---

A variety of numerical methods were developed for the wave propagation analysis in the field of structural health monitoring. In this framework, meshless methods are suitable procedure for the analysis of problems such as damage initiation and its propagation or the fracture of materials. In this study, Hermit-type radial point interpolation method (HRPIM) is investigated for the numerical modeling of flexural wave propagation and damage quantification in Euler-Bernoulli beams using MATLAB. This method employs radial basis function (RBF) and its derivatives for interpolation which leads to Hermitian formulation. The evaluation of performance and capability of HRPIM is based on the comparison between the captured HRPIM ang benchmark signals using the root mean square error (RMSE) and reflection ratio from damage. The algorithm of damage quantification is the analytical solution which relates the reflection ratio to the damage extent. In this study, Gausian-type RBF is utilized and the number of field nodes, the size of support domain, shape parameters of RBF, the number of polynomials in the interpolation formula, the arrangement of background cells and the number of Gaussian points in damage length are the effective parameters on results. Based on the evaluation, the acceptable values and range of theses parameters are presented for correct modeling.

---

Partial differential equations are needed in most of the engineering fields. Analytical solutions to these equations cannot be derived except in some very special cases, making numerical methods more important. Alongside advances in science and technology, new methods have been proposed for solution of partial differential equations, such as meshless methods. Recently, the generalized exponential basis function (GEBF) meshless method has been introduced. In this method the unknown function is approximated as a linear combination of exponential basis functions. In linear problems, the unknown coefficients are calculated such that the homogenous form of main differential equation is satisfied in all points of the grid. In order to solve nonlinear equations, Newton-Kantorovich scheme is first used to linearize them. The linearized equations are then solved iteratively to obtain the result. In this paper, time dependent problems in solid mechanics have been investigated. In order to examine performance of the proposed method, linear and non-linear problems in solid mechanics are considered and the results are compared with analytical solutions. The results show good accuracy (less than 1 percentage error) of the presented method.