works without any propellant and thus provides a wide range of opportunities for highenergy low-cost missions. Offering an efficient way of propulsion, solar sailcraft could close a gap in transportation options for highly demanding exploration missions within our solar system and even beyond. On December 17th, 1999, a significant step was made towards the realization of this technology: a lightweight solar sail structure with an area of 20 m × 20 m was successfully deployed on ground in a large facility at the German Aerospace Center (DLR) at Cologne. The deployment from a package of 60 cm × 60 cm × 65 cm with a total mass of less than 35 kg was achieved using four extremely light-weight carbon fiber reinforced plastics (CFRP) booms with a specific mass of 100 g/m. The paper briefly reviews the basic principles of solar sails as well as the technical concept and its realization in the ground demonstration experiment, performed in close cooperation between DLR and ESA. Next possible steps are outlined. They could comprise the in-orbit demonstration of the sail deployment on the upper stage of a low-cost rocket and the verification of the propulsion concept by an autonomous and free flying solar sail in the frame of a scientific mission. It is expected that the present design could be extended to sail sizes of about (40 m)2 up to even (70 m)2 without significant mass penalty. With these areas, the maximum achievable thrust at 1 AU would range between 10 and 40 mN – comparable to some electric thrusters. Such prototype sails with a mass between 50 and 150 kg plus a micro-spacecraft of 50 to 250 kg would have a maximum acceleration in the order of 0.1 mm/s2 at 1 AU, corresponding to a maximum ∆V-capability of about 3 km/s per year. Two near/medium-term mission examples to a near-Earth asteroid (NEA) will be discussed: a rendezvous mission
and a sample return mission.
Improved collapse loads of thick-walled, crack containing pipes and vessels are suggested. Very deep cracks have a residual strength which is better modelled by a global limit load. In all burst tests, the ductility of pressure vessel steels was sufficiently high whereby the burst pressure could be predicted by limit analysis with no need to apply fracture mechanics. The relative prognosis error increases however, for long and deep defects due to uncertainties of geometry and strength data.
This work is an attempt to answer the question: How to use convex programming in shakedown analysis of structures made of materials with temperature-dependent properties. Based on recently established shakedown theorems and formulations, a dual relationship between upper and lower bounds of the shakedown limit load is found, an algorithmfor shakedown analysis is proposed. While the original problem is neither convex nor concave, the algorithm presented here has the advantage of employing convex programming tools.
An optimization method is developed to describe the mechanical behaviour of the human cancellous bone. The method is based on a mixture theory. A careful observation of the behaviour of the bone material leads to the hypothesis that the bone density is controlled by the principal stress trajectories (Wolff’s law). The basic idea of the developed method is the coupling of a scalar value via an eigenvalue problem to the principal stress trajectories. On the one hand this theory will permit a prediction of the reaction of the biological bone structure after the implantation of a prosthesis, on the other hand it may be useful in engineering optimization problems. An analytical example shows its efficiency.
Mechanical stimulation of the cells resulted in evident changes in the cell morphology, protein composition and gene expression. Microscopically, additional formation of stress fibers accompanied by cell re-arrangements in a monolayer was observed. Also, significant activation of p53 gene was revealed as compared to control. Interestingly, the use of CellTech membrane coating induced cell death after mechanical stress had been applied. Such an effect was not detected when fibronectin had been used as an adhesion substrate.