Y.T. Lee

A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function

In this paper, a meshless method for solving the eigenfrequencies of clamped plates using the radial basis function (RBF) is proposed. The coefficients of influence matrices are easily determined by the two-point function. By employing the RBF in the imaginary-part fundamental solution, true eigensolutions instead of spurious one are obtained for plate vibration. In order to obtain the eigenvalues and boundary modes at the same time, singular value decomposition technique is utilized. Two examples, circular and rectangular clamped plates, are demonstrated to see the validity of the present method.

A Semi-Analytical Approach for Boundary Value Problems with Circular Boundaries

In this paper, a semi-analytical approach is developed to deal with problems including multiple circular boundaries. The boundary integral approach is utilized in conjunction with degenerate kernel and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. Both direct and indirect formulations are proposed. This approach is a semi-analytical approach, since the error stems from the truncation of Fourier series in the implementation. The unknown Fourier coefficients are easily determined by solving a linear algebraic system after using the collocation method and matching the boundary conditions. Five goals: (1) free of calculating principal value, (2) exponential convergence, (3) well-posed algebraic system, (4) elimination of boundary-layer effect and (5) meshless, of the formulation are achieved. The proposed approach is extended to deal with the problems containing multiple circular inclusions. Finally, the general-purpose program in a unified manner is developed for BVPs with circular boundaries. Several examples including the torsion bar, water wave and plate vibration problems are given to demonstrate the validity of the present approach.