We carry out numerical simulations of soft, U-shaped, frictionless particles in $d=2$ dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction $\phi$ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction $\phi_J$ than observed in compression. A growing relaxation time and translational correlation length is found as $\phi$ increases towards $\phi_J$. We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as $\phi$ increases to $\phi_J$. At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as $\phi$ increases, saturating to a plateau just below $\phi_J$, but then increasing again as $\phi$ increases above $\phi_J$.