Coupled Contact Problem of Punch Pressure Under Action of Follower Force

A coupled contact problem involving the interaction of a punch with a half-space under a follower load has been considered. The punch is pressed against the elastic half-space by a force that acts parallel to the punch axis and is offset from the center of the punch base. The direction of the force remains unchanged relative to the punch as the force increases, thus defining it as a follower force.Amathematical model has been formulated, and an analytical solution has been obtained. The specific motion behavior of the punch under increasing force has been analyzed, including the determination of the maximum angle of rotation. The variation in the horizontal motion of the punch depending on the applied force has been studied. Additionally, having considered a modification of the problem where the force direction is reversed, significant differences in the punch displacement have been found.