• Journal of the Korea institute for structural maintenance and inspection
• /
• v.22 no.5
• /
• pp.13-22
• /
• 2018

In this study, a governing differential equation for the bending problem of orthotropic rectangular plate is drived. It's exact solution for various boundary conditions is presented. This solution follows traditional method like Navier's solution or Levy's solution that transforms the governing differential equation into an algebraic equation by using trigonometric series. To obtain a solution by Levy's method, it is required that two opposite edges of the plate be simply supported. And the boundary conditions, for which the Navier's method is applicable, are simply supported edge at all edges. In this study, it overcomes the limitations of the previous Navier's and Levy's methods.This solution is applicable for any combination of boundary conditions with simply supported edge and clamped edge in x, y direction. The plate could be subjected to uniform, partially uniform, and line loads. The advantage of the solution is that it is the exact solution as well as it overcomes the limitations of the previous Navier's and Levy's methods. Calculations are presented for orthotropic plates with nonsymmetric boundary conditions. Comparisons between the result of this paper and the result of Navier, Levy and Szilard solutions are made for the isotropic plates. The deflections were in excellent agreement.

• Structural Engineering and Mechanics
• /
• v.52 no.2
• /
• pp.351-368
• /
• 2014

This study presents a hunting search based optimum design algorithm for engineering optimization problems. Hunting search algorithm is an optimum design method inspired by group hunting of animals such as wolves, lions, and dolphins. Each of these hunters employs hunting in a different way. However, they are common in that all of them search for a prey in a group. Hunters encircle the prey and the ring of siege is tightened gradually until it is caught. Hunting search algorithm is employed for the automation of optimum design process, during which the design variables are selected for the minimum objective function value controlled by the design restrictions. Three different examples, namely welded beam, cellular beam and moment resisting steel frame are selected as numerical design problems and solved for the optimum solution. Each example differs in the following ways: Unlike welded beam design problem having continuous design variables, steel frame and cellular beam design problems include discrete design variables. Moreover, while the cellular beam is designed under the provisions of BS 5960, LRFD-AISC (Load and Resistant Factor Design-American Institute of Steel Construction) is considered for the formulation of moment resisting steel frame. Levy Flights is adapted to the simple hunting search algorithm for better search. For comparison, same design examples are also solved by using some other well-known search methods in the literature. Results reveal that hunting search shows good performance in finding optimum solutions for each design problem.

• Computational Structural Engineering : An International Journal
• /
• v.1 no.1
• /
• pp.49-57
• /
• 2001

This paper presents exact solutions for the modal stress-resultant distributions for vibrating rectangular Mindlin plates involving two opposite sides simply supported while the other two sides free. These exact stress-resultants of vibrating plates with free edges, hitherto unavailable, are very important because they serve as benchmark solutions for checking numerical solutions and methods. Using the exact solutions of a square plate, this paper highlights the problem of determining accurate stress-resultants, especially the transverse shear forces and twisting moments in thin plates, when employing the widely used numerical methods such as the Ritz method and the finite element method. Thus, this study shows that there is a need for researchers to develop refinements to the Ritz method and the finite element method for determining very accurate stress-resultants in vibrating plates with free edges.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.863-875
• /
• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• Steel and Composite Structures
• /
• v.28 no.6
• /
• pp.655-670
• /
• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.18 no.3
• /
• pp.225-240
• /
• 2006

In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

• Structural Engineering and Mechanics
• /
• v.7 no.1
• /
• pp.81-94
• /
• 1999

The dynamic analysis of trusses using the finite element method tends to overlook the effect of local member dynamic behavior on the overall response of the complete structure. This is due to the fact that the lateral inertias of the members are omitted from the global inertia terms in the structure mass matrix. In this paper a condensed dynamic stiffness matrix is formulated and used to calculate the exact dynamic properties of trusses without the need to increase the model size. In the examples the limitations of current solutions are presented together with the exact results obtained from the proposed method.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.17 no.1
• /
• pp.80-86
• /
• 2009

