Sharif Digital Repository

Meshless Methods using kernel approximation like Reproducing Kernel Particle Method (RKPM) are methods for solving partial differential equations that require only nodal data and a description of the geometry without requiring element connectivity data and mesh producing. An innovative method of nonplanar material partitioning method (NMPM) with implementation of RKPM is employed to calculate the stress intensity factor (SIF) at the tip of an anticrack sited in an isotropic plate under a remote applied loading. Numerical examples in comparison with the exact closed form expressions show that accurate SIF for mode I can be obtained.

 

The present research illustrate the finite element modeling of contact between solid bodies, with a special emphasis on the imposing the contact constraints and modification of contact properties on surface in the case of frictional slip. A new approach for both two-dimensional and three-dimensional formulation of contact constraint that allows for a simple and unified treatment of all potential contact scenarios in the presence of large deformations in static case, is presented. The most important outstanding issue in this approach is symmetrical contact stiffness matrix which reduces computational efforts. Based on the observation of numerical results and comparison by experimental models,... 

In this thesis, some new models have been solved via RKPM method, which is one of the meshfree methods family. These models have never been solved via meshfree methods and their analytical solutions do not exist. At first, the RKPM shape functions and their first derivative formulation in 1D and 2D have been presented and then by using FORTRAN program, the shape functions and their first derivative have been obtained. To verifying the code some functions have been reproduced. In the next step by using the governing equations and penalty method whose formulation exists in chapter 2; some famous examples in linear elasticity have been solved via RKPM to verify the FORTRAN code. At last; some...