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Sinusoidal velaroidal shell – numerical modelling of the nonlinear buckling resistance

G. Mathieu
A. S. Markovich
D. Tyekolo


Many works are devoted to linear and nonlinear analyses of shells of classical form. But for thin shells of complex geometry, many things remained to do. Four different sources of nonlinearity exist in solid mechanics. The geometric nonlinearity, the material nonlinearity, the kinetic nonlinearity and the force nonlinearity. The nonlinearity, applied to a sinusoidal velaroidal shell with the inner radius r0, the outer variables radii from 10m to 20m and the number of waves n=8, will give rise to the investigation of its nonlinear buckling resistance. The building material is a high-performant concrete. The investigation emphasizes more on the material and the geometric nonlinearities. The result of the investigation is the buckling force of the shell under self-weight and uniformly vertically distributed load on its area, the corresponding numerical values of displacements and the buckling mode.

Keywords: Nonlinear analysis, nonlinear buckling resistance, numerical modelling, sinusoidal velaroidal shell, geometric nonlinearity, material nonlinearity, kinematic nonlinearity, force nonlinearity.