Impact of pulse dynamic loading direction and surface curvature on the stress-strain state of a three-layered spherical shell




three-layered conical shell, loading direction, stress-strain state, finite element model, axisymmetric pulse load


On two size types of the semispherical three-layered structures, impact of the surface curvature and impact of the pulse dynamic loading on the stress-strain state (SSS) of these structures has been investigated. The layered hemispheres have been analyzed with the clamped footing and diameters (D1=0.30 m, D2=0.60 m), which had similar bearing layers’ thickness (h1=h3=0.010 m), polymeric filler with h2=0.020 m thickness, reinforced with the 5 discrete stiffening rings rigidly bound to the bearing layers.

Values of normal stresses and vertical displacements of the structures’ bearing layers and distribution of these indicators along the spatial coordinate have been determined. Distribution of displacements’ and stresses’ magnitudes along the spatial coordinate α was determined by the software complex Nastran through the direct transient dynamic process algorithm within the time interval 0 ≤ t ≤ 10T. The time interval step duration was 0.25*10-6 s and the total number of steps was 200. The detailed and accurate calculation results have determined the choice of the solid finite element type.

Value of the Gaussian curvature of the layered shell structures impacts their stress-strain state. Increase of the surface curvature of spherical structures under the impact of the dynamic pulse load increases the displacement and stress of their bearing layers.

In addition to the vertical displacements and normal stresses of the bearing layers of the analyzed semispherical three-layered structures, their first natural frequency (f1) was also calculated.

Author Biographies

Viktor Gaidaichuk, Kyiv National University of Construction and Architecture

Doctor of Technical Sciences, Professor, Head of the Department of Theoretical Mechanics

Kostiantyn Kotenko, Kyiv National University of Construction and Architecture

Candidate of Technical Sciences, Associate Professor of Theoretical Mechanics


Lugovoi P. Z., Meish V. F. Dynamics of inhomogeneous shell sysnems under non-stationary loading (survey) // International Applied Mechanics – 2017, 53, № 5 – Р. 481–537.

Dynamic problems in the theory of sandwich shells of revolution with a discrete core under nonstationary loads // International Applied Mechanics – 2002, 38, № 12 – Р. 1501–1507.

Timoshenko S.P., Woinowsky-Krieger S. Theory of Plates and Shells. Second Edition. New York etc.: McGraw-Hill Book Company INC, 1959. 636 p.

Gaidaichuk V.V., Kotenko K.E. Stress - strain state of a three-layer cylindrical shell under internal axisymmetric pulse load с Strength of Materials and Theory of Structures. – 2020. – Issue. 105. – Р. – 145-151.

Lugovoi P.Z., Gaidaichuk V.V., Skosarenko Yu.V., Kotenko K.E. Stress - strain state of the three-layer cylindrical shells with reinforced lightweight filler under nonstationary load // International Applied Mechanics – 2021, 57, № 4 – Р. 23–34.

Novozhilov, V.V. (1948). Fundamentals of the nonlinear theory of elasticity. Leningrad—Moscow: Gostekhizdat (in Russian).