On the applicability limits of the structurally orthotropic shell model in problems of calculating the buckling under axial compression of waffle cylindrical shells

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The article considers the solution of the buckling problem of a waffle cylindrical shell under axial compression using the Euler (bifurcation) approach. Two models are used: a model based on the numerical integration method and a model based on the finite element method. The first model assumes that the stiffeners are structurally an orthotropic shell obeying the Kirchhoff-Love hypotheses, with the assumption of "smearing". The second model uses a tetrahedron element with ten nodes. The study is based on experimental data from tests of one of the waffle cylindrical shell samples under axial compression. The research results show that with an increase in the waffle shell rib thickness, a discrepancy between the calculation results of the two models is observed. With the optimal value of the k parameter, characterizing the ratio of the rib thickness to the rib pitch, equal to 0.035, such a discrepancy is estimated to be about 5%. At the same time, the calculation using the model of a structurally orthotropic shell leads to an underestimation of the critical load compared to the finite element model. This provides an estimate of the loss of stability of a waffle cylindrical shell with a safety margin. For parameter k between 0.02 and 0.05, the difference between the results from the two computational models for critical loads does not exceed 11%.