Published since 1923
DOI: 10.33622/0869-7019
Russian Science Citation Index (RSCI) на платформе Web of Science


  • STRUCTURAL MECHANICS
  • Accuracy Parameters Of Methods For Solving Nonlinear Systems In Problems Of Shell Dynamics
  • UDC 624.074.43+519.622.2
    doi: 10.33622/0869-7019.2025.03.43-51
    Evelina V. SABANOVA, evelina.sabanova@yandex.ru
    Alexey A. SEMENOV, sw.semenov@gmail.com
    Saint Petersburg State University of Architecture and Civil Engineering, 2-ya Krasnoarmeyskaya ul., 4, St. Petersburg 190005, Russian Federation
    Abstract. This paper is aimed at studying the methods for solving the buckling problems of steel shallow shells of double curvature under dynamic loading. The model of deformation of the Timoshenko-type structure is considered and based on the functional of the total deformation energy, taking into account transverse shears and geometric nonlinearity. To minimize the functional, the Kantorovich method is used, which allows one to proceed to solving a rigid system of ordinary differential equations. For comparative analysis, the Runge-Kutta-Felberg method, the Adams method and the Gear method are selected. A computational experiment and collection of numerical data on the value of the critical buckling load are carried out. The influence of the parameters of numerical methods (initial step, specified accuracy, interval of step values, constant for changing the step) on the final result is analyzed. The applicability of the selected numerical methods for solving the considered class of problems is shown, for each of them, sets of the most effective parameters are collected. The features of the application of each method are revealed. Verification of the obtained values of critical loads was performed using the dsolve(rkf45) function in the Maple software.
    Keywords: numerical methods, nonlinear systems, the Runge-Kutta-Felberg method, the Adams method, the Gear method, flat shells of double curvature, buckling
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  • For citation: Sabanova E. V., Semenov A. A. Accuracy Parameters of Methods for Solving Nonlinear Systems in Problems of Shell Dynamics. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2025, no. 3, pp. 43-51. (In Russ.). doi: 10.33622/0869-7019.2025.03.43-51

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