Sharif Digital Repository

A major disadvantage of conventional meshless methods as compared to finite element method (FEM) is their weak performance in dealing with constraints. To overcome this difficulty, the penalty and Lagrange multiplier methods have been proposed in the literature. In the penalty method, constraints cannot be enforced exactly. On the other hand, the method of Lagrange multiplier leads to an ill-conditioned matrix which is not positive definite. The aim of this paper is to boost the effectiveness of the conventional reproducing kernel particle method (RKPM) in handling those types of constraints which specify the field variable and its gradient(s) conveniently. Insertion of the gradient term(s),... 

In this paper, an application of the reproducing kernel particle method (RKPM) is presented in plasticity behavior of pressure-sensitive material. The RKPM technique is implemented in large deformation analysis of powder compaction process. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. The essential boundary conditions are enforced by the use of the penalty approach. The support of the RKPM shape function covers the same set of particles during powder compaction, hence no instability is encountered in the large deformation computation. A double-surface plasticity model is developed in numerical simulation of pressure-sensitive material.... 

In this paper, an application of the Reproducing Kernel Particle Method is presented in numerical simulation of powder forming processes using a cap plasticity model. A double-surface cap plasticity is developed within the framework of large deformation analysis in order to predict the non-uniform relative density distribution during powder die pressing. The RKPM technique is employed in the analysis of 2D compaction simulation. Numerical examples are presented to illustrate the applicability of the algorithm in modelling of powder forming processes  

A meshless method called reproducing kernel particle method (RKPM) is exploited to cope with elastic-plastic fracture mechanics (EPFM) problems. The idea of arithmetic progression is assumed to place particles within the refinement zone in the vicinity of the crack tip. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. Also, a tracking to find the appropriate diffraction parameter is performed. To assess the suggestions made, two mode I numerical simulations, pure tension and pure bending tests, are executed. Results including J integral, crack mouth opening displacement (CMOD), and plastic zone size and shape are compared with... 

An accurate numerical methodology for capturing the field quantities across the interfaces between material discontinuities, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called augmented corrected collocation method is introduced; this technique is an extension of the corrected collocation method used for imposing essential boundary conditions (EBCs). The robustness of this methodology is shown by utilizing it to solve two benchmark problems of material discontinuities, namely the problem of circular inhomogeneity with uniform radial eigenstrain, and the problem of interaction between a crack... 

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal EulerBernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural...