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GRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients

Hashemian, Alireza | 2008

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 41686 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. 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 that it enforced essential boundary conditions including not only the field function but also the derivative of the field function exactly. The efficacy of the proposed method is examined in beam-columns and plate problems in which slopes should be applied as derivative type of EBCs. On the other hand, the ability of GRKPM in modeling high gradients is scrutinized. From one dimensional advection-diffusion problem with high gradient in the boundary layer to nonlinear evolutionary partial differential equations of Burgers and Buckley-Leverett, in which the large gradient spreads within the domain as time elapsed, are studied . The capability of GRKPM in function reconstruction is another remarkable issue which is investigated
  9. Keywords:
  10. Laminated Composite Panel ; Gradient Reproducing Kernel Particle Method ; Function Reconstruction ; Derivative Type Essential Boundary Condition ; Nonlinear Partial Differential Equation with Large Gradient

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