1,721,037 research outputs found
Design equation for offshore overlap tubular K-joints under in-plane bending
No full textOverlap tubular K-joints are generally regarded as having higher axial strength than similar simple gap K-joints due to their more direct load transfer between braces. Due to congestion at the nodes in steel jackets, overlap K-joints are used as key structural elements in many existing offshore platforms. However, relatively little experimental research has been done to quantify their strength and this has prevented engineers from taking full advantage of overlapping in the design of new structures as well as in the life extension assessment of existing platforms. This paper presents the results of a numerical study on gap and overlap K-joints under in-plane bending. The parametric study reveals new insight into how the behavior and strength varies across the practical range of geometrical parameters.
Based on the finite element strength database, a capacity equation has been derived and presented herein using nonlinear regression
analysis techniques
Remarks on the 3D Stokes eigenvalue problem under Navier boundary conditions
Full text linkWe study the Stokes eigenvalue problem under Navier boundary conditions in C1,1-domains Ω ⊂ R3. Differently from the Dirichlet boundary conditions, zero may be the least eigenvalue. We fully characterize the domains where this happens and we show that the ball is the unique domain where the zero eigenvalue is not simple, it has multiplicity three. We apply these results to show the validity/failure of a suitable Poincaré-type inequality. The proofs are obtained by combining analytic and geometric arguments
Boundary Conditions for Planar Stokes Equations Inducing Vortices Around Concave Corners
No full textLinear theory for beams with intermediate piers
Full text linkThe full linear theory for hinged beams with intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem. Well-posedness results are provided and the possible loss of regularity, due to the presence of the piers, is analyzed. A complete spectral theorem is then proved, explicitly determining the eigenvalues according to the position of the piers and exhibiting the fundamental modes of oscillation. A related second-order eigenvalue problem is also studied, showing that it may display nonsmooth eigenfunctions and that the fourth-order problem cannot be seen as the square of a second-order problem
An Explicit Threshold for the Appearance of Lift on the Deck of a Bridge
Full text linkWe set up the analytical framework for studying the threshold for the appearance of a lift force exerted by a viscous steady fluid (the wind) on the deck of a bridge. We model this interaction as in a wind tunnel experiment, where at the inlet and outlet sections the velocity field of the fluid has a Poiseuille flow profile. Since in a symmetric configuration the appearance of lift forces is a consequence of non-uniqueness of solutions, we compute an explicit threshold on the incoming flow ensuring uniqueness. This requires building an explicit solenoidal extension of the prescribed Poiseuille flow and bounding some embedding and cutoff constants
Optimal Control for the Moon Lander: The Classical Problem and Variants
No full textThese notes concern a classical optimal control problem in aerospace engineering, how to land safely a spacecraft on the moon. Starting from an analysis of the original problem proposed by Miele in 1962, consisting in minimizing the consumption of fuel used for landing, we study a variant of the problem consisting in minimizing the landing time with a different thrust control.
We prove that the optimal control (if it exists) is piecewise constant and provides the exact landing strategy,
in dependence of the initial data (height, velocity, and fuel of the lander)
Web functions: survey of results and perspectives
No full textWe recall some of our previous results on web functions, we give some new
numerical results concerning a simple model and we state some open problems
Model of coordinated crowd dynamics
No full textThis paper presents a mathematical model of synchronisation of multiple people during cyclic activities such as walking, running, jumping and bouncing. Providing that quality models of individual loading for these activities do exist, the sync model is the key component towards an urgently needed yet reliable model of artificial dynamic loading due to multiple active occupants. A model proposed here describes the effect of external and internal factors on the crowd dynamics. The former includes periodic external stimuli on the body motion of individuals, such as perceptible vibration of the ground and music beats. The later addresses the mutual interaction between individuals, such as possibility to see, hear or touch each other. Modelling approach is inspired by the existing models of coupled pendulums while the governing equations feature Mathieu-type behaviour. For the sake of simplicity and efficiency, the model is kept linear and deterministic. All modelling parameters have a physical interpretation and their values can be calibrated to match experimental measurements
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
No full textWe study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second order equations, several differences and difficulties arise. In order to overcome these difficulties new ideas are needed. But still, in some cases we are able to extend only partially the well-known results for second order equations. The theoretical and numerical study of radial solutions in the ball also reveal some new phenomena, not available for second order equations. These phenomena suggest a number of intriguing unsolved problems, which we quote in the final section
On a long-standing conjecture by Polya-Szego and related topics
No full textThe electrostatic capacity of a convex body is usually not simple
to compute. Almost one century ago, Aichi-Russell
suggested a simple approximate formula which
involves the 2-dimensional measure of the boundary of the convex
body. This approximation is estimated by what physicists usually
call ``shape factor'', roughly speaking the ratio between the
capacity and the approximate capacity. We discuss a long-standing
conjecture by P\'olya-Szeg\"o. It says that the
minimum of the ratio is attained by the 2-dimensional disk
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