Sharif Digital Repository

The aim of this work is to study a cohesive crack in an elastic solid with meshless method. The procedure uses Reproducing Kernel Particle Method (RKPM) formulation in conjunction with Penalty method for implementing all constraints, including the Essential Boundary Conditions (EBCs) and the constraints related to cohesive crack. Meanwhile subdomain technique is employed to diminish the compiling process to facilitate one. Study of Stress Intensity Factor (SIF) at the tip of the cohesive crack has also been dealt with particular interest  

Due to special characteristics, nowadays functionally graded materials are of great interest of researchers. Continuous change of properties in these materials,decreases undesirable phenomena such as stresscon centration. On the other hand knowing vibration parameters of structures such as natural frequencies, to avoid damage, is important. So far, many researches have been devoted to vibration analysis of structures, such as beams.In this dissertation, free vibration analysis of FGM beams, are investigated, using RKPM, a meshlesh method. The system of equations of motion is derived using Lagrange’s method under the assumption of Euler-Bernoulli beam theory. Buckling analysis of FGM beams... 

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...