## 1 Introduction  
Due to the increasing use of shell-type structures in spacecrafts, submarines, buildings, and storage tanks, there has been a corresponding increase in the interest of researchers and practical engineers in the stability of shells. Hemispherical shells are the most important structural element in engineering applications because they can resist higher pure internal pressure loads than any other geometric vessel with the same wall thickness and radius. In practice, most pressure vessels experience external loads due to hydrostatic pressure or external shocks-. Therefore, they should be designed to withstand the worst load combinations without failure. Loads transmitted by cylindrical rigid actuators applied on top of the sphere are considered common external loads. Therefore, it is important to study its effect on the initial buckling behaviour of such shells. Meanwhile, corrosion is defined as the gradual destruction of a material due to chemical reactions within the environment. The most common type of corrosion is uniform corrosion or general corrosion, which is distributed almost uniformly over the entire exposed surface. General wear can occur both with the formation of a fully protective ultra-thin coating of corrosion products and without an oxide layer. The formation of a blocking passivation film, as well as changes in the concentration of one or the other reactants, may inhibit when the corrosion rate should decay exponentially (decline) with time [1; 2; 3]. On the other hand, as with other types of damage (e.g., [4]), corrosion can be enhanced by the applied load [5]. Experimental data suggests that there is a stress corrosion threshold, after which mechanical stress accelerates corrosion [5; 6; 7]. In this case, the stress changes due to the reduction in shell thickness, and the changed stress in turn enhances the corrosion process. In general, for the strength analysis of structural elements under mechano-chemical corrosion conditions, an initial boundary value problem with unknown evolutionary boundaries must be solved. In addition to stress, there are many other effects that can affect the corrosion rate, such as temperature; it has a great influence on the rate of galvanic corrosion of metals. In the case of neutral-solution corrosion (oxygen depolarization), elevated temperature has a favourable effect on the overpotential and oxygen diffusion rate for oxygen depolarization but leads to a decrease in oxygen solubility. When corrosion (hydrogen depolarization) occurs in acidic media (such as sea water), the corrosion rate increases exponentially with increasing temperature due to the reduced hydrogen evolution overpotential. An Arrhenius-type experimental dependence was observed between corrosion rate and temperature [8]. The effect of temperature on acid corrosion, most commonly in hydrochloric and sulfuric acid, has been the subject of extensive research [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. In hydrochloric acid, the effective activation energies for corrosion processes vary from 57.7 to 87.8 kJ mol/L, where most are concentrated around 60.7 kJ mol/L. In some cases, studies were performed at only three temperature values using a single experimental method, which increased the likelihood of erroneous determination of the corrosion activation energy. In this regard, further research is advisable, as it may provide a reliable comparative basis for discussing the obtained results. In summary, we know that temperature has a great influence on corrosion rate, corrosion and stress can interact with each other, and finally, they can jointly affect the stability of the shell. In this regard, we should explore the relationships of temperature, corrosion, and stress to shell stability. Experimental [23], analytical [24; 25; 26; 27; 28], and numerical methods [29; 30; 31] were used to study the buckling of (uniformly compressed hemispherical of moderate thickness) metal shells using corrosion and temperature.