article · Physical Mesomechanics
A higher-order shear and normal deformation theory evaluates the static behaviour of thick rectangular plates made from functionally graded porous materials. The mathematical formulation incorporates thickness stretching effects, allowing material properties to vary continuously through the plate thickness according to a specific function. Governing equations are derived using the principle of virtual displacements, leading to exact analytical solutions for stresses and displacements in simply supported plates subjected to sinusoidal loading. Numerical evaluations and validation examples demonstrate the accuracy of this quasi-3D approach in predicting bending responses. Analysis reveals that the structural field variables, specifically displacement and stress distributions, exhibit high sensitivity to changes in the porosity factor as well as the functionally graded material distribution.
Porous functionally graded materials offer adaptable mechanical characteristics, but accurately predicting their behaviour requires reliable mathematical models. Incorporating thickness stretching effects into bending analyses provides precise calculations of stress and deformation under load. This refined analytical capability allows engineers and designers to better understand how internal voids and graded material compositions alter overall structural stability and performance.
The research represents early-stage theoretical work focused on mathematical modelling and numerical validation. The analytical expressions could inform developers of structural analysis software and engineering simulation tools used to design composite components. However, the abstract provides no specific details regarding target industrial sectors, manufacturing readiness, or direct commercial application pathways.
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This paper presents a higher-order shear and normal deformation theory for the static problem of functionally graded porous thick rectangular plates. The effect of thickness stretching in the functionally graded porous plates is taken into consideration. The functionally graded porous material properties vary through the plate thickness with a specific function. The governing equations are obtained via the virtual displacement principle. The static problem is solved for a simply supported plate under a sinusoidal load. The exact expressions for displacements and stresses are obtained. The influences of the functionally graded and porosity factors on the displacements and stresses of porous plates are discussed. Some validation examples are presented to show the accuracy of the present quasi-3D theory in predicting the bending response of porous plates. The effectiveness of the present model is evaluated by numerical results that include displacements and stresses of functionally graded porous plates. The field variables of functionally graded plates are very sensitive to the variation of the porosity factor.
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DOI: 10.1134/s1029959920010051
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