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The motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the first time studying all necessary measures that increase the accuracy of the obtained results. These parameters are essential to perform a completely nonlinear analysis and consider the effects of the Earth's rotation around its axis. Unlike most modeling of nonlinear partial differential equations in applied mechanics that only considers nonlinear effects in a particular direction, the general nonlinear terms are considered in the present study, which increases the accuracy of the amount of displacement of the Earth's inner layers. Also, the fully nonlinear and dynamic differential equations are solved by a semi-analytical polynomial method which is an innovative and efficient method. Determining the amount of critical pressure at the fault location that will cause phenomena such as earthquakes is one of the useful results that can be obtained from the mathematical modeling in this research. [ABSTRACT FROM AUTHOR]

In this article, a highly efficient quasi-three-dimensional theory has been used to study the nonlinear hygro-thermo-mechanical bending analysis of a very thick functionally graded material (FGM) rotating disk in hygro-thermal environment considering the porosity as a structural defect. Two applied quasi-three-dimensional displacement fields are assumed in which the strain along the thickness ( ε z ) is not zero unlike most of the other plate theories. By considering the nonlinear strains (von Kármán's assumptions) the large deformations have also been taken into account in order to obtain more accurate results. Finally, some factors that affect the results have been studied further. [ABSTRACT FROM AUTHOR]

In this article, vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) such as armchair, chiral, and zigzag carbon nanotubes have been investigated considering the effects of surface energy and surface residual stresses. The nanotubes are embedded in the elastic substrate of the Winkler type and are also exposed to low and high-temperature environments. A new refined beam theory namely, one-variable shear deformation beam theory has been combined with Hamilton's principle to develop the governing equations of the proposed model. The size-dependent behavior of the SWCNTs is addressed by Eringen's nonlocal elasticity theory whereas the model is investigated analytically by employing Navier's technique. Also, a parametric study has been conducted to analyze the effects of various scaling parameters such as small scale parameter, temperature change, thermal environments, Winkler modulus, and length of the beam. The results are also validated with previously published articles in special cases witnessing robust agreement. [ABSTRACT FROM AUTHOR]