• Structural Engineering and Mechanics
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• v.22 no.5
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• pp.631-645
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• 2006

Buckling capacity of compression members may change due to inadvertent changes in the member section dimensions or material properties. This may be the result of repair, modification of section properties or degradation of the material properties. In some occasions, enhancement of buckling capacity of compression members may be achieved through splicing of plates or utilization of composite materials. It is very important for a designer to predict the buckling resistance of the compression member and the important parameters that affect its buckling strength once changes in section and/or material properties took place. This paper presents an analytical approach for determining the buckling capacity of a compression member whose geometric and/or material properties has been altered resulting in a multi-step non-uniform section. This analytical solution accommodates the changes and modifications to the material and/or section properties of the compression member due to the factors mentioned. The analytical solution provides adequate information and a methodology that is useful during the design stage as well as the repair stage of compression members. Three case studies are presented to show that the proposed analytical solution is an efficient method for predicting the buckling strength of compression members that their section and/or material properties have been altered due to splicing, coping, notching, ducting and corrosion.

• Geomechanics and Engineering
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• v.8 no.2
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• pp.237-255
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• 2015

From the related engineering principles, analytical solutions for horizontal crack initiation and propagation on a coal panel floor-underlying strata interface due to coal panel excavation are derived in this paper. Two important concepts, namely the critical panel width of horizontal crack initiation on the panel floor-underlying strata interface and the critical panel width of vertical fracture (crack) initiation in the panel floor, have been presented. The resulting analytical solution indicates that: (1) the first criterion can be used to express the condition under which horizontal plane cracks (on the panel floor-underlying strata interface or in the panel floor because of delamination) due to the mining induced vertical stress will initiate and propagate; (2) the second criterion can be used to express the condition under which vertical plane cracks (in the panel floor) due to the mining induced horizontal stress will initiate and propagate; (3) this orthogonal set of horizontal and vertical plane cracks, once formed, will provide the necessary weak network for the flow of gas to inrush into the panel. Two characteristic equations are given to quantitatively estimate both the critical panel width of vertical fracture initiation in the panel floor and the critical panel width of horizontal crack initiation on the interface between the panel floor and its underlying strata. The significance of this study is to provide not only some theoretical bases for understanding the fundamental mechanism of a longwall floor gas inrush problem but also a benchmark solution for verifying any numerical methods that are used to deal with this kind of gas inrush problem.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.335-348
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• 2018

The structural dynamics (SD) behavior of Elastic Flapping Wings (EFWs) is investigated analytically as a novel approach in EFWs analysis. In this regard an analytical SD solution of EFW undergoing a prescribed rigid body motion is initially derived, where the governing equations are expressed in modal space. The inertial forces are also analytically computed utilizing the actuator induced acceleration effects on the wing structure, while due to importance of analytical solution the linearity assumption is also considered. The formulated initial-value problem is solved analytically to study the EFW structural responses, where the effect of structure-actuator frequency ratio, structure-flapping frequency ratio as well as the structure damping ratio on the EFW pick amplitude is analyzed. A case study is also simulated in which the wing is modeled as an elastic beam with shell elements undergoing a prescribed sinusoidal motion. The corresponding EFW transient and steady response in on-off servo behavior is investigated. This study provides a conceptual understanding for the overall EFW SD behavior in the presence of inertial forces plus the servo dynamics effects. In addition to the substantial analytical results, the study paves a new mathematical way to better understanding the complex role of SD in dynamic EFWs behavior. Specifically, similar mathematical formulations can be carried out to investigate the effect of aerodynamics and/or gravity.

• Coupled systems mechanics
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• v.11 no.2
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• pp.151-166
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• 2022

Peltier cells have low efficiency, but they are becoming attractive alternatives for affordable and environmentally clean cooling. In this line, the current article develops closed-form and semianalytical solutions to improve the temperature distribution of Bi₂Te₃ thermoelements. From the distribution, the main objective of the current work-the optimal electric intensity to maximize cooling-is inferred. The general one-dimensional differential coupled equation is integrated for linear and quadratic geometry of thermoelements, under temperature constant properties. For a general shape, a piece-wise solution based on heat flux continuity among virtual layers gives accurate analytical solutions. For variable properties, another piece-wise solution is developed but solved iteratively. Taking advantage of the formulae, the optimal intensity is directly derived with a minimal computational cost; its value will be of utility for more advanced designs. Finally, a parametric study including straight, two linear, barrel, hourglass and vase geometries is presented, drawing conclusions on how the shape of the thermoelement affects the coupled phenomena. A specially developed coupled and non-linear finite element research code is run taking into account all the materials of the cell and using symmetries and repetitions. These accurate results are used to validate the analytical ones.

