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Gradient reproducing kernel particle method
, Article Journal of Mechanics of Materials and Structures ; Volume 3, Issue 1 , 2008 , Pages 127-152 ; 15593959 (ISSN) ; Shodja, H. M ; Sharif University of Technology
Mathematical Sciences Publishers
2008
Abstract
This paper presents an innovative formulation of the RKPM (reproducing kernel particle method) pioneered by Liu. A major weakness of the conventional RKPM is in dealing with the derivative boundary conditions. The EFGM (element free Galerkin method) pioneered by Belytschko shares the same difficulty. The proposed RKPM referred to as GRKPM (gradient RKPM), incorporates the first gradients of the function in the reproducing equation. Therefore in three-dimensional space GRKPM consists of four independent types of shape functions. It is due to this feature that the corrected collocation method can be readily generalized and combined with GRKPM to enforce the EBCs (essential boundary...
A model for the evolution of concrete deterioration due to reinforcement corrosion
, Article Mathematical and Computer Modelling ; Volume 52, Issue 9-10 , November , 2010 , Pages 1403-1422 ; 08957177 (ISSN) ; Kiani, K ; Hashemian, A ; Sharif University of Technology
2010
Abstract
One of the most crucial factors affecting the service life of reinforced concrete (RC) structures attacked by aggressive ions is reinforcement corrosion. As the steel corrosion progresses, crack propagation in concrete medium endangers the serviceability and the strength of RC structural members. In this study, a nonlinear mathematical model for determining the displacement and stress fields in RC structures subjected to reinforcement corrosion is introduced. For corrosion products, a nonlinear stress-strain relation which has been previously confirmed by experimental data is incorporated in the present analysis. In formulation of the governing equations for steel-rust-concrete composite,...
Modeling Material Discontinuities Via An Augmented RKPM and Performance of GRKPM in Fracture Mechanics
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
During the past decade, element free methods have achieved great successes. One of these methods is the so called RKPM which has a suitable structure for use in fracture mechanics problems. Despite all characteristic abilities of element free methods; these methods due to their higher order continuous differentiable approximations fail to model discontinuous material properties of the subjected domains. In this study by improving the collocation method in RKPM treatment of such conditions have been achieved. Also in this study performance of a new meshfree method in fracture mechanics problems has been analyzed. GRKPM is one of these methods which its suitable accuracy and convergence has...
GRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients
, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so...
A numerical solution of 2D Buckley-Leverett equation via gradient reproducing kernel particle method
, Article CMES - Computer Modeling in Engineering and Sciences ; Volume 32, Issue 1 , 2008 , Pages 17-33 ; 15261492 (ISSN) ; Hashemian, A ; Sharif University of Technology
2008
Abstract
Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations...