Static and dynamic behavior of shallow shells under the influence of quickly changing temperature and force impacts

Deformable body mechanics


Belostochny G. N.*, Myltcina O. A.**

Saratov State University named after N. G. Chernyshevsky, 83, Astrakhanskaya str., Saratov, 410012, Russia



The paper investigates two classes of shallow shells, such as bicurved and constant twisting shells, based on desultory thermoelasticity.

The bicurved shell is subjected to linear temperature field through shell thickness as well as quickly changed power load along spacial coordinate on two opposite edges.

The constant twisting shell stays in convective heat exchange state with the environment through main surfaces. At a certain time instant, the external surface of the shell is subjected to a concentrated force for a time interval. During this time interval an abrupt change of temperature occurs (loss and restoration of thermal protection). It leads to temperature difference change.

Thermal conductivity and thermoelasticity solutions were obtained by trigonometric series superposition methods with variable coefficients over spacial coordinate and products of polynomials by the Heaviside functions. In case of constant twist shell we used double trigonometric series wing coefficients variable over time coordinate. Equations for coefficients of approximating series were obtained in closed forms that are extremely convenient for quantitative analysis. We obtained numerous 3D static images of bicurved shell deflection surface, and graphs of forms of deflection and middle surface points movement of a constant twist shell versus geometric parameters, BIO number and thermal and force effects.

Quantitative analysis of the obtained analytical solutions has revealed a number of regularities in the behavior of shallow shells subjected to quickly changed temperature and force effects useful for engineering analysis in well-known technical areas.


generalized functions, thermoelasticity, shallow shell, statics, dynamics, amplitude, frequency


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