Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field.

• Torsional buckling of a nano-composite shell is analyzed by means of first-order shear deformation shell theory. • Both stiffness-softening and stiffness-hardening of the nanoshell are considered based on the nonlocal strain gradient theory. • The magnetic field is investigated concerning three-dimensional magnetic effects. • Three-dimensional analysis of the magnetic field presents that the transverse effect of the field is the most significant influence on the torsional stability of the shell. • It is crucial to study the magnetic field in three dimensions while the higher values of circumferential half-wave numbers are taken into account. This paper considers a single-walled composite nano-shell (SWCNS) exposed in a torsional critical stability situation. As the magnetic field affects remarkably nanostructures in the small size, a three-dimensional magnetic field is assessed which contains magnetic effects along the circumferential, radial and axial coordinates system. Based on the results of the nonlocal model of strain gradient small-scale approach and the first-order shear deformation shell theory (FSDST), the problem is estimated. Afterward, the numerical results are taken analytically and compared with other existing literature. Hereafter, the influences of various factors, such as the magnetic field, are discussed deeply. It is observed that when the magnetic field is studied in three dimensions, the transverse magnetic effect is the most serious factor that affects fundamentally the torsional stability of the shell. [ABSTRACT FROM AUTHOR]