QA215 : Meshfree method for boundary value problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2013
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Abstarct: An extended meshfree method is presented for treating boundary value problems,
where the total solution is expressed by a combination of particular and homogeneous solutions, each of which is assigned a specific role. The particular solution is
any analytical (or numerical) exxpression satisfying the governing differential equation
containing the source term but not necessarily the boundary conditions. A general
method is presented for constructing this solution. Thus, the problem is reduced to
a homogeneous equation where the original boundary conditions are modified by the
particular solution. Herein, the meshfree method is used to solve this homogeneous
equation, which involves a lower order behavior so that a relatively coarse discretization is acceptable. Several boundary value problems from potential theory as well as
from shear deformable plate theory are solved, where linear exactness [Int. J. Numer.
Methods Engrg. 50 (2001) 435; Int. J. Numer. Methods Engrg. 53 (2002) 2587]
and bending exactness [Comput. Methods Appl. Mech. Engrg. 193 (2004) 1065],
respectively, are imposed in their meshfree approximation fields. Numerical results
demonstrate that this extended meshfree approach significantly improves the solution
accuracy with commensurately less computational effort compared to the conventional
meshfree formulation.
Keywords:
#Shape function #Weight function #Particular solution #Homogeneous solution #Meshfree; MLS #FEM #Boundary value problem Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
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