• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 가을 학술발표회 논문집
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• pp.28-33
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• 1990

This paper presents an efficient and accurate method for nonlinear analysis of frame structures by idealized structural unit method. The main idea behind the present method is to minimize the cost of the computational effort by reducing the number of unknowns. An explicit form of the tangential elastic stiffness matrix of the element is derived by using updated Lagrangian approach. An ultimate limit state of the element is judged on the basis of the formation of a plastic hinge mechanism. The elasto-plastic stiffness matrix and the post-ultimate stiffness matrix of the element are formulated by plastic node method. A comparison between the present method is very efficient and accurate because the computing time required is very small while giving the accurate solution.

• Structural Engineering and Mechanics
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• 제4권2호
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• pp.139-148
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• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

• Structural Engineering and Mechanics
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• 제33권3호
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• pp.307-323
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• 2009

This article presents the differential system that governs the mechanical behaviour of a curved-beam element, with varying cross-section area, subjected to generalized load. This system is solved by an exact procedure or by the application of a new numerical recurrence scheme relating the internal forces and displacements at the two end-points of an increase in its centroid-line. This solution has a transfer matrix structure. Both the stiffness matrix and the equivalent load vector are obtained arranging the transfer matrix. New structural matrices have been defined, which permit to determine directly the unknown values of internal forces and displacements at the two supported ends of the curved-beam element. Examples are included for verification.

• 한국산학기술학회논문지
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• 제11권7호
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• pp.2661-2669
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• 2010

본 연구에서는 매트릭스가 손상된 적층복합판의 비선형 거동을 분석하기 위한 일차전단변형이론에 기초한 유한요소 정식을 유도하였다. Duan and Yao가 제안한 Matrix 균열의 강성 치환 방법을 적용하여 다방향 강성저하식을 구성하였다. 발생된 Matrix 균열은 탄성계수, 전단탄성계수 및 프아송비의 변화로 표현할 수 있으며, 이를 이용하여 판의 국부 강성 변화를 예측할 수 있다. 가정된 자연변형률 방법을 적용한 쉘요소를 이용하여 면내 및 전단잠김 현상이 발생하지 않았다. 적층복합판의 선형해석은 물론 비선형 해석결과들은 참고문헌의 결과들에 수렴되었다. 매트릭스가 손상된 적층복합판의 해석 결과들은 향후 연구에 비교자료로 활용될 수 있을 것이다.

• 한국소음진동공학회논문집
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• 제19권10호
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• pp.1021-1027
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• 2009

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping. In the second stage, a damping matrix is estimated with the mass and stiffness matrices fixed. Methods to estimate a damping matrix for this purpose are proposed in this paper. For a system with proportional damping, a damping matrix is estimated using the modal parameters extracted from the measured responses and the modal matrix calculated from the mass and stiffness matrices from the first stage. For a system with non-proportional damping, a damping matrix is estimated from the impedance matrix which is the inverse of the FRF matrix. Only one low or one column of the FRF matrix is measured, and the remaining FRFs are synthesized to obtain a full FRF matrix. This procedure to obtain a full FRF matrix saves time and effort to measure FRFs.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.759-769
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• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.192-199
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• 2002

The use of frequency-dependent dynamic stiffness matrix (or spectral element matrix) in structural dynamics may provide very accurate solutions, while it reduces the number of degrees-of-freedom to improve the computational efficiency and cost problems. Thus, this paper develops a spectral element model for the thin plates moving with constant speed under uniform in-plane tension. The concept of Kantorovich method is used in the frequency-domain to formulate the dynamic stiffness matrix. The present spectral element model is evaluated by comparing its solutions with the exact analytical solutions. The effects of moving speed and in-plane tension on the flexural wave dispersion characteristics and natural frequencies of the plate are numerically investigated.

• Structural Engineering and Mechanics
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• 제21권5호
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• pp.539-551
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• 2005

Finite elements based on isoparametric formulation are known to suffer spurious stiffness properties and corresponding stress oscillations, even when care is taken to ensure that completeness and continuity requirements are enforced. This occurs frequently when the physics of the problem requires multiple strain components to be defined. This kind of error, commonly known as locking, can be circumvented by using reduced integration techniques to evaluate the element stiffness matrices instead of the full integration that is mathematically prescribed. However, the reduced integration technique itself can have a further drawback - rank deficiency, which physically implies that spurious energy modes (e.g., hourglass modes) are introduced because of reduced integration. Such instability in an existing stiffness matrix is generally detected by means of an eigenvalue test. In this paper we show that a knowledge of the dimension of the solution space spanned by the column vectors of the strain-displacement matrix can be used to identify the instabilities arising in an element due to reduced/selective integration techniques a priori, without having to complete the element stiffness matrix formulation and then test for zero eigenvalues.

• 한국농공학회논문집
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• 제46권5호
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• pp.61-68
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• 2004

Methodologies of the finite element and boundary element are combined to achieve an efficient and accurate analysis model of frame structure containing shear wall. This model analyzes the frame by employing the finite element method and the shear wall by boundary element method. This study is applicable to a specific situation, where the boundary element is surrounded by finite elements. By employing FE dominant method in which boundary stiffness matrix is transformed into finite element stiffness matrix, boundary element and finite element method are combined to analyze frame structure with walls.

• 한국정밀공학회지
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• 제27권2호
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• pp.109-116
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• 2010

It is important to make a mechanical structure precisely and reasonably in predicting the dynamic characteristics, controlling the vibration, and designing the structure dynamics. In finite element analysis model updating is appropriate as the design parameter is used to analyze the dynamic system. The errors can be contained from the physical parameters and the element modeling. From the dynamic test, more precise dynamic characteristics can be obtained. In this paper, model updating algorithm is developed using frequency difference between experiment and calculation. Modal frequencies are obtained by experiment and finite element analysis for beams with various cross section and shapes which have added masses and holes in the middle. For plates with and without groove, experiment and analyses are carried out by applying free boundary conditions as well. Mass and stiffness matrices are updated by comparing test and analytical modal frequencies. The result shows that the updated frequencies become closer to the test frequencies in case that both matrices are updated. An improved analytical model is obtained by changing model parameters such that the discrepancy between test and finite element frequencies is minimized. For beam and plate models updating of mass and stiffness matrices can improve the dynamical behavior of the model by acting on the physical parameters such as masses and stiffness.