Nonlocal elasticity theory for thermo-elastic analysis of nanoscale spherical shell subjected to thermal shock

In this paper، an analytical method is presented to study thermo-elastic behavior of nanoscale spherical shell subjected to thermal shock based on nonlocal elasticity theory. The shell is considered as elastic، homogeneous and isotropic solid. The nonlocal differential equation of motion is derived in terms of radial displacement. The analytical solution of equation of motion is obtained by Laplace transform and differential transform method (DTM). Mechanical boundary conditions are used to obtain unknown parameters that get in recurrence equation in Laplace domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform method (FLIT). Accuracy of obtained results is evaluated by well-known similar articles. The results have a good agreement in comparison with published data in pervious literatures. Also، the effects of nonlocal parameter and wall thickness of shell on the dynamic characteristics of nanoscale spherical shell are studied in various points across the thickness of shell under thermal shock. The present analytical method provides an appropriate field for analysis of times histories of radial and hoop stresses in a nanoscale shells subjected to various time dependent thermo-mechanical loads.