An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

in this paper free vibration analysis of two rectangular isotropic plates, which are connected to each other by two translational and rotational springs along the edges, are investigated. the equation of motion and associated boundary and continuity conditions are derived using the extended hamilton principle. to solve the eigenvalue problem, the ritz method is utilized. numerical investigation...

in this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. the fgm shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. these constituents are graded th...

Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the learning method works is falling far behind its empirical success. In this paper, we provide rigorous numerical analysis on Ritz (DRM) \cite{wan11} for second order elliptic equations with Neumann boundary conditions. We establish first nonasymptotic convergence rate in $H^1$ norm DRM using $\m...

in this study, the free vibration of partially fluid-filled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using rayleigh-ritz method. the analysis has been carried out with strain-displacement relations based on love’s thin shell theory and the contained fluid is assumed irrotational, incompressible and inviscid. after determining the...