Thermomechanical Buckling Analysis of the E&P-FGM Beams Integrated by Nanocomposite Supports Immersed in a Hygrothermal Environment

Due to the widespread use of sandwich structures in many industries and the importance of understanding their mechanical behavior, this paper studies the thermomechanical buckling behavior of sandwich beams with a functionally graded material (FGM) middle layer and two composite external layers. Both composite skins are made of Poly(methyl methacrylate) (PMMA) reinforced by carbon-nano-tubes (CNTs). The properties of the FGM core are predicted through an exponential-law and power-law theory (E&P), whereas an Eshelby–Mori–Tanaka (EMT) formulation is applied to capture the mechanical properties of the external layers. Moreover, different high-order displacement fields are combined with a virtual displacement approach to derive the governing equations of the problem, here solved analytically based on a Navier-type approximation. A parametric study is performed to check for the impact of different core materials and CNT concentrations inside the PMMA on the overall response of beams resting on a Pasternak substrate and subjected to a hygrothermal loading. This means that the sensitivity analysis accounts for different displacement fields, hygrothermal environments, and FGM theories, as a novel aspect of the present work. Our results could be replicated in a computational sense, and could be useful for design purposes in aerospace industries to increase the tolerance of target productions, such as aircraft bodies.

Theoretical Analysis and Semi-Analytical Formulation for Efficient Thermal-Hydraulic-Mechanical Reservoir Simulation

The research of multiphysical thermal-hydraulic-mechanical (THM) simulation has achieved significant progress in the past decade. Currently, two general approaches for poromechanical simulation co-exist in the reservoir simulation community, namely the stress approach with stress as the primary variable for the mechanical governing equations and the displacement approach with displacement as the primary variable. In this work, we aim to provide a theoretical foundation and a practical semi-analytical solution for the stress approach based on the Navier-Beltrami-Michell Equations. Moreover, we will clarify the relationship (and equivalence) between the two approaches. We have firstly proven the existence and uniqueness of the stress solution of Navier-Beltrami-Michell equation with given pressure and temperature field. Moreover, we have demonstrated the equivalence of the stress formulation to the displacement formulation. Based on Fourier's expansion, we have developed a general semi-analytical solution for thermal-hydraulic-mechanical process. The semi-analytical solution takes the pressure solution from the hydraulic simulation module (or a commercial reservoir simulator) and directly predicts the stress tensor of the multiphysical system. As such, the solution can be programmed fully coupled with the hydraulic simulation module to predict the stress field with varying pressure and temperature of homogeneous poroelastic rocks under given stress boundary conditions. From the work above, we have laid a theoretical foundation for the stress approach. The derived semi-analytical solution of the stress field shows excellent accuracy. The solution has been used to predict the transient stress field of a dual-porosity system during primary depletion. This paper is arguably the first trial to clarify the relationship between the stress approach and the displacement approach. Moreover, the derived semi-analytical solution provides a convenient yet precise way to obtain the stress field without time-consuming numerical simulation.

Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.

A Zonal Displacement Approach via Grid Point Weighting in Building Generalization

When generalizing a group of objects, displacement is an essential operation to resolve the conflicts arising between them due to enlargement of their symbol sizes and reduction of available map space. Although there are many displacement methods, most of them are rather complicated. Therefore, more practical methods are still needed. In this article, a new building displacement approach is proposed. For this purpose, buildings are grouped and zones are created for them in the blocks via Voronoi tessellation and buffering. Linear patterns are then detected through buffer analyses and the respective zones are narrowed to be able to preserve these patterns. After all the buildings are displaced inside their zones, grid points are generated and then weighted through kernel density estimation and buffer analyses to find suitable locations. Accordingly, the buildings are displaced toward the computed locations iteratively. The proposed approach directly enforces minimum distance and positional accuracy constraints while several indirect mechanisms are used for preserving spatial patterns and relationships. For the quality evaluation of the displacement, the angle, length and shape comparison measures are introduced, computed based on the (Delaunay) triangles or the azimuth comparison measure of the connection lines, generated for the buildings. The quality evaluation criteria are yielded according to the visual assessment of the displacement quality and the quantitative analysis of the measures. The findings demonstrate that the proposed approach is quite effective and practical for zonal building displacement.