The optimal design of structures that interact with an aggressive environment is considered on the example of a thin-walled shell exposed to the internal pressure of the aggressive gas. The simplicity of the above research object is related to quite simple equations describing the stress-strain state (SSS) of the structure. Any mathematical model simulating the corrosion damage process includes empirical coefficients characterizing the degree of influence of certain factors on the corrosion rate. Some coefficients (mainly those describe the corrosive environment behavior, which controls the temperature, concentration of certain substances, etc.) are constant, while others that describe the SSS effect on the corrosion damage rate of the structure, according to earlier findings of the author, vary during the optimal design procedure, significantly affecting the final design results. It should be noted that the proposed method should be applied not at the operation stage of the structure but at its design stage. To define the coefficients of the mathematical model of corrosion damage, a numerical method for multiple identifications of the mathematical model based on experimental data was proposed. This method gives satisfactory results but is quite cumbersome and time-consuming. The analytical method of polynomial approximation gives results comparable in efficiency but is more flexible and fast. Two modifications of the method of polynomial approximation to define the “optimal” set of coefficients of mathematical models of corrosion damage are developed. Numerical simulations are performed for the optimal design of a thin-walled cylindrical shell exposed to an aggressive environment.

在暴露于侵蚀性气体内部压力的薄壁壳体上，考虑了与侵蚀性环境相互作用的结构的最佳设计。上述研究对象的简单性与描述结构的应力-应变状态（SSS）的非常简单的方程式有关。任何模拟腐蚀破坏过程的数学模型都包括经验系数，这些经验系数表征了某些因素对腐蚀速率的影响程度。根据作者先前的发现，一些系数（主要是描述腐蚀环境行为，控制温度，某些物质的浓度等）是恒定的，而其他一些系数则描述了SSS对结构腐蚀破坏率的影响。 ，在最佳设计过程中会有所不同，严重影响最终设计结果。应当注意，所提出的方法不应应用于结构的操作阶段，而应应用于其设计阶段。为了定义腐蚀损伤数学模型的系数，提出了一种基于实验数据的数学模型多重辨识的数值方法。该方法给出令人满意的结果，但是相当麻烦且费时。多项式逼近的解析方法给出的结果在效率上可比，但是更加灵活和快速。开发了多项式逼近方法的两种修改形式，以定义腐蚀损伤数学模型的“最佳”系数集。