Avoiding undesirable thermal stress or damage of a target vessel is an essential subject in high-intensity beam irradiation for accelerator-driven neutron production. A promising method to tailor the transverse beam intensity distribution for uniform beam irradiation on the target is the use of multipole magnets. We, therefore, study the transformation and uniformization of the transverse intensity distribution by means of nonlinear focusing induced from multipole magnets. It is theoretically described how the intensity distribution is transformed and made uniform by the nonlinear focusing force. Large-area uniform proton and heavy-ion beams are experimentally formed using octupole magnets at the azimuthally-varying-field cyclotron in Japan Atomic Energy Agency.