Eight node continuum elements with one Gauss point
and hourglass control are used for concrete in the FE model.
There are five types of smoothing elements ((i) split smoothing element: there is one Gauss point
on each boundary segment for split smoothing element; (ii) split-blending smoothing element: one Gauss point
on each boundary segment is sufficient; (iii) tip smoothing element: five Gauss points
on a segment of smoothing element are sufficient; (iv) tip-blending smoothing element: five Gauss points
on each boundary segment are sufficient; (v) standard smoothing element: one Gauss point
on each boundary segment is sufficient) being used for numerical integration as mentioned in .
In practical work, some Gauss point
has the same nodes as some neighboring computational points.
As we explained in previous sections, the RKEM shape functions are piecewise rational shape functions, therefore, we need to use many Gauss point
to evaluate the integrals such that we can obtain a well conditioned, non singular system of equations (15).
The values of principal stress obtained from Gauss point
of element were [[sigma].sub.11][member of] (-l17,21.2)MPa and [[sigma].sub.22][member of] ( -120, 4.14) MPa.
It can produce a graph between variables like, load and deflection, stress and strain, convergence details, single and multiple Gauss point
[[sigma].sup.c.sub.ij] is the concrete stress distribution along the thickness, [[sigma].sup.sk.sub.ij] represents the steel stress of a layer placed at [x.sub.3sk], while [A.sub.sk] represents the steel bar cross section, being [N.sub.s] the reinforced layer number and [[delta].sub.ij] the Kronecker delta, [[xi].sub.IG] is the Gauss point
where [[psi].sub.m] is the value of [[psi].sub.m] of the NI-th Gauss point
; [c.sub.pi,r]=1 is the value of [c.sub.pi,r]=1 of the NI-th Gauss point
; Wt(NI) is the weight value of the NI-th Gauss point
; GJ is the proportion factor of the integral transformation, and GJ=dz/d[zeta]=[h.sub.e]/2.
Positions of Gauss Points
. Gauss Point
(/) 1 2 3 4 5 6 [y.sub.l] (= [y.sub.l]/h) 0.013 0.067 0.160 0.283 0.426 0.574 Gauss Point
(/) 7 8 9 10 [y.sub.l] (= [y.sub.l]/h) 0.717 0.840 0.933 0.987
The results shown were calculated at the Gauss point
just above the center-line.
So the direction cosines [[lambda].sub.x'], [[lambda].sub.yx'], and [[lambda].sub.z'] of the local coordinate system established at different Gauss point
with respect to the global coordinate system are different with each other.
At each element, the smoothed value for each stress component considered is obtained computing the average of the corresponding Gauss point
values at FS line and PS line, respectively.