• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Journal of Korea Water Resources Association
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• v.36 no.3 s.134
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• pp.481-494
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• 2003

Flow through the culvert is very complex depending on the characteristics of hydraulic conditions. A design method using a monograph is normally employed due to the wide range of flow characteristics and the difficulty of calculating inlet water depth. The present study suggests the method for determining the inlet water depth of box culvert using Bernoulli's equation. By employing the explicit equation of inlet water depth, a standard design method of box culvert is developed for a wide range of flow characteristics. Explicit solution techniques are proposed to determine the width and height, slope and discharge of box culvert.

• Wind and Structures
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• v.20 no.3
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• pp.423-448
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• 2015

In this paper the unsteady fluid-structure interaction (FSI) problems with large structural displacement are solved by partitioned solution approaches in the arbitrary Lagrangian-Eulerian finite element framework. The incompressible Navier-Stokes equations are solved by the characteristic-based split (CBS) scheme. Both a rigid body and a geometrically nonlinear solid are considered as the structural models. The latter is solved by Newton-Raphson procedure. The equation governing the structural motion is advanced by Newmark-${\beta}$ method in time. The dynamic mesh is updated by using moving submesh approach that cooperates with the ortho-semi-torsional spring analogy method. A mass source term (MST) is introduced into the CBS scheme to satisfy geometric conservation law. Three partitioned coupling strategies are developed to take FSI into account, involving the explicit, implicit and semi-implicit schemes. The semi-implicit scheme is a mixture of the explicit and implicit coupling schemes due to the fluid projection splitting. In this scheme MST is renewed for interfacial elements. Fixed-point algorithm with Aitken's ${\Delta}^2$ method is carried out to couple different solvers within the implicit and semi-implicit schemes. Flow-induced vibrations of a bridge deck and a flexible cantilever behind an obstacle are analyzed to test the performance of the proposed methods. The overall numerical results agree well with the existing data, demonstrating the validity and applicability of the present approaches.

• Advances in concrete construction
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• v.7 no.3
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• pp.151-166
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• 2019

This paper introduces a new efficient analytical method, based on shear deformations obtained with 2D elasticity theory approach, to perform an explicit closed-form solution for calculation the interfacial shear and normal stresses in plated RC beam. The materials of plate, necessary for the reinforcement of the beam, are in general made with fiber reinforced polymers (Carbon or Glass) or steel. The experimental tests showed that at the ends of the plate, high shear and normal stresses are developed, consequently a debonding phenomenon at this position produce a sudden failure of the soffit plate. The interfacial stresses play a significant role in understanding this premature debonding failure of such repaired structures. In order to efficiently model the calculation of the interfacial stresses we have integrated the effect of shear deformations using the equilibrium equations of the elasticity. The approach of this method includes stress-strain and strain-displacement relationships for the adhesive and adherends. The use of the stresses continuity conditions at interfaces between the adhesive and adherents, results pair of second-order and fourth-order coupled ordinary differential equations. The analytical solution for this coupled differential equations give new explicit closed-form solution including shear deformations effects. This new solution is indented for applications of all plated beam. Finally, numerical results obtained with this method are in agreement of the existing solutions and the experimental results.

• Geotechnical Engineering
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• v.11 no.3
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• pp.17-26
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• 1995

Embracing a suggestion by Sullivan(1984) and minimizing the sum of the estimation variances at all thresholds, a rigorous solution to order relatioll problems in multiple indi gator kriging is formulated. By utilizing the particular structure of the resulting optimization problem, a solution algorithm is developed that requires little computational effort beyond the initial indicator kriging. Thus, this proposed solution is computationally efficient, mathematically consistent, and based upon an explicit statistical foundation-unlike many of the ad hoc solutions currently in use.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.5
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• pp.434-441
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• 2016

Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

• Proceedings of the KIEE Conference
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• 2001.04a
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• pp.231-233
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• 2001

This paper describes an analytical solution of the voltage commands for instantaneous torque control of an I.M. The analytical solution is expressed as a simple explicit function of the instantaneous torque commands and motor speed. On the basis of the derived analytical solution, the maximum torque change rate of an I.M with a limited voltage-source is analyzed, and also the dynamic influence of rapid changes in motor speed on output torque derivations is investigated. The detailed results of these two analyses are approximated here in term of first-order linear differential equations, and their validities are confirmed through the demonstrative numerical simulations. This paper includes the simulation results of the instantaneous torque control with varied motor parameters for sensitivity analysis.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.1
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• pp.55-71
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• 2006

We perform a computational study on 0-1 knapsack problems generated under explicit correlation induction. A total of 2000 100-variable test problems are solved. We use two solution methods: (1) a well known heuristic and (2) a representative branch and bound type algorithm. Two different performance measures are considered: (1) the number of nodes needed to find an optimal solution and (2) the relative error of the heuristic solution. We also examine the effect of different joint probability mass functions (pmfs) for the coefficient values on the performance of the solution procedure.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.1
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• pp.49-66
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• 2022

The G-Euler process has been proposed to overcome the difficulties of the calculation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko's graphs are reliable.

• Computers and Concrete
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• v.3 no.6
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• pp.423-437
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• 2006

Stress wave propagation through concrete is simulated by finite element analysis. The concrete medium is modeled as a homogeneous material with smeared properties to investigate and establish the suitable finite element analysis method (explicit versus implicit) and analysis parameters (element size, and solution time increment) also suitable for rigorous investigation. In the next step, finite element analysis model of the medium is developed using a digital image processing technique, which distinguishes the mortar and aggregate phases of concrete. The mortar and aggregate phase topologies are, then, directly mapped to the finite element mesh to form a heterogeneous concrete model. The heterogeneous concrete model is then used to simulate wave propagation. The veracity of the model is demonstrated by evaluating the intrinsic parameters of nondestructive ultrasonic pulse velocity testing of concrete. Quantitative relationships between aggregate size and testing frequency for nondestructive testing are presented.