• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.141-148
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• 1999

변위 근거 유한요소해석을 사용하는 대부분의 위상 최적화 기법은 요소의 안정성 부족으로 인하여 체스판 무늬가 주기적 형태로 반복하여 설계영역 내부에 나타난다. 본 연구에서는 선형요소를 이용하면서 최적화 알고리즘의 안정성에 영향을 주지 않고 간단하게 모든 최적화 알고리즘에 이용 가능한 체스판무늬 형성 방지책을 개발하였다. 본 연구의 체스판무늬 형성 방치책에서는 먼저 각 선형요소를 구성하는 절점들의 부치분율을 설계변수로 선정하고, 요소내부의 부피분율을 설계변수로 표현하기 위한 선형 보간함수로 선형요소들의 형상함수를 선정하였다. 그리고, 설계변수와 등가 재료상수와의 상관 관계식은 평균장 근사이론을 이용하여 균질화된 재료에 벌칙인자가 도입된 관계식을 이용하였다. 또한, 본 연구에서는 순차이차계획법인 PLBA 알고리즘을 이용하여 위상 최적화문제를 해석하였다.

• Computational Structural Engineering
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• v.9 no.4
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• pp.117-126
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• 1996

Damage detection methods using structural tests can be divided into two methods, i.e., static and dynamic. The static methods which use the stiffness properties of the structure are simpler than the dynamic methods. However, static approaches are very sensitive to the displacement measurement noises and modeling errors. The dynamic methods also have limitations in acquiring the natural frequencies and mode shapes of the high frequencies. In this study, a method for the structural damage assessment using sensitivity matrices is developed, in which the drawbacks of the static and dynamic methods can be compensated. Based on the measurement data for the static displacements and dynamic modal properties, the damage locations and the degree of damage are determined using the presented sensitivity matrix method. The efficiency of the proposed method has been examined through numerical simulation studies on truss type structures.

• Journal of the Korean Geotechnical Society
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• v.15 no.4
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• pp.221-234
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• 1999

This paper deals with the application of joint element in the finite element modeling of discontinuities encountered during rock tunneling. A nodal displacement joint element was implemented in a two dimensional finite element program GEOFE2D. The applicability of the joint element for modeling of discontinuities and the numerical stability of the implemented algorithm were examined by comparing the results of reduced small scale model tests as well as commercially available FEM program. The GEOFE2D was then used to analyze a tunnel crossed by a major discontinuity for the purpose of understanding the effect of discontinuity on the tunnel behavior. In addition, a modeling technique for the junction of discontinuity and shotcrete lining was presented. The results of analysis indicated that the stress-strain field around the tunnel is significantly altered by the presence of discontinuity, and that the stresses in the shotcrete lining considerably increase at the junction of the shotcrete lining and the discontinuity. It is therefore concluded that the major discontinuities must be carefully modeled in the finite element analysis of a tunneling problem in order to obtain more reliable results close to actual tunnel behavior.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.4 s.235
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• pp.534-539
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• 2005

Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian furmulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacement sand traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large deformations are analyzed to demonstrate the efficiency and validity of the proposed method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.2 no.3
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• pp.75-86
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• 1982

The degeneration of two classes of thick beam elements has been conducted, one (DB6) based on the conventional Timoshenko beam assumptions whereas the other (DB7) based on the assumed cubic axial displacement profile. While an adjustable shear correction factor is required for the DB 6 element to compensate for the unrealistic distribution of shear strain across the thickness, the DB 7 element assumes the more realistic quadratic profile of shear strain at the outset. With the plane-stress continuum solution as reference, solutions obtained by these two element models are compared with the analytical Timoshenko solution, the analytical thin beam solution and several available solutions of other existing beam elements. The result indicates that the performance of the higher order beam element DB 7 is consistently superior to any others. This is true for the whole range of aspect ratios of beam, in both static and free vibration analyses.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.67-76
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• 1992

