• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.3
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• pp.111-116
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• 2011

Analytical solutions for laterally loaded piles were derived. Critical pile length which can be considered as the length for behaving as long pile was investigated varying with densities of sandy soils. Lateral behaviors obtained from analytical solution and numerical solution were also investigated. Non-dimensional critical pile lengths obtained from analytical solutions for three types of pile head boundary conditions were 2.3~3.2. By comparing analytical solutions with numerical solutions, distribution of pile deflection and that of moment were similar and it can be seen that pile head deflection obtained by analytical method is conservative. And the values of moments were not too different between analytical solution and numerical solution.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.71-82
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• 2023

In this article, we find the approximate solutions of Abel differential equation (ADE) with uncertainty using residual power series (RPS) method. This method helps to calculate the sequence of solutions of ADE. Finally, numerical illustrations demonstrate the applicability of the method.

• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.243-291
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• 2020

In this paper, multi-block generalized backward differentiation methods for numerical solutions of ordinary differential and differential algebraic equations are introduced. This class of linear multi-block methods is implemented as multi-block boundary value methods (MB₂ VMs). The root distribution of the stability polynomial of the new class of methods are determined using the Wiener-Hopf factorization of a matrix polynomial for the purpose of their correct implementation. Numerical tests, showing the potential of such methods for output of multi-block of solutions of the ordinary differential equations in the new approach are also reported herein. The methods which output multi-block of solutions of the ordinary differential equations on application, are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output only a block of solutions per step. The MB₂ VMs introduced herein is a novel approach at developing very large scale integration methods (VLSIM) in the numerical solution of differential equations.

• East Asian mathematical journal
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• v.34 no.5
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• pp.623-632
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• 2018

In [7, 8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.4
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• Steel and Composite Structures
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• v.16 no.5
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• pp.521-531
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• 2014

In this paper we consider a periodic solution for nonlinear free vibration of conservative systems for thick circular sector slabs. In Energy Balance Method (EBM) contrary to the conventional methods, only one iteration leads to high accuracy of the solutions. The excellent agreement of the approximate frequencies and periodic solutions with the exact ones could be established. Some patterns are given to illustrate the effectiveness and convenience of the methodology. Comparing with numerical solutions shows that the energy balance method can converge to the numerical solutions very rapidly which are valid for a wide range of vibration amplitudes as indicated in this paper.

• Journal of Biomedical Engineering Research
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• v.5 no.1
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• pp.9-14
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• 1984

The asymptotic solution using the Tailor series has been given explicit form for the solute concentration and overall solute removal in hemodiafilter using one dimensional model. The numerical solutions have been calculated within 0.001% error by the Romberg integration method. Compared with the numerical solutions, the oneterm asymptotic solutions were found to be within 3% error for the condition > 3.0 and three-terms asymtotic solutions were required for the condition >0.7 where denotes measure of convection over diffusional transport and a the ratio of blood flow rate over dialysate flow rate.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.313-334
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• 2012

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1157-1176
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• 2015

This study presents optimizing structural topology patterns using regularization of Heaviside function. The present method needs not filtering process to typical SIMP method. Using the penalty formulation of the SIMP approach, a topology optimization problem is formulated in co-operation, i.e., couple-signals, with design variable values of discrete elements and a regularized Heaviside step function. The regularization of discontinuous material distributions is a key scheme in order to improve the numerical problems of material topology optimization with 0 (void)-1 (solid) solutions. The weak forms of an equilibrium equation are expressed using a coupled regularized Heaviside function to evaluate sensitivity analysis. Numerical results show that the incorporation of the regularized Heaviside function and the SIMP leads to convergent solutions. This method is tested using several examples of a linear elastostatic structure. It demonstrates that improved optimal solutions can be obtained without the additional use of sensitivity filtering to improve the discontinuous 0-1 solutions, which have generally been used in material topology optimization problems.