Meshless Implementations Of Local Integral
Equations For Bending Of Thin Plates
Author(s)
V. Sladek, J. Sladek & L. Sator
Abstract
In this paper, we show that the decomposition of the biharmonic equation into
two Poisson equations is applicable to the general case of boundary conditions
and any shape of the boundary edge of the plate, if we use the Local Integral
Equation (LIE) formulation and a meshless approximation for primary field
variables. Moreover, the spatial dependence of the bending stiffness does not
give rise to any difficulties in this formulation. Such a formulation enables us to
decrease the order of the derivatives of the field variables and so to increase the
accuracy of numerical solutions. The efficiency and accuracy of several
formulations is discussed in numerical tests using two alternative meshless
approximations.
Keywords: Kirchhoff theory, biharmonic equation, Poisson equations, mesh-free
methods, field derivatives.
1 Introduction
It is well known that high order derivatives of field variables in the governing
equations give rise to difficulties in solution of boundary value problems because
of worse accuracy of numerically evaluated high order derivatives. The order of
the differential operator can be decreased mathematically by decomposing this
operator into two lower order differential operators with introducing new field
variables. However, the formulation of the physical boundary conditions in terms
of new field variables can be problematic. Basically, it is possible to express all
the original boundary densities in terms of the new fields and their derivatives as
long as a domain-type approximation is employed in the numerical
implementation. The question is, however, if the order of the derivatives is lower
Keywords
Kirchhoff theory, biharmonic equation, Poisson equations, mesh-free
methods, field derivatives.
Related Book
Other papers in this volume
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