Mathematical Modeling in Shell Structure Analysis Tasks

被引：0
作者：
Semenov A. [1 ]
机构：
[1] Department of Information Technologies, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg
来源：
International Journal for Engineering Modelling | 2022年 / 35卷 / 01期
关键词：
buckling; computer simulation; method of L.V. Kantorovich; Ritz method; shell structures;
D O I：
10.31534/engmod.2022.1.ri.03m
中图分类号：
学科分类号：
摘要：
Studying shell structures while accounting for all necessary factors is a significantly nonlinear problem that requires serious mathematical tools and sufficient computing capacities. We propose an approach to solving such problems based on the following numerical methods. We propose the use of the Ritz method, the best parameter continuation method, and the Euler method under static loading. Under dynamic loading, the Kantorovich and the Rosenbrock methods are used. Software implementation was carried out using the Maple analytical software package. This paper also provides examples of simulating the deformation process in shell structures. © 2022, University of Split. All rights reserved.
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页码：43 / 55
页数：12
相关论文
共 22 条
  • [1] Fan H.-G., Chen Z.-P., Feng W.-Z., Zhou F., Cao G.-W., Dynamic Buckling of Cylindrical Shells with Arbitrary Axisymmetric Thickness Variation under Time Dependent External Pressure, International Journal of Structural Stability and Dynamics, 15, 3, (2015)
  • [2] Gavryushin S.S., Nikolaeva A.S., Method of change of the subspace of control parameters and its application to problems of synthesis of nonlinearly deformable axisymmetric thin-walled structures, Mechanics of Solids, 51, 3, pp. 339-348, (2016)
  • [3] Grigorenko Ya.M., Avramenko Yu.A., Refined Stress Analysis of Orthotropic Toroidal Shells, International Applied Mechanics, 49, 4, pp. 461-474, (2013)
  • [4] Karpov V.V., Models of the shells having ribs, reinforcement plates and cutouts, International Journal of Solids and Structures, 146, pp. 117-135, (2018)
  • [5] Karpov V., Variational method for derivation of equations of mixed type for shells of a general type, Architecture and Engineering, 1, 2, pp. 43-48, (2016)
  • [6] Karpov V.V., Semenov A.A., Dimensionless models of deformation of stiffened shell structures, PNRPU Mechanics Bulletin, 1-2, pp. 37-49, (2018)
  • [7] Kumar Y., The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review, Journal of Vibration and Control, (2017)
  • [8] Kuznetsov E.B., Continuation of solutions in multiparameter approximation of curves and surfaces, Computational Mathematics and Mathematical Physics, 52, 8, pp. 1149-1162, (2012)
  • [9] Liew K.M., Lee Y.Y., Ng T.Y., Zhao X., Dynamic stability analysis of composite laminated cylindrical panels via the mesh-free kp-Ritz method, International Journal of Mechanical Sciences, 49, 10, pp. 1156-1165, (2007)
  • [10] Maksimyuk V.A., Storozhuk E.A., Chernyshenko I.S., Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review), International Applied Mechanics, 48, 6, pp. 613-687, (2012)
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