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The objective of this paper\footnote{ Authorized republication, with minor
modifications, of a paper that was presented at the
48th AIAA/ASME/ASCE/AHS/ASE Structures, Structural Dynamics and
Materials Conference in Honolulu, Hawaii, and appeared in the CD of
conference proceedings, American Institute of Aeronautics and
Astronautics, pp. 1-15.} is a rational determination of safety factors
of quasibrittle structures, taking into account their size and shape. To
this end, it is necessary to establish the probability density
distribution function (pdf) of the structural strength. For perfectly
ductile and perfectly brittle materials, the proper pdf's of the nominal
strength of structure are known to be Gaussian and Weibullian,
respectively, and are invariable with structure size and geometry.
However, for quasibrittle materials, many of which came recently to the
forefront of attention, the pdf has recently been shown to depend on
structure size and geometry, varying gradually from Gaussian pdf with a
remote Weibull tail at small sizes to a fully Weibull pdf at large
sizes. This recent result is reviewed, and then mathematically extended
in two ways: 1) to a mathematical description of structural lifetime as
a function of applied (time-invariable) nominal stress, and 2) to a
mathematical description of the statistical parameters of the pdf of
structural strength as a function of structure size and shape.
Experimental verification and calibration is relegated to a subsequent
journal article. |
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