A hierarchical formulation based on p-version of the finite element method for linear elastic axisymmetric stress analysis is presented. This is accomplished by introducing additional nodal variables in the element displacement approximation on the basis of integrals of Legendre polynomials. Since the displacement approximation is hierarchical, the resulting element stiffness matrix and equivalent nodal load vectors are hierarchical also. The merits of the propoosed element are as follow: i) improved conditioning, ii) ease of joining finite elements of different polynomial order, and iii) utilizing previous solutions and computation when attempting a refinement. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, robustness and overall superiority of the present formulation. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.2
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• pp.132-139
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• 1992

This paper presents geometrically nonlinear formulation of shell problems using the three-dimensional curved shell element, which includs large displacements and large rotations. Formulations of the geometrically nonlinear problems can be derived in a variety of ways, but most of them have been obtained by assuming that nodal rotations are small. Hence, the tangent stiffness matrix is derived under the assumptions that rotational increments are infinitesimal and the effect of finite rotational increments have to be considered during the equilibrium iterations. To study the large displacement and large rotation problems, the restrictions are removed and the formulations of the curved shell element including the effect of large rotational increments are developed in this paper. The displacement based finite element method using this improved formulation are applied to the analyses of the geometrically nonlinear behaviors of the single and double curved shells, which are compared with the results by others.

• Computational Structural Engineering
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• v.7 no.4
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• pp.103-111
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• 1994

Based on a variational principle of the consistent shear deformable discrete laminate theory derived in the companion paper Part I, a finite element procedure for the vibration analysis of laminated composite plates is presented. The present formulation takes the in-plane displacements of an arbitrary layer, the rotations of the cross section of each layer and transverse displacement of the plate as the state variables at a nodal point of finite element, resulting in total nodal degree of freedom of 2(n+l) +1 for the n-layered laminate. Thus, it allows to specify displacement boundary conditions of layer stretching and/or rotation of layer cross sections around the plate edge and/or lateral displacement. The developed procedure is applied to the free vibration problem for sandwich-type hybrid laminates composed of layers with drastically different material properties whose elasticity solutions are known. Comparison of analysis results with other FEM solutions showed that the present formulation yields better accuracy.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.3A
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• pp.447-455
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• 2006

A general purpose of 4-node co-rotational resultant shell element is developed for the solution of nonlinear problems of reinforced concrete, steel and fiber-reinforced composite structures. The formulation of the geometrical stiffness presented here is defined on the mid-surface by using the second order kinematic relations and is efficient for analyzing thick plates and shells by incorporating bending moment and transverse shear resultant forces. The present element is free of shear locking behavior by using the ANS (Assumed Natural Strain) method such that the element performs very well as thin shells. Inelastic behaviour of concrete material is based on the plasticity with strain hardening and elasto-plastic fracture model. The plasticity of steel is based on Von-Mises Yield and Ivanov Yield criteria with strain hardening. The transverse shear stiffness of laminate composite is defined by an equilibrium approach instead of using the shear correction factor. The proposed formulation is computationally efficient and versitile for most civil engineering application and the test results showed good agreement.

• Computational Structural Engineering
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• v.6 no.1
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• pp.91-98
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• 1993

Minimum weight design of the boom of an excavator with stress and displacement constraints was performed. The procedure of analysis consists of the following steps. The finite element model of the boom was built up by using 227 triangular plate elements each of which has three nodes. And then the finite element program was implemented and its accuracy was verified by comparing its results with those of the commercial structural analysis package-ANSYS 4.4A. For the constraints of stresses and displacements, the design sensitivities of those were computed using direct differentiation method. To verify the reliability of them the results were compared with those of the finite difference method. The optimum design value was obtained by using PLBA(Pshenichny-Lim-Belegundu-Arora)non-linear optimization program which adopts the active set strategy. Using the above results, minimum weight design of an excavator boom showed an effect of 27% reduction in weight.