Abstract: The organic combination of additive manufacturing and topology optimization will greatly promote the development of high-performance products. However, most of the existing researches on design performance and manufacturability based on topology optimization are carried out separately. And, they often focus on traditional stiffness problems and lack the consideration of the most important strength problems in practical engineering. In this paper, an additive manufacturing-oriented topology optimization model for the structural optimization problem that considers strength and manufacturability connectivity collaboratively is established, viz, a structural stress minimization under material volume and connectivity-based scalar field constraints. An effective optimization strategy is introduced to overcome various numerical problems in the solution. The P-norm based global scalar field constraint measure is employed, together with the stability transformation method-based error correction technique to realize the effective control of the local scalar field. The corresponding sensitivity is derived in detail. The rationality and effectiveness of the proposed model and method are demonstrated by typical numerical examples. Optimized results show that the stiffness maximization design considering only the connectivity constraint may not necessarily avoid local high stress concentration, and the design is not necessarily equivalent to the stress minimization connectivity design. Sufficient material allowance and appropriate connectivity constraint boundary conditions are important to improve the performance of the design studied. Moreover, the value of the stress aggregation parameter is not the bigger the better, only a reasonable value can help to obtain a high-performance design. To some extent, the results also demonstrate the necessity and feasibility of considering the strength problem in manufacturing-oriented topology optimization.