## 3 Stiffened Shell Structures
### Mechanics of Ring Stiffened Cylinder and Numerical Approaches  
Due to the high stresses caused by axial pressure, bending, and circumferential pressure, ring stiffeners were often used in combination with thick plates. This resulted in either the stiffener or the shell failure first considering their isolation, but also the interaction of both components had to be taken into account. Traditionally, there are three main types of simplified models for stiffened shell structures in stability research. The first is to consider the stiffened shell structure by simplifying it to an equivalent orthotropic anisotropic structure [46]. This model is more suitable for densely stiffened structures with equivalent spacing, and it is difficult to determine a consistently satisfied equivalent value of orthogonal anisotropy for sparsely stiffened structures where the distance between the stiffeners is possibly greater than the buckling wavelength. In addition, this model is also difficult to simplify for nonequally spaced, nonuniformly stiffened shell structural types. The second method, called the beam-column method, is based on the consideration of stiffeners with their adjacent structural parts of the shell as a slat model [47]. This method is also not applicable to the cases of sparsely stiffened and non-uniform stiffeners. The third model is called the finite strip method [48]. The basic idea of this approach is to decompose the stiffened structure into the main structure and the stiffeners for separate investigations, which are related by displacement conditions and force equilibrium conditions at the junctions. This model is widely used in numerical methods, such as the finite-strip method and the finite-difference method. However, when applying the finite bar method for the stability analysis of stiffened shell and plate structures, it is still difficult to treat the issue of transverse stiffeners very effectively. Over the past few decades, researchers have also conducted a large number of experimental studies for ring-stiffened cylindrical shells. According to the experimental results  
Figure 4: Collapse figure of ring-stiffened cylindrical shell structures with different stiffeners. of [PERSON], either local shell buckling, global instability, or an axisymmetric plastic collapse regularly turns out to be the cause of failure. As early as 1967, [PERSON] described in his experimental results that depending on the geometry, axisymmetric, or checkerboard, buckling patterns can show up as the failure pattern. Even with local failure, the ring stiffeners have a recognizable stiffening effect, and close ring stiffeners constrain the shell specimens to buckle in an axisymmetric shape. Global and local failure can interact and reduce the achievable ultimate buckling load. Although experiments for medium-length cylindrical shells show a high scattering of results, this cannot be transferred to the test results on short-length cylinders. One reason for this is the typically axisymmetric failure shape, which was classified by [PERSON] as not imperfection sensitive due to the stable post-buckling behaviors. The second reason may be due to the greater influence of the torsional restraint at the edges of the shell specimen. One of the focuses of attention has also been the post-buckling shape. According to [PERSON]'s results, the chequerboard buckling pattern, which is typical of unstiffened cylindrical shells, could also be observed in the post-buckling area of widely stiffened cylinders with torsional weak ring stiffeners. However, on the other hand, if the stiffeners have high torsional stiffness, it is likely that a local, axisymmetric failure pattern will occur. Then, it is obvious that global failure is typical for thin-walled ring-stiffened cylinders with weak ring stiffeners. A thicker cylindrical shell specimen usually leads to an axisymmetric buckling or ring buckling in tightly as well as arbitrary ring-stiffened cylinders.