  The oxygen isotope effect on the superconductivity, stripe phase and
structure transition is systematically investigated in
La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_4$ with static stripe phase. Substitution of
$^{16}$O by $^{18}$O leads to a decrease in superconducting transition
temperature T$_C$, while enhances the temperature of the structural transition
from low-temperature-orthorhombic (LTO) phase to low-temperature-tetragonal
(LTT) phase. Compared to the Nd free sample, a larger isotope effect on $T_C$
is observed in La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_4$. These results indicate
that the distortion of CuO$_2$ plane suppresses the superconductivity, giving a
direct evidence for the competing of stripe phase and superconductivity because
the distortion of CuO$_2$ plane enhances the stripe phase.
