Dynamic thermal buckling of spherical porous shells

S Talebi,R Hedayati,M Sadighi,A.R Ashoori

doi:10.1016/j.tws.2021.108737

Abstract

The aim of present work is to address nonlinear dynamic thermal buckling of shallow spherical functionally graded porous shells subjected to transient thermal loading using the first order shear deformation theory (FSDT). A power-law distribution as well as cosine-type porosity distribution are used to model the variation of constituents through the shell thickness. Thermomechanical properties are assumed to be temperature dependent. Using Crank–Nicolson time marching scheme, an iterative procedure is employed to solve nonlinear transient heat conduction equation. For thermal boundary conditions, the outer surface of shells is kept at a reference temperature, while the inner surface experiences a sudden temperature rise. Geometrical type of nonlinearity in the sense of von-Karman is taken into account. The highly coupled nonlinear governing equations of motion are extracted by constructing the appropriate weak form and also using multi-term Ritz–Chebyshev method. The resulting ODEs are then reduced to a system of nonlinear algebraic equations by employing the well-known Newmark family of time integration schemes. The latter equations are solved by means of Newton–Raphson iteration procedure. Budiansky criterion is used to recognize critical parameters of dynamic instability of shells due to applied thermal shocks. Some comparison studies are conducted in order to verify the accuracy of results of the present work. Moreover, various parametric studies are performed to assess the influence of involved parameters.

Highlights

Since the primary work of Boley [1] in 1956, the subject of thermally induced vibrations of solid structures have been pursued in hundreds of publications
As the literature survey demonstrates, no work, to the best of the authors’ knowledge, has been reported on nonlinear dynamic snapthrough instability of temperature-dependent spherical functionally graded porous shells subjected to thermal shock
The procedure outlined in the previous sections is implemented here to investigate the nonlinear dynamic snap-through instability of temperature-dependent spherical FGM porous shells subjected to transient thermal loading

Summary

Introduction

Since the primary work of Boley [1] in 1956, the subject of thermally induced vibrations of solid structures have been pursued in hundreds of publications. Dynamic instability analysis of isotropic spherical shells subjected to various loading and boundary conditions has been presented based on different numerical methods [22,23,24]. Ganapathi and Varadan [28] studied the dynamic snap-through instability of externally pressurized spherical FGM shells in which kinematic assumptions are according to first order shear deformation theory and von-Karman geometrical nonlinearity. Taking into account the geometrical nonlinearity, Wang and Zu [34] conducted a study on the vibrations of rectangular functionally graded plates with porosities and moving in thermal environment. As the literature survey demonstrates, no work, to the best of the authors’ knowledge, has been reported on nonlinear dynamic snapthrough instability of temperature-dependent spherical functionally graded porous shells subjected to thermal shock. Various parametric studies are presented to investigate the influence of involved parameters

Preliminaries

Governing equations

A12 R2 cot φ

Solution procedure

Results and discussions

Conclusion