Thermal instability of deep spherical shells made of functionally graded material (FGM) is studied in this paper. The governing equations are based on the first-order theory of shells and the Sanders nonlinear kinematics equations. It is assumed that the mechanical properties are linear functions of thickness coordinate. The constituent material of the functionally graded shell is assumed to be a mixture of ceramic and metal. The analytical solutions are obtained for three types of thermal loadings including the uniform temperature rise (UTR), the linear radial temperature (LRT), and the nonlinear radial temperature (NRT). Results are validated with the known data in literature.
Key words Low velocity impact, composite laminated beam, temperature dependent, Ritz method, first order shear deformation beam theory.In this research, dynamic behaviour of a composite laminated beam subjected to multiple projectiles is analysed. Temperature elevation is also taken into account. Hertz law of contact is used to model the impact phenomenon between the projectiles and the target. Beam obeys the first order shear deformation theory assumptions. Governing motion equations of the beam and projectiles are obtained using the Hamilton principle. Conventional Ritz method suitable for arbitrary in-plane and out-of-plane boundary conditions is implemented to reduce the partial differential equations into time-dependent ordinary differential equations. Time domain solution of such equations is extracted by means of the well-known fourth-order Runge-Kutta method. After validating the proposed model with the available numerical data, parametric studies are conducted to investigate the influences of multiple impactors, beam characteristics, boundary conditions and thermal environment. It is shown that, temperature elevation decreases the contact force and increases the contact time.
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