Oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography

On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed using matched eigenfunction expansions. Different from previous studies, the effects of a wave incident angle, a plate draft, three different plate edge conditions （free, simply supported and built-in） and a sea-bottom topography are all taken into account. Moreover, the plate edge conditions are directly incorporated into linear algebraic equations for determining unknown expansion coefficients in velocity potentials, which leads to a simple and efficient solving procedure. Numerical results show that the convergence of the present solution is good, and an energy conservation relation is well satisfied. Also, the present predictions are in good agreement with known results for special cases. The effects of the wave incident angle, the plate draft, the plate edge conditions and the sea-bottom topography on various hydrodynamic quantities are analyzed. Some useful results are presented for engineering designs.

ON THE CONDITIONAL EDGE CONNECTIVITY OF ENHANCED HYPERCUBE NETWORKS

Let G =（V, E） be a connected graph and m be a positive integer, the conditional edge connectivity λ;is the minimum cardinality of a set of edges,if it exists, whose deletion disconnects G and leaves each remaining component with minimum degree δ no less than m. This study shows that λ;(Q;) = 2 n,λ;(Q;) = 4 n-4（2 ≤ k ≤ n-1, n ≥ 3） for n-dimensional enhanced hypercube Q;. Meanwhile, another easy proof about λ;（Q;） = 4 n-8, for n ≥ 3 is proposed. The results of enhanced hypercube include the cases of folded hypercube.

Laser-based manufacturing concepts for efficient production of tailor welded sheet metals

Laser welding is an established manufacturing technology for a large variety of automotive applications due to its attractive properties such as low heat input, high precision and fast welding speed. Especially when welding high strength steels, which are dominantly used in today＇s car body construction, the low heat input by laser welding bears significant advantages with regard to the properties of the weld seam. The exploitation of the full application potential of laser welding in mass production requires an appropriate manufacturing concept and corresponding auxiliary technologies. The present paper demonstrates the integration of laser welding into the surrounding manu- facturing concepts by a modular setup with different levels of automation. This approach offers flexible solutions for individual needs thereby optimizing investment cost, labor cost and productivity. Recently available laser sources enable exceptionally high welding speed on thin gauged sheet metals but require efficient material handling con- cepts to utilize the full speed potential. Industrial concepts are presented offering efficient material handling and high process robustness for mass production welding.

Free-Surface Wave Interaction with a Very Large Floating Structure

The free-surface wave interaction with a pontoon-type very large floating structure(VLFS) is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem(BVP) equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.