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article · International Journal of Applied Mechanics

Size-Dependent Hygro-Thermal Buckling of Porous FGM Sandwich Microplates and Microbeams Using a Novel Four-Variable Shear Deformation Theory

In plain language

This study investigates the hygro-thermal buckling behaviour of porous functionally graded material sandwich microplates and microbeams. Using a modified couple stress theory, the model incorporates a material length scale parameter that accounts for size-dependent effects absent in classical elasticity models. A novel four-variable shear deformation theory with a new shape function is applied to derive stability equations through the principle of virtual work. The analysed sandwich structures feature an isotropic, homogeneous core between two porous functionally graded face layers whose properties vary along their thickness. Analytical solutions evaluate thermal buckling under uniform, linear, and non-linear distributions of temperature and moisture concentration. Comparative analyses against existing literature validate the formulations, while parametric evaluations clarify how factors such as moisture concentration, length scale parameters, power-law exponents, and core thickness influence structural stability.

Key takeaways

  • A four-variable shear deformation theory combined with modified couple stress theory captures small-scale effects on microplates and microbeams.
  • The analytical model accounts for thermal buckling under uniform, linear, and non-linear distributions of heat and moisture.
  • The microstructures consist of a homogeneous, isotropic core enclosed by porous functionally graded material face layers.
  • Structural stability is significantly influenced by moisture levels, material length scale parameters, core thickness, and the power-law exponent.

Why it matters

Microscopic mechanical components operating in harsh environments can fail when exposed to combined heat and humidity. Understanding how size effects and porosity influence structural stability allows engineers to better predict when small-scale sandwich structures will buckle. This theoretical framework provides accurate analytical tools to evaluate advanced composite microbeams and microplates under realistic operational conditions.

Commercialisation angle

This work is early-stage theoretical research focused on mathematical modelling and analytical solutions. While it could eventually assist microelectromechanical systems designers and composite material engineers in assessing heat and moisture resilience, the abstract does not indicate any prototype testing, experimental validation, or direct application pathway.

AI-generated from the published abstract. Always read the original work before citing.

Abstract

Based on a new shear deformation theory and the modified couple stress theory, in this paper, the hygro-thermal buckling of porous FGM sandwich microplates and microbeams is investigated. Unlike the classical elasticity theory, the present model involves a material length scale parameter, and, thereby, can capture the small size effect. The four-variable shear deformation theory with a new shape function is utilized to derive the governing stability equations for the microplates and microbeams from the principle of virtual work. The present microstructures are composed of three layers and subjected to hygro-thermal conditions. The core is assumed to be fully homogeneous and isotropic material. While, the face layers are made from porous functionally graded materials that vary only in the thickness direction. The governing equations are solved analytically to obtain the thermal buckling of FGM sandwich microplates and microbeams under humidity effects. The temperature rise and moisture concentration are graded uniformly, linearly or nonlinearly through the thickness. Comparison studies are made between the present results and those available in the literature to check the validity of the obtained formulations and results. Moreover, the effects played by the length scale parameter, power-law exponent, moisture concentration, core thickness and other parameters on the thermal buckling of microplates and microbeams are all investigated.

Research topics

  • Nonlocal and gradient elasticity in micro/nano structures
  • Composite Structure Analysis and Optimization
  • Numerical methods in engineering

Read the original research

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DOI: 10.1142/s1758825120500179

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