Reconfigurable fixturing for welding

A system for joining at least two components by welding includes a magnetic base for receiving the components for welding and a flexible magnetic member configurable to correspond to a weld path defining a weld joining the components. The flexible magnetic member exerts a retention force on the components in response to a magnetic field produced by selective activation of the magnetic base. The system can include a magnetic locating element positioned adjacent a perimeter edge of the component to be welded, for generating a repulsive magnetic force between the flexible magnetic member and the magnetic locating element to locate the flexible magnetic member relative to the perimeter edge and provide clearance for a welding device to access a continuous weld path defined by the perimeter edge, such that the welding device can form a continuous weld along the weld path. A welding method using the system is provided.