• 대한기계학회논문집A
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• 제25권4호
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• pp.574-581
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• 2001

Transient linear elastodynamic problems are numerically analyzed in a time-domain by the Finite Element Method, for which the variational formulation based upon the equations of motion in convolution integral is newly derived. This formulation is implicit and does not include the time derivative terms so that the computation procedure is simple and less assumptions are required comparing to the conventional time-domain dynamic numerical algorithms, being able to get the improved numerical accuracy and stability. That formulation is expanded using the semi-discrete approximation to obtain the finite element equations. In the temporal approximation, the time axis is divided equally and constant and linear time variations are assumed in those intervals. It is found that unconditionally stable numerical results are obtained in case of the constant time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Advances in aircraft and spacecraft science
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• 제1권2호
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• pp.145-175
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• 2014

The results of a series of numerical experiments are presented to verify some of the important developments made in the first part of this paper. Firstly, the static solution of an algebraic system obtained through Strong Formulation Finite Element Method (SFEM) is presented. Secondly, the stress and strain recovery procedure is descripted for the present technique. It will be clear that the present approach is suitable for any strong formulation finite element methodology, due to the presented general approach based on the unknown displacements and on the elasticity equations. Thirdly, the numerical solutions for some classical and other numerical results found in literature are exposed. Finally, an arbitrarily shaped composite plate is solved and good agreement is observed for all the presented cases.

• 한국철도학회논문집
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• 제2권1호
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• pp.47-55
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• 1999

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can be partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• 한국철도학회:학술대회논문집
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• 한국철도학회 1998년도 추계학술대회 논문집
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• pp.437-444
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• 1998

In this paper, an efficient and accurate formulation for the transient analysis of constrained multibody systems is presented. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix: it can improve the efficiency of the formulation. Furthermore, the formulation partitions the coefficient matrix of linear and nonlinear equations into several sub-matrices using kinematic uncoupling. This can solve the equations more efficiently. The proposed formulation can be used to perform dynamic analysis of systems which can he partitioned into several sub-systems such as train systems. One numerical example is given to demonstrate the efficiency and accuracy of the formulation, and another numerical example is given to show its application to the train systems.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.171-184
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• 2001

A direct discrete formulation suitable for the nonlinear analysis of masonry structures is presented. The numerical approach requires a pair of dual meshes, one for describing displacement fields, one for imposing equilibrium. Forces and displacements are directly used (instead of having to resort to a model derived from a set of differential equations). Associated and nonassociated flow laws are dealt with within a complementarity framework. The main features of the method and of the relevant computer code are discussed. Numerical examples are presented, showing that the numerical approach is able to describe plastic strains, damage effects and crack patterns in masonry structures.

• 한국지반공학회논문집
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• 제29권6호
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• pp.77-86
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• 2013

연약지반위에 성토를 할 경우 초기 비배수 상태 뿐만 아니라 압밀 과정 중에도 큰 변형이 발생한다. 기존의 미소변형률 이론은 변형률이 작고 초기의 기하학적인 형상이 변형과정 동안 변하지 않는다고 가정하므로 큰 변형이 유발되는 지반공학 문제들을 해석하기 위해서는 대변형 해석을 수행하여야 한다. 힘평형 방정식과 유체 연속방정식이 결합된 압밀지배 방정식을 Updated-Lagrangian 형태로 수식화하고, Jaumann stress rate을 이용하여 역학적 구성관계를 표현하였다. 그리고 Nagtegaal이 제안한 회전을 고려한 구성관계를 적용하여 Newton의 반복과정을 통한 해의 수렴성과 정확도를 향상시켰다. 개발된 대변형 압밀해석 프로그램을 검증하기 위하여 켄틸레버보와 이차원 압밀문제를 해석하였다. 수치해석 결과는 큰 변형률과 기하학적 회전을 포함하는 대변형 문제를 효과적으로 묘사할 수 있음을 보여주었다. 기존의 미소변형이론에 근거한 유한요소 프로그램은 제안한 방법을 통하여 대변형 해석 프로그램으로 용이하게 전환될 수 있다.

• 한국전산유체공학회지
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• 제5권1호
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• pp.43-59
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• 2000

Characteristic boundary conditions are discussed in conjunction with a flux-difference splitting formulation as modified from Roe's linearization. Details of how one can implement the characteristic boundary conditions which are made compatible with the interior point formulation are described for different types of boundaries including subsonic outflow and adiabatic wall. The validity of boundary conditions are demonstrated through computation of transonic airfoil, supersonic ogive-cylinder, hypersonic cylinder, and S-duct internal flows. The computed wall pressure distributions are compared with published experimental and computed data. Objectives of this paper are thus to give insight of formulation procedure of a flux-difference splitting method and to pave ways for other users to adopt present boundary procedure on their numerical methods.

• Structural Engineering and Mechanics
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• 제14권1호
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• pp.71-84
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• 2002

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Coupled systems mechanics
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• 제1권2호
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• pp.183-204
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• 2012

A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.