Abstract
The article presents the results of theoretical and experimental studies of complex shape shells performed by the method of curvilinear grids in order to optimize the calculation of strength and stability. It is analyzed the existing numerical methods for calculating shells, such as finite difference method, variational difference method and finite element method. To improve the convergence of finite difference method by reducing error of approximation of hard offset functions the finite element method was used for the first time. Due to this method finite difference approximation was obtained by averaging the tangential strains in a differential interval by using integration of Simpson’s formula. This new finite difference scheme was called method of curvilinear grids, the essence of it is that vector differential relations are firstly replaced by their vector of finite difference analogues, and then the transition to scalar ratios is performed by designing in the local basis. The method of curvilinear grids is applied to calculate a complex shell, formed by a combination of four hypars. The result of calculation is a graph with the dependence of the critical load of the stability loss on the cross-sectional area of the edges. The study of convergence with the obtained results was performed by different methods at different mesh density.
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Pasichnyk, R., Pasichnyk, O., Uzhegova, O., Andriichuk, O., Bondarskii, O. (2020). Calculation Optimization of Complex Shape Shells by Numerical Method. In: Ivanov, V., et al. Advances in Design, Simulation and Manufacturing II. DSMIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-22365-6_64
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DOI: https://doi.org/10.1007/978-3-030-22365-6_64
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