Shear Deformation Theories for Functionally Graded Structures

Functionally graded structures are engineered composites whose material properties vary smoothly through their thickness to optimise performance under mechanical, thermal and environmental loads. Classical plate and beam theories, which neglect transverse shear deformation, often yield significant errors in thick or highly heterogeneous components. First-order shear deformation theories introduced linear transverse shear strains at the expense of empirical correction factors. Higher-order shear deformation theories (HSDT) further enrich the displacement field with nonlinear terms that satisfy traction-free boundary conditions and eliminate shear correction factors. Quasi-three-dimensional approaches additionally account for thickness stretching, improving predictions of deflection, stress and natural frequencies in functionally graded beams, plates and sandwich panels. Recent advancements incorporate modified strain gradient theories to capture micro-scale size effects and novel shape functions to enhance convergence and accuracy. These refined models underpin the reliable design of aerospace panels, micro-electromechanical sensors, smart actuators and civil engineering elements under complex thermo-hygro-magnetic loading.

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Research from all publishers

Recent studies have advanced refined shear deformation models for functionally graded structures under multi-field loading. One investigation applied a modified strain gradient theory coupled with first-order shear deformation and the differential quadrature method to analyse bending, buckling and vibration of microcomposite circular-annular sandwich plates under hydro-thermo-magneto-mechanical conditions. Results highlighted the influence of material length scales, facesheet-to-core thickness ratios and environmental effects on deflection, critical load and natural frequencies, offering guidance for micro-device design. Another effort introduced a quasi-3D sinusoidal shear and normal deformation theory for hygro-thermo-mechanical bending of functionally graded piezoelectric plates. Exact closed-form solutions elucidated how moisture, thermal gradients and piezoelectric coupling modify mechanical displacements, electric potential and stress fields, informing adaptive sensing technologies. A further contribution proposed a higher-order shear deformation theory for functionally graded beams, incorporating a new displacement field with hyperbolic shear stress distribution. Free of shear correction factors, this approach accurately predicted bending, buckling and vibration responses and demonstrated the critical role of material gradient profiles and thickness stretching when compared with classical and three-dimensional references.

Shear Deformation Theories for Functionally Graded Structures publication trend

The graph below shows the total number of articles in shear deformation theories for functionally graded structures across all publications each year (not limited to Nature Index journals).

Technical terms

Functionally Graded Material (FGM): Composite with continuous variation in composition and properties across its volume.

First-Order Shear Deformation Theory (FSDT): Beam or plate theory accounting for constant transverse shear strain, requiring empirical correction factors.

Higher-Order Shear Deformation Theory (HSDT): Model including higher-order terms in displacement field to satisfy shear boundary conditions without correction factors.

Quasi-3D Theory: Approximate three-dimensional formulation incorporating transverse normal deformation to capture thickness stretching.

Modified Strain Gradient Theory: Continuum approach adding higher-order strain gradients to include material length-scale effects at micro/nano dimensions.

Differential Quadrature Method (DQM): Numerical technique that approximates derivatives by weighted sums of discrete function values.

Hamilton’s Principle: Variational principle stating the actual dynamic path extremises the action, defined as the time integral of kinetic minus potential energy.

References

1. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM. International Journal of Smart and Nano Materials (2017).
2. Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory. Latin American Journal of Solids and Structures (2019).
3. Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory. Fracture and Structural Integrity (2020).
4. New Shape Function for the Bending Analysis of Functionally Graded Plate. Materials (2018).