Stiffened shells and plates are widely used in engineering, but their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, structures with modules are beneficial, since it allows for increased quality control and more accessible mass production. The aim of this work is to develop a method that simultaneously optimizes the topology of the modular stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of module stiffeners which are subject to density based topology optimization and a mapping of these modules to a ground structure of stiffeners. To illustrate potential applications, several stiffened plates and shell examples are presented. After optimization, these examples were converted to three-dimensional physical structures using additive manufacturing. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout on the base.