Computational algorithm for calculating the stress-strain state and buckling of thin-walled shells

Introduction. The studies of the processes of deformation of shells are mainly carried out using computational algorithms that implement the application of various numerical methods. These algorithms must ensure obtaining accurate results and high speed of calculations, and must also be resistant to changes in input parameters (geometry, material). The purpose of this work is to develop a computational algorithm for calculating the stress-strain state (SSS) and buckling of shells, based on the application of the Ritz method and the Newton method, ensuring high productivity and stability of the solution.

Materials and methods. The deformation of shell structures is described by a geometrically nonlinear mathematical model of the Timoshenko – Reissner type, which considers transverse shears and orthotropy of the material. The mathematical model is written as a functional of the total potential energy of deformation of the shell. The study of the stress-strain state and buckling of the structure is reduced to finding the minimum of the functional. Using the Ritz method, this problem is reduced to solving a system of nonlinear algebraic equations. The solution of the resulting system is carried out using the Newton method. A distinctive feature of this algorithm is the use of an adaptive step by load when solving a system of nonlinear algebraic equations.

Results. Calculations of structures were performed: shallow shells of double curvature and cylindrical panels made of isotropic and orthotropic materials. The obtained values of critical loads have good agreement with the results of other authors: for shallow shells of double curvature, the maximum discrepancy of results was 8,05 %, and for cylindrical panels 7,29 %.

Conclusions. A computational algorithm for calculating the stress-strain state and buckling of shells that is stable to changes in geometry and material of the structure has been developed. High performance of the algorithm is ensured by using an adaptive step by load when solving a system of nonlinear algebraic equations. The possibility of using this algorithm when studying shallow shells of double curvature and cylindrical panels has been substantiated.

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