Main bearing cap is one of the essential structural elements in internal combustion engine. Main bearing cap guides and holds the crankshaft, withstanding the full combustion and inertia loads of the engine. A seamless design methodology using FEA has been proposed to produce a reliable design of main bearing cap. A Levy's thick cylinder model was applied to calculate the contact pressure between bearing shell and housing bore. A calculated contact pressure at housing bore is within the allowed limit comparing with that from bearing shell model. An adequate FEA model was suggested to obtain reliable solutions for the durability of main bearing cap. 3D global model consists of engine bulkhead, main bearing cap, and bolts. Sub-model consisting of cap and part of bolts is used to get detailed solution of main bearing cap. A very careful contact modeling practice is needed to resolve the convergence problems frequently encountering during combined geometric and material non-linear problems. A proposed methodology has been applied to the main bearing cap model successfully and obtained reliable stress results and fatigue safety factors.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.16 no.9
• /
• pp.2846-2866
• /
• 2022

Caenorhabditis elegans exhibits sophisticated chemotaxis behavior through two parallel strategies, klinokinesis and klinotaxis, executed entirely by a small nervous circuit. It is therefore suitable for inspiring fast and energy-efficient solutions for autonomous navigation. As a random search strategy, the Lévy walk is optimal for diverse animals when foraging without external chemical cues. In this study, by combining these biological strategies for the first time, we propose a spiking neural network model for search and contour tracking of specific concentrations of environmental variables. Specifically, we first design a klinotaxis module using spiking neurons. This module works in conjunction with a klinokinesis module, allowing rapid searches for the concentration setpoint and subsequent contour tracking with small deviations. Second, we build a random exploration module. It generates a Lévy walk in the absence of concentration gradients, increasing the chance of encountering gradients. Third, considering local extrema traps, we develop a termination module combined with an escape module to initiate or terminate the escape in a timely manner. Experimental results demonstrate that the proposed model integrating these modules can switch strategies autonomously according to the information from a single sensor and control steering through output spikes, enabling the model worm to efficiently navigate across various scenarios.

• Journal of Pharmaceutical Investigation
• /
• v.6 no.3
• /
• pp.58-69
• /
• 1976

It is well established that dissolution is freruently the rate limiting step in the gastrointestinal absorpton of a drug from a solid dosage from. The relationship between the dissolution rate and absorption is particularly distinct when considering drugs of low solubility. Consequently, numerous attempts have been made to modify the dissolution characteristics of poorly water soluble drugs. Since dissolution rate is directly proportional to surface area, one may increase the rate by decreasing the particle size of the drug. Levy has considered a number of methods by which a drug may be presented to the GI fludids in finely divided from. The direct method is the utilization of microcrystalline or micronized particles. A second method involves the administration of solutions from which, upon dilution with gastric fluids, the dissolved drug will precipitate in the form of very fine particles. A more unique way of obtaining microcrystalline dispersions of a drug has been ercently suggested by Sekiguchi et al. They have first proposed the formation of a eutectic mixture of a poorly water soruble drug with a physiologically inert, easily soluble carrier. When such systems are exposed to water or GI fluids, the soluble carrier will dissolve rapidly and the finely dispersed drug particles will then be released. It has been suggested by Shefter and Higuchi that the formation of crystalline solvate could be a powerful tool in affecting rapid disslution of highly insoluble substances. Goldberg et al. have noted that the formation of solid solution could reduce the particle size to a minimum and increase the dissolution rate as well as the solubility of the durgs. It has also been shown that the rates of solution of drugs were appreciably increased by coprectipitating the drug with soluble polymers. The increase was found to be sensitive to the method of preparation, the molecular weight of polymer and the particular ratio of drugs to polymer. Although several investigations have demontrated that the solubility and/or dissolution rates of drugs can be increased in this manner, little information is available in the literature related to the in vivo absorption pattern of drugs orally administered as PVP coprecipitates. Recently, however, it was demonstrated that both the rate and extent of absorption of the insoluble drug could be markedly enhanced when orally administered to rats in the form of a coprecipitate with PVP. The purpose of the present investigation was to ascertain the general appility of soluble polymer coprectation technique as a method for enhancing the in vitro dissolution rate of hydrophobic indomethacin. To accomplish this aim, the dissolution characteristics of pure indomethacin, indomethcin-polymer physical mixtures and indomethacin-polymer coprecipitates were quantitatively studied by comparing their relative dissolution rates. The solubility and dissolution behavior of these systems were also examined.