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Heat Transfer Distributed Parameter Systems
Published in Nayef Ghasem, Modeling and Simulation of Chemical Process Systems, 2018
An important case is a spherical shell, a geometry often encountered in situations where fluids are pumped and heat is transferred. The inner and outer temperatures are T1 and T2 at r1 and r2, respectively. Show that the temperature distribution in the shell of the sphere is: T=T1−(T1−T2)1−(r1/r)1−(r1/r2)
Nonlinear axisymmetric dynamic buckling of functionally graded graphene reinforced porous nanocomposite spherical caps
Published in Mechanics of Advanced Materials and Structures, 2021
M. Haboussi, A. Sankar, M. Ganapathi
It can be opined from the review of literature on graphene reinforced structures that major investigations are made in the absence of porosity in the matrix or metal foam and considering fairly thin straight beams and plates, and very few instances of work on cylindrical shells. Among various shell structures, spherical shell structure has some special features such as high strength as compared to the cylindrical shell and has wide applications in the area of aerospace and mechanical engineering. Design of such structural members considering only static loading may not withstand dynamic loading situations. Therefore, it is worthwhile investigating the structural behavior of spherical shells made of functionally graded nanocomposite reinforced by graphene under dynamic conditions. The most significant contributions related to the spherical shell dynamics are briefly mentioned in the next paragraph.
Elastic–plastic buckling of externally pressurised hemispherical heads
Published in Ships and Offshore Structures, 2019
Y. Zhu, Y. Zhang, X. Zhao, J. Zhang, X. Xu
Research on the buckling of spherical shells is generally based on these previous three theories. A hemispherical shell is axisymmetric, similar to a spherical shell, and is a part of an entire spherical shell. Under deep-sea pressure loading conditions, hemispherical shells and full spherical shells are subjected to torque-free axially symmetrical loads. Existing theoretical calculation methods for buckling instability of external hemispherical heads are based on the instability of spherical shells. Table 3 lists the theoretical predictions of buckling loads of test heads #1–5, for which the average wall thickness and the average radius (Table 2) were used. In addition, average Young’s modulus and average Poisson’s ratio (Table 1) were used. In Table 3, the buckling load calculated using the small deformation theory is the greatest, and the buckling load calculated using energy analysis is the least. The maximum values were approximately 3.35 times the minimum values. The difference in the buckling loads calculated using the large deformation theory and the energy analysis method was approximately 1.7%.
Simple first-order shear deformation theory for free vibration of FGP-GPLRC spherical shell segments
Published in Mechanics of Advanced Materials and Structures, 2023
Van-Loi Nguyen, Suchart Limkatanyu, Huu-Tai Thai, Jaroon Rungamornrat
Spherical shell segments find numerous applications in engineering, including pressure vessels, cooling towers, water tanks, rotor systems, and drive shafts. It is crucial to have an understanding of the vibrational behavior of these structures to carry out design, construction, and operation tasks. Many studies on the free vibration of spherical shell segments have been conducted in recent years. For instance, Su et al. [51] conducted the free-vibration analysis of spherical shell segments made of FGM under general boundary conditions using the FSDT together with the Ritz method. Xie et al. [52] utilized the FSDT and the Haar Wavelet Discretization (HWD) method to examine the free vibrational behavior of spherical and parabolic FGM shells with different boundary conditions. Xie et al. [53] also utilized a semi-analytical solution method to determine the free-vibration response of spherical shell segments with a discontinuity in the shell’s thickness and under elastic restraints, where the shell structure was divided into narrow strips in a meridional direction. Wang et al. [54] applied Rayleigh-Ritz method together with the FSDT to study the free vibration of spherical shells made of composite which is reinforced by carbon nanotubes (CNTs). Recently, Li et al. [55] utilized the FSDT, artificial spring technique, and the Ritz method with Jacobi polynomials in the meridional direction to present the free vibration analysis of spherical shell segments made of FGP material. Hu et al. [56] investigated the free vibration of an annular spherical shell using the FSDT theory and the Ritz method, considering various classical and non-classical boundaries. Kim et al. [57] utilized the FSDT theory and the HWD method to present the free vibration characteristics of laminated composite spherical shells. Notably, different authors [58, 59] recently investigated and studied on free vibrations of stepped FGM spherical shells. It is evident that shell structures made of FGMs and FGP material with GPL reinforcement have been the main interests during many past years. Also, the Rayleigh-Ritz method is widely and efficiently utilized for various structures, such as plates [60, 61] and shell structures [54, 62, 63].