• 한국구조물진단유지관리공학회 논문집
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• 제15권2호
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• pp.125-135
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• 2011

유연도법 기반의 공식화에서는 변위영역의 형상함수를 라그랑지언(Lagrangian)보간법에 의한 곡률로부터 횡방향 변위를 유도한다. 곡률변위보간법으로 유도한 매트릭스를 사용한 기하학적 비선형 해석방법과 강성도법을 기반으로 한 비선형 기존의 유한요소 해석 프로그램의 결과를 비교하여 적용이 가능함을 확인하였고, Spacone의 이론을 확장시켜 기하학적 비선형 거동을 예측할 수 있는 유연도법의 알고리즘을 제안하였다. 예제를 통하여 실제 문제에 대한 기하학적 비선형 해석을 수행하였다.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.1-18
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• 2020

For the large deformation of shear walls under vertical and horizontal loads, there are difficulties in obtaining accurate simulation results using the response analysis method, even with fine mesh elements. Furthermore, concrete material nonlinearity, stiffness degradation, concrete cracking and crushing, and steel bar damage may occur during the large deformation of reinforced concrete (RC) shear walls. Matrix operations that are involved in nonlinear analysis using the traditional finite-element method (FEM) may also result in flaws, and may thus lead to serious errors. To solve these problems, a planar four-node element was developed based on vector mechanics. Owing to particle-based formulation along the path element, the method does not require repeated constructions of a global stiffness matrix for the nonlinear behavior of the structure. The nonlinear concrete constitutive model and bilinear steel material model are integrated with the developed element, to ensure that large deformation and damage behavior can be addressed. For verification, simulation analyses were performed to obtain experimental results on an RC shear wall subjected to a monotonically increasing lateral load with a constant vertical load. To appropriately evaluate the parameters, investigations were conducted on the loading speed, meshing dimension, and the damping factor, because vector mechanics is based on the equation of motion. The static problem was then verified to obtain a stable solution by employing a balanced equation of motion. Using the parameters obtained, the simulated pushover response, including the bearing capacity, deformation ability, curvature development, and energy dissipation, were found to be in accordance with the experimental observation. This study demonstrated the potential of the developed planar element for simulating the entire process of large deformation and damage behavior in RC shear walls.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권2호
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• pp.55-68
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• 2008

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

• Structural Engineering and Mechanics
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• 제62권1호
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• pp.85-95
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• 2017

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

• 대한기계학회논문집B
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• 제24권2호
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• pp.316-323
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• 2000

A nonlinear low-Reynolds-number heat transfer model is developed to predict turbulent flow and heat transfer in separated and reattaching flows. The $k-{\varepsilon}-f_{\mu}$ model of Park and Sung (1997) is extended to a nonlinear formulation, based on the nonlinear model of Gatski and Speziale (1993). The limiting near-wall behavior is resolved by solving the $f_{\mu}$ elliptic relaxation equation. An improved explicit algebraic heat transfer model is proposed, which is achieved by applying a matrix inversion. The scalar heat fluxes are not aligned with the mean temperature gradients in separated and reattaching flows; a full diffusivity tensor model is required. The near-wall asymptotic behavior is incorporated into the $f_{\lambda}$ function in conjunction with the $f_{\mu}$ elliptic relaxation equation. Predictions of the present model are cross-checked with existing measurements and DNS data. The model preformance is shown to be satisfactory.

• Composites Research
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• 제12권4호
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• pp.1-7
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• 1999

비선형 하중/변위 거동을 나타내는 모재 지배 복합재료의 피로수명 예측을 이론과 실험에 의해 연구하였다. 재료의 비선형성을 고려하기 위해 초기 피로계수와 탄성계수의 관계를 나타내는 응력함수를 도입하였다. 피로계수와 참고계수 개념을 기반으로 하여 새로운 피로수명 예측식이 가한 하중 수위의 함수로 유도되었다. 예측 결과는 직교이방성 탄소섬유/에폭시 적층판을 사용한 원통형 시편의 비틀림 피로 실험과 비교되었으며, 제안된 식은 실험치와 잘 일치하였다.

• 항공우주시스템공학회지
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• 제10권1호
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• pp.21-28
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• 2016

Orbit determination problems have been interest of many researchers for long time. Due to the high nonlinearity of the equation of motion and the measurement model, it is necessary to linearize the both equations. To avoid linearization, the filter based on Fokker-Planck equation is designed. with the extended Kalman filter update mechanism, in which the associated Fokker-Planck equation was solved efficiently and accurately via discrete quadrature and the measurement update was done through the extended Kalman filter update mechanism. This filter based on the DQMOM and the EKF update is applied to the orbit determination problem with appropriate modification to mitigate the filter smugness. Unlike the extended Kalman filter, the hybrid filter based on the DQMOM and the EKF update does not require the burdensome evaluation of the Jacobian matrix and Gaussian assumption for the system, and can still provide more accurate estimations of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the hybrid filter based on the DQMOM and the EKF update make it a promising alternative to the extended Kalman filter for orbit estimation problems.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 하계학술대회 논문집 B
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• pp.584-586
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• 1997

The orthogonal polynomials have been widely employed to solve control problems, but the LQG(linear quadratic gaussian) problem remains unsolved. In this paper, we obtained the solutions of Riccati equation and covariance matrix Riccati equation by two point boundary problem and matrix fraction method using BPF(Block Pulse Function), respectively. This solutions are solved the problem of the LQG controller design.

• 대한기계학회논문집A
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• 제30권10호
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• pp.1249-1254
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• 2006

Existing adaptive observers may cause the parameter drifts due to disturbances even if state estimation errors remain small. To avoid the drift phenomena in the presence of bounded disturbances, several robust adaptive observers have been introduced addressing bounds in state and parameter estimates. However, it is not easy for these observers to manipulate the size of the bounds with the selection of the observer gain. In order to reduce estimation errors, this paper introduces the (equation omitted) gain minimization problem in the adaptive observer structure, which minimizes the (equation omitted) gain between disturbances and estimation errors. The stability condition of the adaptive observer is reformulated as a linear matrix inequality, and the observer gain is optimally chosen by solving the convex optimization problem. The estimation performance is demonstrated through a numerical example.

• Structural Engineering and Mechanics
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• 제20권5호
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• pp.575-587
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• 2005

Using the nonlinear load transfer function for pile side soil and the linear load transfer function for pile end soil, a combined approach of the incremental load transfer matrix method and the approximate differential equation solution method is presented for the nonlinear analysis of interaction between flexible pile group and soil. The proposed method provides an effective approach for the solution of the nonlinear interaction between flexible pile group under rigid platform and surrounding soil. To verify the accuracy of the proposed method, a static load test for a nine-pile group under a rigid platform is carried out. The finite element analysis is also conducted for comparison purposes. It is found that the results from the proposed method match very well with those from the experimental test and are better in comparison with the finite element method.