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Magnetic skyrmions emerge as promising quasi-particles for encoding information in nextgeneration spintronic devices. Their innate flexibility in shape is essential for the applications although they were often ideally treated as rigid particles. In this work, we investigated the voltagecontrolled uniform strain mediated dynamics of deformed skyrmions in heterostructures with a flower-shaped magnetic nanostructure, using micromagnetic simulations. The simulated results revealed the possible states of isolated skyrmion nucleated in the nanostructure, which can be mutually switched by applying suitable in-plane strain pulses. In addition, it was found that the skyrmion motions are driven by the emerging internal forces and strain force, which originate from the asymmetric deformation of skyrmion structures. Furthermore, an analytical model of deformed skyrmions was proposed to interpret the dependences of internal forces and strain force on the asymmetric deformation of skyrmion, with some formulae derived for these forces in a semi-analytical approach. Further calculations based on these formulae verified the forces appearing in the skyrmion motion, with the resulting forces showing consistence with the simulated data. This suggested that our semi-analytical model successfully captures the main physics responsible for the motion of deformed skyrmion in the nanostructure. Our work extends the understanding of the mechanics emerging in deformed skyrmion, and provides an effective approach for deterministic manipulation of deformed skyrmion motion via strain forces and internal forces, which may be instructive to design of skyrmion-based spintronic devices.