Abstract:Elastic bulk wave characteristics of doubly curved nanoshell made of functionally graded (FG) anisotropic material are studied. The effective properties of FG anisotropic material vary along the thickness direction. A higher-order shear deformation shell theory and the Bi-Helmholtz nonlocal strain gradient theory are, respectively, utilized to model the nanoshell as a continuum model and predicting the size-dependent behavior. The Hamiltonian principle is adopted to obtain the governing equations of wave motio… Show more
“…According to the research literature of relevant shell structures [31][32][33][34][35], assuming that the expansion cone is expanded uniformly and is considered as a quasi-static process, the force on the expandable cone is shown in Figure 3. e geometric parameters in Figure 3 include the initial inner diameter r 0 , the initial wall thickness t 0 , the inner diameter after expansion r 1 , and the wall thickness after expansion t 1 .…”
Section: Mechanical Equilibrium Equations Of the Expandable Processmentioning
The expansion experiment of the expansion liner hanger is a one-time failure process, so in order to save cost, the finite element technology needs to be used to simulate the expansion experiment. Obtaining the mechanical parameters of the expansion liner hanger can effectively optimize the size of the expansion liner hanger structure and guide the expansion completion. Firstly, main structure and principle of expandable liner hanger were introduced. Secondly, mechanical equilibrium equations of the expandable process were established to obtain pressure of the expandable fluid, and pressure of the expandable fluid is obtained. Thirdly, finite element (FE) simulation mechanical model of the expansion of the Ø244.5 mm × Ø177.8 mm expandable liner hanger was established to analyze the hang mechanism and the change rule of mechanical parameters during the expansion. The FE results have shown that radial displacement and residual stress of the inner wall of hanger varied in 5 cycles, and the expansion ratio of the expandable tube was 7.4% during the expansion. The expansion force did not change stably but gradually increased in stages. And the hydraulic pressure required for the expandable cone to continuously move down was 18 MPa. According to the contact stress generated on five rubber cylinders and the contact stress generated on five metal collars, the total hang force has been calculated, which exceeds 1000 kN and meets the design requirements. Lastly, the expansion test results have shown that expansion pressure was 19 MPa, and the expansion rate was 7.1%. The mechanical analysis results of the expandable liner hanger were in good agreement with the experiment results in this study, which provide important mechanical parameters for well completion with expandable liner hanger.
“…According to the research literature of relevant shell structures [31][32][33][34][35], assuming that the expansion cone is expanded uniformly and is considered as a quasi-static process, the force on the expandable cone is shown in Figure 3. e geometric parameters in Figure 3 include the initial inner diameter r 0 , the initial wall thickness t 0 , the inner diameter after expansion r 1 , and the wall thickness after expansion t 1 .…”
Section: Mechanical Equilibrium Equations Of the Expandable Processmentioning
The expansion experiment of the expansion liner hanger is a one-time failure process, so in order to save cost, the finite element technology needs to be used to simulate the expansion experiment. Obtaining the mechanical parameters of the expansion liner hanger can effectively optimize the size of the expansion liner hanger structure and guide the expansion completion. Firstly, main structure and principle of expandable liner hanger were introduced. Secondly, mechanical equilibrium equations of the expandable process were established to obtain pressure of the expandable fluid, and pressure of the expandable fluid is obtained. Thirdly, finite element (FE) simulation mechanical model of the expansion of the Ø244.5 mm × Ø177.8 mm expandable liner hanger was established to analyze the hang mechanism and the change rule of mechanical parameters during the expansion. The FE results have shown that radial displacement and residual stress of the inner wall of hanger varied in 5 cycles, and the expansion ratio of the expandable tube was 7.4% during the expansion. The expansion force did not change stably but gradually increased in stages. And the hydraulic pressure required for the expandable cone to continuously move down was 18 MPa. According to the contact stress generated on five rubber cylinders and the contact stress generated on five metal collars, the total hang force has been calculated, which exceeds 1000 kN and meets the design requirements. Lastly, the expansion test results have shown that expansion pressure was 19 MPa, and the expansion rate was 7.1%. The mechanical analysis results of the expandable liner hanger were in good agreement with the experiment results in this study, which provide important mechanical parameters for well completion with expandable liner hanger.
“…Khordad et al [36] have investigated the effects of the Rashba spin-orbit interaction and applied magnetic field on thermodynamic properties of a quasi-one-dimensional quantum wire at low temperatures. There are also some studies investigating thermal, and magnetic effects on other type of structures [37][38][39][40][41][42][43].…”
We solve the Schrödinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give analytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, α, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties.On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.
“…Thus, based on this new model, many studies have been conducted by developing and providing nonlocal beam models for the prediction of mechanical behaviors of homogenous and nonhomogeneous nanobeams. 31–52 Zhang et al. 53 carried out a free vibration study of nonlocal Timoshenko beams made of FGMs by employing symplectic method; the influences of various parameters were presented.…”
The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.
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