  We investigate the response of excitons in two-dimensional semiconductors
subjected to controlled non-uniform strain fields. In our approach to
non-uniform strain-engineering, a WS$_2$ monolayer is suspended over a
triangular hole. Large ($>2\;\%$), strongly non-uniform ($>0.28\;\%/\mu m$),
and in-situ tunable strain is induced in the monolayer by pressurizing it with
inert gas. We observe peak shifts and spectral shape changes in the
photoluminescence spectra of strained WS$_2$. We interpret these changes as a
signature of increased free electron density and resulting conversion of
neutral excitons to trions in the region of high strain. Our result establishes
non-uniform strain engineering as a novel and useful experimental `knob' for
tuning optoelectronic properties of 2D semiconductors.
