No abstract

This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. Based on the local Petrov–Galerkin formulation and the center difference method for time discretization, a system of nonlinear discrete equations is obtained. The numerical examples are presented and the numerical solutions are found to be in good agreement with the results in the literature to validate the ability of the present meshless method to handle the 2 + 1-dimensional sine-Gordon equation related problems.

<p>It is well known that the vertical axial force in pylon of long-span cable-stayed bridge and suspension bridge is extremely large. To enhance the structural transverse stability, the crossbeams are generally positioned among the top of the towers. The paper presents an innovative pan-pipes shape pylon different from the traditional pylons. The pylon is composed of two separated main towers and several affiliated towers besides it. Two main towers of the pylon are connected by a crossbeam under rather than above the main girder (stiffening girder). Meanwhile, affiliated towers are positioned beside the main tower to guarantee the transverse stiffness of the structure. The number of the affiliated towers for each main tower and the height ratio among the towers are considered to guarantee the harmonious beauty of the whole pylon structure and the transverse stability of the main tower.</p>