• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.1057-1069
• /
• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Structural Engineering and Mechanics
• /
• v.85 no.4
• /
• pp.485-500
• /
• 2023

The non-linear static analysis of reinforced concrete (RC) structures using the three-dimensional (3D) finite element method is a time-consuming and challenging task. Moreover, this type of analysis encounters numerical problems such as the lack of convergence of results in the stages of growth and propagation of cracks in the structure. The time integration analysis along with the mass scaling (MS) technique is usually used to overcome these limitations. Despite the use of this method in the 3D finite element analysis of RC structures, a comprehensive study has not been conducted so far to assess the effects of the MS method on the accuracy of results. This study aims to evaluate the accuracy of the MS method in the non-linear quasi-static finite element analysis of RC structures. To this aim, different types of RC structures were simulated using the finite element approach based on the implicit time integration method and the mass scaling technique. The influences of effective parameters of the MS method (i.e., the allowable values of increase in the mass of the RC structure, the relationship between the duration of the applied load and fundamental vibration period of the RC structure, and the pattern of applied loads) on the accuracy of the simulated results were investigated. The accuracy of numerical simulation results has been evaluated through comparison with existing experimental data. The results of this study show that the achievement of accurate structural responses in the implicit time integration analyses using the MS method involves the appropriate selection of the effective parameters of the MS method.

• Structural Engineering and Mechanics
• /
• v.51 no.1
• /
• pp.89-110
• /
• 2014

In this study, two beam-column elements based on the Elasto-Fiber element theory for reinforced concrete (RC) element have been developed and compared with each other. The first element is based on Elasto Fiber Approach (EFA) was initially developed for steel structures and this theory was applied for RC element in there and the second element is called as Fiber & Bernoulli-Euler element approach (FBEA). In this element, Cubic Hermitian polynomials are used for obtaining stiffness matrix. The beams or columns element in both approaches are divided into a sub-element called the segment for obtaining element stiffness matrix. The internal freedoms of this segment are dynamically condensed to the external freedoms at the ends of the element by using a dynamic substructure technique. Thus, nonlinear dynamic analysis of high RC building can be obtained within short times. In addition to, external loads of the segment are assumed to be distributed along to element. Therefore, damages can be taken account of along to element and redistributions of the loading for solutions. Bossak-${\alpha}$ integration with predicted-corrected method is used for the nonlinear seismic analysis of RC frames. For numerical application, seismic damage analyses for a 4-story frame and an 8-story RC frame with soft-story are obtained to comparisons of RC element according to both approaches. Damages evaluation and propagation in the frame elements are studied and response quantities from obtained both approaches are investigated in the detail.

• International Journal of Precision Engineering and Manufacturing
• /
• v.2 no.2
• /
• pp.5-10
• /
• 2001

This paper attempt to explore the shape of stress wave propagation of 3-dimensional stress field which in made in the process of the time increment. A finite element program about 3-dimensional stress wave propagation is developed for investigating the changing shape of the stress by the impact load. The finite element program, which is the solution for the 3-dimensional stress wave analysis, based on Galerkin and Newmark-${\beta}$ method at time increment step. The tensile stress and compressive stress become larger with the order of the middle , the upper and the opposite layers when the impact load is applied. In a while the shear stress become larger according to the order of the upper, the middle and the opposite layers when impact load applied.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.10a
• /
• pp.421-428
• /
• 1999

The elastic critical load of a slender compression member plays an important role when the proper design of that member is required. For the tapered compression members, however, there are cases when the conventional neutral equililbrium or energy method can't be applied to the determination of critical loads of those members. In this paper, finite element method is applied to the approximate determination of the symmetrically tapered bars. Here in this paper, the bars are assumed to take sinusoidally changing shapes along their axes. The parameters considered in this study are taper parameter, $\alpha$ and the sectional property parameter, m. The computed results by finite element method are represented in the forms of algebraic equations. Regression technique is employed to determine the coefficients of algebraic equations. The critical loads estimated by the proposed algebraic equations coincide fairly well with those of finite element method.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.299-306
• /
• 2000

The elastic critical load of a slender compression member plays an important role when the proper design of that member is required. For tapered compression members, however, there are cases when the conventional neutral equilibrium or energy method can't be applied to the determination of critical loads. In this paper, the finite element method is applied to the approximate determination of the linearly tapered members. In this paper, the bars are assumed to be tapered linearly along their axes. The parameters considered in this study are taper parameter, α and the sectional property parameter, m. The member ends are either hinged or fixed. The computed results using the finite element method are represented in the forms of algebraic equations. The regression technique is employed to determine the coefficients of the algebraic equations. Critical loads estimated by the proposed algebraic equations coincide flirty well with those employing the finite element method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.173-195
• /
• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Tunnel and Underground Space
• /
• v.4 no.1
• /
• pp.17-23
• /
• 1994

This study consists of two procedures on back analysis and forward analysis which is a basic tool of the former. For a safe and economical construction of underground structures, it is required to identify the structural parameters and analyze the structural behavior as exactly as possible. In this paper, a boundary element method to analyze the behavior of multi-alyered underground structures is studied, in which body forces and initial stresses are considered. That is, each layer is discritized into subregions using infinite fundamental solutions, and terms of body forces and initial stresses are transformed into boundary integral where the applied direct integral method is used. And the system of equations containing body forces and initial stresses are considered. That is, each layer is discritized into subregions using infinite fundamental solutions, and terms of body forces and initial stresses are transformed into boundary integral where the applied direct integral method is used. And the system of equations containing body forces and initial stresses are composed, then the method to solve unknowns is used with applying compatibility and equilibrium conditions between interfaces. As well, the direct search method is applied in back analysis problems. By Powell's method as a technique to search unknown parameters, assuming displacements calculated from boundary element analysis as in-situ displacements, elastic moduli and initial stresses are presumed. As consequences of this study, the results of boundary element analysis of the behavior of multilayered structure considering body forces and initial stresses are agreed with those of finite element analysis. And results of back analysis of elastic moduli and initial stresses in each layers are agreed with exact values with a little difference. Therefore, it is known that this study can be efficiently applied for analyzing the behavior of underground structures including back analysis problems.

• Structural Engineering and Mechanics
• /
• v.2 no.4
• /
• pp.395-402
• /
• 1994

An improved finite element-transfer matrix method is applied to the transient analysis of plates with large displacement under various excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix method is changed into the transfer of generally incremental stiffness equations of every section from left to right. Furthermore, in this method, the propagation of round-off errors occurring in recursive multiplications of transfer and point matrices is avoided. The Newmark-${\beta}$ method is employed for time integration and the modified Newton-Raphson method for equilibrium iteration in each time step. An ITNONDL-W program based on this method using the IBM-PC/AT microcomputer is developed. Finally numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for dynamic large deflection analysis of plates with random boundaries under various excitations.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.10a
• /
• pp.11-18
• /
• 2001

In this paper, a new algorithm of coupling Element-Free Galerkin Method(EFGM) and Boundary Element Method(BEM) using the variational formulation is presented. A global variational coupling formulation of EFGM-BEM is achieved by combining the variational form on each subregion. In the formulation, Lagrange multiplier method is introduced to satisfy the compatibility conditions between EFGM subregion and BEM subregion. Some numerical examples are studied to verify accuracy and efficiency of the proposed method, in which numerical performance of the method is compared with that of conventional method such as EFGM-BEM direct coupling method, EFGM and BEM. The proposed method incorporating the merits of EFGM and BEM is expected to be applied to special engineering problems such as the crack propogation problems in very large domain, and underground structures with joints.