• Journal of Korean Tunnelling and Underground Space Association
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• v.11 no.4
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• pp.427-435
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• 2009

This study deals with the analytical solution for soil-lining interaction in a deep and circular tunnel. Simple closed-form analytical solutions for thrust and moment in the circular tunnel lining due to static and seismic loadings are developed by considering the relations between displacement and interaction forces at the soil-lining interface. The interaction effect at the soil-lining interface is considered with new ratios (the normal and shear stiffness ratios). The effects of the ratios on the normalized thrust and the normalized moment are investigated.

• Geomechanics and Engineering
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• v.37 no.1
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• pp.1-8
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• 2024

Buckling failure is one of the classical types of catastrophic landslides developing on inclination-paralleled rock slopes, which is mainly governed by its self-weight, earthquake and ground water. However, nearly none of the existing studies fully consider the influence of slope self-weight, earthquake and ground water on the mechanical model of buckling failure. In this paper, based on energy equilibrium principle and elastoplastic slab theory, a thorough mechanical analysis on bucking slopes has been carried out. Furthermore, an analytical solution for slip bucking failure of rock slopes has been proposed, which fully considers the effect of slope self-weight, seismic force and hydrostatic pressure. Finally, the methodology is used to conduct comparative analysis with other analytical solutions for three practical buckling studies. The results show that the proposed approach is capable of providing a more accurate and reasonable evaluation for stability of rock slopes with potential buckling failure.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.657-661
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• 2017

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn't need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.9
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• pp.878-887
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• 2001

Experimental investigation has been carried out to examine the operating characteristics of a bubble pump for diffusion absorption refrigerator. The effects of heat input and delivery height on generation rate of refrigerant vapor and circulation rate of solution have been investigated. as a result heat input and delivery height increase, circulation rate of solution increases. And the smaller the tube diameter, the larger the circulation rate of solution. Pumping ratio increases to a critical point and then decrease with the increase of heat input, and it increases with the increase in delivery height. In this paper, Marcus's analytical theory was also examined. It was found that the Marcus\`s analytical theory of a bubble pump was not appropriate for a bubble pump using ammonia aqueous solution as a working fluid.

• Journal of Magnetics
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• v.20 no.1
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• pp.79-85
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• 2015

This paper presents a comparative study of a Tubular Linear Machine (TLM) with an Axially Magnetized Single-sided Permanent Magnet (AMSPM) and an Axially Magnetized Double-sided Permanent Magnet (AMDPM) based on analytical field calculations. Using a two-dimensional (2-D) polar coordinate system and a magnetic vector potential, analytical solutions for the flux density produced by the stator windings are derived. This technique is significant for the design and control implementation of electromagnetic machines. The field solution is obtained by solving Maxwell's equations in the simplified boundary value problem consisting of the air gap and coil. These analytical solutions are then used to estimate the self and mutual inductances. Two different types of machine are used to verify the validity of these model simplifications, and the analytical results are compared to results obtained using the finite element method (FEM) and experimental measurement.

• Journal of Korean Society of Steel Construction
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• v.22 no.3
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• pp.241-251
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• 2010

This paper presents the development of a new analytical solution to the governing differential equation for isotropic annular sector plates subjected to uniform loading in a three-dimensional polar coordinate system. The 4th order governing partial differential equation (PDE) was converted to an ordinary differential equation (ODE) by assuming the Levy-type series solution form and the subsequent mathematical operations. Finally, a series-type solution was assembled with homogeneous and nonhomogeneous solution parts after operating real values and complex conjugates derived from the characteristic equation. To demonstrate the convergence rate and the accuracy of the featured method, several examples with various sector angles were selected and solved. The deflections and internal moments in the example annular sector plates that were obtained from the proposed solution were compared with those obtained from other analytical studies and numerical analyses using the finite element analysis package program, ABAQUS. Very good agreement with the results of other analytical and numerical methodologies was shown.