# Evaluation of the Flexural Rigidity of Underground Tanks Manufactured by Rotomodiding
## 1 Introduction  
Every successful application of thermoplastics is conditioned by a qualified determination of the dimensions and shape of the proposed structure in addition to thorough design and technological preparation. Thermoplastics are generally relatively low in stiffness and strength, have a significant tendency to creep, a high thermal expansion, and a marked dependence on temperature as regards their mechanical characteristics. These properties usually appear to be disadvantageous. On the other hand, however, there are undeniable advantages to this, for example, ease of processing, low energy consumption, high manufacturing productivity, and the wide range of applicable new technologies. Furthermore, it is the excellent resistance to aggressive substances and environments that makes thermoplastics suitable for the construction of equipment operating in harsh operating [1, 2] conditions, e.g., in the chemical and food industries. The specific mechanical behavior of thermoplastics brings with it peculiarities and difficulties for design compared to conventional materials. The nature of the technology and the desire to limit the weight and cost of the product lead to the design of thermoplastic structures with thin walls. Due to low stiffness values (modulus of elasticity) or time-dependent stiffness (modulus of creep), deformation states rather than yield states are often decisive in product design [3, 4]. Thus, very often, the limit states are decisive, causing a loss of structural stability. In the industry, the current issues are the assessment of the possibility of replacing the homogeneous walls of rotationally cast large-volume underground tanks [5, 6] with structural walls [7, 8, 9], to promote flexural rigidity and, therefore, stability capacity. It is necessary to investigate the possibilities of potential material savings by combining lightweight and non-lightweight layers of the tank wall, thus creating three-layer sandwichwalls. This implies the need for computational predictions of the flexural rigidity values of tank walls for different wall structure concepts. Although the topic of underground tanks produced using rotomolding technology is very current, as we observed in the relevant review, there is no practical attention paid to this issue in the literature. Many authors address potential problems such as strength, the failure mechanism, and structural vessel optimization [10,11]. [PERSON] [12] reported that functionally graded material (FGM) layers are convenient to reduce shear and normal stress gradients. Furthermore, the FGM layers lead to benefits in terms of the buckling load; however, the use of FGM requires different manufacturing technology to that explored in this study. In the case of ground or underground horizontal cylindrical tanks, the wall of the cylindrical shell of a tank is subject to non-homogeneous stress. As [PERSON] [13] states, the regions where compression occurs, buckling becomes possible. It was found that, for underground and above-ground tanks with similar loads, the critical thickness of the wall of underground tanks exceeds that of their above-ground counterparts. In the study of [PERSON] [14], he statistically evaluates the random geometric imperfection stability for an asymmetrical cylindrical vessel under external pressure, while the relevant EN standard controls the relevant safety at the limit of the stability capacity with respect to geometric imperfections. In [15], the authors focus on electrolyte and recirculation tanks considering the technology itself but not the stability, confirming the need for safe rigidly stable tanks, although this is outside of the scope of our study. On the basis of the application of the technical theory of bending of inhomogeneous layered walls, the flexural rigidity values of tank walls for individual concepts of the wall structure (a homogeneous, three-layer sandwich structure) were computationally determined.