Temperature-dependent nonlinear analysis of shallow shells: A theoretical approach

Abstract

The paper presents a theoretical formulation for the computation of temperaturedependent nonlinear response of shallow shells with single and double curvatures subjected to transverse mechanical loads while being exposed to through-depth non-uniform heating regimes such as those resulting from a fire. The material nonlinearity arises from taking into consideration the degradation of the material elastic behaviour at elevated temperatures under quasi-static conditions. Two types of boundary conditions are considered, both of which constrain the transverse deflections and allow the rotations about the edge axis to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). A number of examples are solved for shallow shells under different types of loading conditions including: an exponential "short hot" fire leading to a high temperature over a relatively short duration; and an exponential "long cool" fire of lower temperature over a longer duration. The limits of the shallow shell equations are investigated through comparison studies. Results show that while current numerical approaches for analysis of laterally restrained shallow shells are often computationally intensive, the proposed approach offers an adequate level of accuracy with a rapid convergence rate for such structures.

Temperature and Pressure Dependent Creep Stress Analysis of Spherical Shell

“…Kashkoli et al [6] assumed that the thermo-creep response of the material is governed by Norton's law and an analytical solution of the problem is presented for the determination of time-dependent creep stresses and displacements of homogeneous thick-walled pressure vessels. Usmani et al [7] presented the theoretical approach for the determination of a temperature-dependent non-linear response of shells subjected to a transverse mechanical load. The non-linear behavior of the material arises by taking into consideration the elastic-plastic behavior at high temperatures under quasi-static conditions.…”