A Least Square Solution Applied To Plate Analyses
Using The Traction Boundary Integral Equation
Author(s)
L. Palermo Jr.
Abstract
The least square method was used to solve an overdetermined system of
equations in a boundary element formulation, which had the number of integral
equations greater than the number of nodes. The solution with the least square
method was so good that a regular solution would present similar accuracy only
if a fine mesh was used (i.e. double the number of nodes.)The analysis
considered the traction boundary integral equation (BIE) to solve a plate bending
problem instead of the displacement BIE. Two formulations for traction BIEs
were considered, which had the strong singularity reduced with the tangential
differential operator (TDO). The strong singularity was reduced in the first
formulation without changing other fundamental solution kernels. In the second
formulation, the TDO was applied to all fundamental solution kernels involving
the multiplication of generalized displacements to reduce the singularities, and
the resulting kernels were combinations of those from the displacement BIE.
Keywords: least square solution, traction boundary integral equation, plate
bending, Reissner’s model, Mindlin’s model.
1 Introduction
Traction BIEs are important when an additional boundary equation is necessary
in some problems that do not degenerate solutions using displacement BIEs, like
those used in fracture mechanic problems. Strong singularities appear in the
fundamental solution kernels of traction BIEs and in stress BIEs at boundary
points, which are intrinsically related. The collocation point positions, which are
internal points in the boundary element, and the strategy for treating improper
integrals are the essential features studied in numerical implementations for
Keywords
least square solution, traction boundary integral equation, plate
bending, Reissner’s model, Mindlin’s model.
Related Book
Other papers in this volume
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