... of Technology, etc. The research team of structure and design method was established in 2019. And this paper is one of the research achievements of the project team. logic programming mathematical model coefficient exact solution partial differential equation frequency boundary condition...

... nonlinearity. Then, Fokker-Planck equation is used to study the probability density distribution of the process. Because the exact solution of Fokker-Planck equation is difficult to solve, the approximate results are calculated by the path integral solution. The innovation of this paper is to apply this method...

... of the research on ship stability. probability density distribution ship motion response spectrum equation artificial intelligence filter model differential equation fpk equation finite difference method noise stability white noise coefficient exact solution drift coefficient filter 2...

... ABSTRACT: Whitham derived the nonlinear Schrödinger equation from the most general form of the nonlinear wave dispersion relation. The NLS equation was analyzed from the second-order Stokes' nonlinear deepwater wave dispersion relation. The exact solutions of the nonlinear wave were obtained...

... wave equation small parameter rational solution double curvilinear method exact solution special small parameter application research equation riccati equation deformation equation reservoir characterization wave equation Application Research of Homotopy Analysis Method in Nonlinear...

... with circular hole and the results are compared with the exact solution. Quadratic, cubic and quartic NURBS are considered. After generating the circular cylinder geometry based on the control points and knot vectors, the effects of the knot insertion (h-refinement) and the order elevation of the basis (p...

... on traditional mechanics of structures, in which the coupling of flexure and torsion was taken into account. Further, Tufekci and Dogruer (2006) obtained the exact solution of out-of-plane problems of a plane arch with varying curvature and cross section. In order to investigate the reason of in- plane damage...

... The Exact Solutions of Tower-Yoke Mooring Systems Yonghui (Allen) Liu SOFEC, Inc. Houston, TX, USA ABSTRACT Tower-yoke mooring system, which consists of a tower fixed at the seabed and a mooring yoke assembly connecting a platform with the tower and utilizes pendant linkages to hang a heavy weight...

... loose sand fluid phase nc clay equation gravel flow in porous media water pressure exact solution shear stress reservoir characterization excess pore water pressure effective vertical stress pore water pressure upstream oil & gas formulation Coupled Analysis of the Behavior...

... Wave Model, the Geometrical Theory of Diffraction (GTD) is introduced and complex coastlines are replaced by simple geometries such as semi-infinite breakwaters or wedges. By expanding the exact solution with respect to the non dimensional distance to the pointed end of the wedge, kr, the diffraction...

...-resultants to satisfy the natural boundary conditions but they magnify the oscillations. Based on existing exact solutions of rectangular plates with simply supported and free edges, it was found that the aforementioned problem can be remedied by a post-processing step involving the curve fitting...

..., imperfections, pipelines, thermal loading, upheaval NOMENCLATURE A2, A4 E I k L Lr Lb P P, Pb constants used in exact solution, eqn (24) elastic modulus of pipeline second moment of area of pipeline parameter introduced for exact solution, eqn (24) length of uplifted region of pipeline length of continuous...

.... Using this fact we can obtain exact solutions to the equation developed by Gibson et al.. In view of the nonlinear character of the finite strain theory of soil consolidation, any exact solutions are important and noteworthy because they frequently reveal interesting phenomena and serve as a benchmark...

... bottom which are caused by earthquakes. integration surface wave coastal engineering frequency compressibility exact solution reservoir characterization phase lag earthquake water surface amplitude japan upstream oil & gas water depth cable tension water compressibility fluid...

... eigenvalue long vertical pipe frequency discrete element method exact solution displacement freedom stress stiffening effect eth element pipe huttelmaier vertical pipe matrix fundamental frequency pipe system derivation formulation discrete element relative displacement...

... model experiment and exact solution. INTRODUCTION Because of the high-duty alloy being used in the large submarine, the ratio of the thickness to the radius of the ring-stiffened cylinder shell reduces and the lateral rigidity of the frames increases. For this kind of structure, the critical buckling...

.... process zone point stress source stress field stress distribution sensitive analysis formulation procedure macrocrack crack interaction equation exact solution microcrack k-dominant stress field microcrack 2 real stress distribution maincrack crack tip fracture mechanics Proceedings...