Abstract
In this work, the nonlinear dynamic response of suddenly heated functionally graded shells is studied through nonlinear transient analysis. To this end, a triangular shell finite element with 15 degrees of freedom is developed using the invariant-based approach and the concept of the surface of mass. Equations of motion of the shell finite-element model are integrated numerically by the Newmark method combined with iterative refinement of the solution using the Newton–Raphson procedure. For each time increment, the transient temperature field across the shell thickness is determined by iteratively solving the unsteady heat-conduction equation taking into account temperature-dependent properties of the material. The predicted temperature profile is used to compute the nodal thermal loads and temperature-dependent stiffness characteristics of the shell element. The proposed finite-element element formulation is validated against the available solutions of dynamic problems of plates and shells. A number of examples are given to demonstrate nonlinear capabilities of the proposed formulation and to estimate the effect of dynamic thermal loading on buckling instability of FGM plates and shells.
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Levyakov, S.V. (2023). Dynamic Buckling of Functionally Graded Plates and Shells Subjected to Thermal Shock. In: Altenbach, H., Eremeyev, V. (eds) Advances in Linear and Nonlinear Continuum and Structural Mechanics. Advanced Structured Materials, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-031-43210-1_19
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