<p>In this paper, an ordinary differential equation (ODE)-driven boundary penalization method (BP) combined with isogeometric analysis (IGA) is proposed to deal with structural topology and shape optimization problems. Different from the traditional level-set method (LSM) evolving level-set function (LSF) along the structure boundary, LSF in the present proposed method (IGA-BP) only varies freely along the direction perpendicular to the structural interface, making the LSF updates more efficiently. This method penalizes the element density of boundary cutting to ensure that the optimization is stable. Moreover, the Non-Uniform Rational B-splines (NURBS) basis function is adopted for constructing both IGA and LSF, which not only makes the geometric model represented more accurately in comparison to the conventional finite element method but also provides an explicit spline (hyper) surface representation for the LSF that drives the topological boundary evolution of the structure. This representation of LSF makes integrating the structural topology and shape optimization results easy with CAD software. The present IGA-BP method avoids the checkerboard problem without introducing additional filtering. The IGA-BP method simplifies the extension to higher-order elements. Numerical examples of topology optimization, topology, and shape collaborative optimization of solid and shell structures are investigated. Specifically, the IGA-BP method is used to synergistically optimize the topology and shape of the Schwarz P-surface shell structure, resulting in novel and interesting design results that further demonstrate the effectiveness and superiority of the proposed method.</p>