Thermal and Mechanical Stresses in Functionally Graded Cylindrical Structures

Functionally graded cylindrical structures employ continuous variations of material composition through their thickness to tailor thermal and mechanical performance under service conditions. By grading from metal to ceramic or between dissimilar alloys, these cylinders can withstand steep temperature gradients, high internal pressures and dynamic loads with reduced stress concentrations. Thermal stresses arise when non-uniform temperature fields induce differential expansion, while mechanical stresses develop under internal or external pressure, centrifugal loads and applied traction. The interplay of these stresses is governed by the gradient profile, geometry and boundary conditions.

Analytical, semi-analytical and numerical approaches are routinely applied to predict stress distributions. Power-law and exponential grading functions are common, and higher-order shear deformation theories capture transverse shear effects in thick shells. Finite element modelling enables complex loading scenarios, including asymmetric thermal fields and defects, and supports the optimisation of gradient indices to minimise peak stresses. Recent efforts have extended conventional one-dimensional grading to two-dimensional schemes, improving load alleviation under combined thermo-mechanical actions.

Beyond elastic analyses, studies of elasto-plastic behaviour and time-dependent creep under high temperatures have highlighted the importance of long-term durability. Secondary creep models and homogenisation schemes inform design codes for pressure vessels and rotating machinery operating in harsh environments. Manufacturing considerations, such as material uncertainties and layer discretisation, further influence predictive accuracy and guide quality control in advanced fabrication routes like additive manufacturing and thermal spraying.

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One study employed a finite element method to examine thermo-mechanical stresses in a hollow FGM cylinder subjected to varied temperature profiles and material inhomogeneity. Power-law gradation of elastic and thermal properties was shown to control radial and circumferential stresses, with steeper gradients reducing peak values under uniform and non-uniform heating. The work underscored the sensitivity of stress distributions to both temperature boundary conditions and gradient index, offering guidance for thermal management in energy systems.

Advances in two-dimensional grading were demonstrated through a comparison of radially and tangentially graded cylinders under asymmetric mechanical and thermal loads. The 2D-FGM scheme achieved up to a 63% reduction in tangential stress and a 61% drop in axial stress compared to conventional radial gradation alone. This approach permits strategic tailoring of material functions to address complex load patterns encountered in aerospace and automotive components.

Long-term performance under high temperature and rotational loading was addressed by a secondary creep analysis of a rotating FGM cylinder with exponential, linear and quadratic reinforcement profiles. Closed-form solutions for steady-state creep stresses and strain rates revealed that exponential gradation offered superior creep resistance in both radial and tangential directions. The findings support the design of turbine casings and boiler tubes where sustained loads at elevated temperatures govern service life.

Thermal and Mechanical Stresses in Functionally Graded Cylindrical Structures publication trend

The graph below shows the total number of articles in thermal and mechanical stresses in functionally graded cylindrical structures across all publications each year (not limited to Nature Index journals).

Technical terms

Functionally Graded Material (FGM): A composite whose material properties vary continuously through one or more dimensions to achieve spatially tailored performance.

Thermal stress: Stress induced by restrained thermal expansion or contraction when a structure experiences temperature gradients.

Hoop stress: Circumferential stress acting tangentially around the circumference of a cylindrical shell under internal or external pressure.

Gradient index: Parameter defining the rate of change of material properties across the thickness of an FGM.

Finite Element Method (FEM): A numerical technique for solving field problems by discretising a domain into smaller elements and approximating governing equations.

Secondary creep: The stage of creep deformation characterised by an approximately constant strain rate under sustained high temperature and stress.

References

1. Finite element method for stress and strain analysis of FGM hollow cylinder under effect of temperature profiles and inhomogeneity parameter. Nonlinear Engineering (2021).
2. Thermoelastic stresses alleviation for two-dimensional functionally graded cylinders under asymmetric loading. Journal of Thermal Stresses (2022).
3. Secondary Creep Analysis of FG Rotating Cylinder with Exponential, Linear and Quadratic Volume Reinforcement. Materials (2022).
4. Thermo-Elastic Analysis of Clamped-Clamped Thick FGM Cylinders by Using Third-Order Shear Deformation Theory. Latin American Journal of Solids and Structures (2016).
5. Numerical analysis of the elastic-plastic behavior of a tubular structure in FGM under pressure and defect presence. Fracture and Structural Integrity (2021).
6. Effects of parameter uncertainties on the forecasted behavior of thermomechanically loaded thick-walled functionally graded spherical structures. Acta Mechanica (2022).