• 대한기계학회논문집
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• 제15권2호
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.199-214
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• 2020

This paper describes the development of a parallel computational algorithm based on the finite element tearing and interconnecting (FETI) method that uses a local Lagrange multiplier. In this approach, structural computational domain is decomposed into non-overlapping sub-domains using local Lagrange multiplier. The local Lagrange multipliers are imposed at interconnecting nodes. 8-node solid element using extra shape function is adopted by using the representative volume element (RVE). The parallel computational algorithm is further established based on message passing interface (MPI). Finally, the present FETI-local approach is implemented on parallel hardware and shows improved performance.

• 대한기계학회논문집
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• 제17권5호
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• pp.1138-1149
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• 1993

본 연구에서는 임의 형태의 경계조건을 갖는 부분구조 모드를 이용하여 구조물의 고유치해석을 수행할 수 있는 새로운 혼합경계합성법을 제시한다. 각 부분 구조의 모드특성으로는 기존의 고정, 자유, 그리고 하중경계모드가 모두 사용될 수 있으며 고정 및 하중경계모드를 사용한 경우에는 두번의 연속적인 모드변환식이 사용 된다. 부분구조간의 연결부에서 정의되는 경계자유도만을 이용하여 고유치해석을 수행하며 고유치해석의 최종적인 특성방정식은 경계자유도의 갯수와 같은 연립방정식 에서 비롯되는 다항식이 된다. 제시한 방법은 유한요소법 뿐만 아니라 실험적 모드 해석을 통해 모형화된 부분구조를 쉽게 고려할 수 있는 장점이 있다. 제시한 방법을 간단한 집중질량계에 적용하여 부분구조모드의 특성과 수렴성 및 최적의 부분구조 모 드의 조합이 존재함을 보인다.

• Structural Engineering and Mechanics
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• 제88권2호
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• pp.129-140
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• 2023

To increase the stiffness and strength of a reinforced concrete shear wall, steel plates are bolted to the sides of the wall. The general behavior of a composite concrete-steel shear wall is dependent on the buckling of the steel plates that should be prevented. In this paper, the unilateral buckling of steel plates of a composite shear wall is studied using the Rayleigh-Ritz method. To model the unilateral buckling of steel plate, the restraining concrete wall is described as an elastic foundation with high stiffness in compression and zero stiffness in tension. To consider the effect of bolt connections on the plate's buckling, a constrained optimization problem is solved by using Lagrange multipliers method. This process is used to obtain the critical elastic local buckling coefficients of unilaterally-restrained steel plates with various numbers of bolts, subjected to pure compression, bending and shear loading, and the interaction between them. Using these results, the spacing between shear bolts in composite steel plate shear walls is estimated and compared with the results of the AISC seismic provisions (2016). The results show that the AISC seismic provisions(2016) are overly conservative in obtaining the spacing between shear bolts.

• Journal of Applied and Pure Mathematics
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• 제6권3_4호
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• pp.141-154
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• 2024

This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.369-380
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• 2018

In this paper, a multi-layered finite element model for laminated glass plates is introduced. A layer-wise theory is applied to the analysis of laminated glass due to the combination of stiff and soft layers; the independent layers are connected via Lagrange multipliers. The von $K{\acute{a}}rm{\acute{a}}n$ large deflection plate theory and the constant Poisson ratio for constitutive equations are assumed to capture the possible effects of geometric nonlinearity and the time/temperature-dependent response of the plastic foil. The linear viscoelastic behavior of a polymer foil is included by the generalized Maxwell model. The proposed layer-wise model was implemented into the MATLAB code and verified against detailed three-dimensional models in ADINA solver using different hexahedral finite elements. The effects of temperature, load duration, and creep/relaxation are demonstrated by examples.

• 한국전산구조공학회논문집
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• 제23권6호
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• pp.693-702
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• 2010

In this paper, FETI(Finite Element Tearing and Interconnecting) method is introduced in order to improve numerical efficiency of Staggered method. The porous media theory, the Staggered method and the FETI method are briefly introduced in this paper. In addition, we account for the MPI(Message Passing Interface) library for parallel analysis, and the proposed combined Staggered method with FETI method. Finally Lagrange multipliers and CG(Conjugate Gradient) algorithm to solve decomposed domain are proposed, and then the proposed method is verified to be numerically efficient by MPI library.

• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.29-45
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. We propose a numeric model and an algorithm in order to compute the first two moments of inter-departure process. Entropy enables us to examine the convergence of this process and to derive measurable relations of this process. Also, lower bound on the variance of inter-departure process plays an important role in proving the existence and uniqueness of an optimal solution for a numeric model and deriving the convergence order of augmented Lagrange multipliers method applied to a numeric model. Through these works, we confirm some structural properties and numeric examples how the validity and applicability of our study.

• 한국광학회지
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• 제12권2호
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• pp.109-114
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• 2001

광학설계의 최적화에서는 광학수차를 줄이면서 광학계의 제한조건을 유지시켜야하며, 이를 위하여 Lagrange 부정승수법이 사용되고 있다. 이 과정에서 제한조건이 merit function의 error 항보다 우선적으로 보정된다. 본연구에서는 이를 이용하여 merit function에서 절대값이 큰 error의 보정조건을 제한조건으로 변경하여 우선적으로 보정하는 최적화의 능동적 제어법을 제안하고 이를 사진렌즈계의 최적화에 적용하였다.

• International Journal of Aeronautical and Space Sciences
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• 제16권2호
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• pp.177-189
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• 2015

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the sub-domain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.