• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.18 no.4 s.70
• /
• pp.385-393
• /
• 2005

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. The Newmark direct integration method and the Newton-Raphson iteration are employed here for the numerical study which is to demonstrate the efficiency of the proposed formulation.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.35 no.5
• /
• pp.249-257
• /
• 2022

This paper presents an improved computational framework for the direct-solution-based finite element tearing and interconnecting (FETI) algorithm. The FETI-local algorithm is further improved herein, and localized Lagrange multipliers are used to define the interface among its subdomains. Selective inverse entry computation, using a property of the Boolean matrix, is employed for the computation of the subdomain interface stiffness and load, in which the original FETI-local algorithm requires a full matrix inverse computation of a high computational cost. In the global interface computation step, the original serial computation is replaced by a parallel multi-frontal method. The performance of the improved FETI-local algorithm was evaluated using a numerical example with 64 million degrees of freedom (DOFs). The computational time was reduced by up to 97.8% compared to that of the original algorithm. In addition, further stable and improved scalability was obtained in terms of a speed-up indicator. Furthermore, a performance comparison was conducted to evaluate the differences between the proposed algorithm and commercial software ANSYS using a large-scale computation with 432 million DOFs. Although ANSYS is superior in terms of computational time, the proposed algorithm has an advantage in terms of the speed-up increase per processor increase.

• Structural Engineering and Mechanics
• /
• v.51 no.3
• /
• pp.377-402
• /
• 2014

In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.05a
• /
• pp.666-671
• /
• 2002

For a large structure, substructure based SDM(structural dynamics modification) method is very effective to raise its dynamic characteristics. Dividing into smaller substructures has a major advantage in the aspect of computation especially for getting sensitivities, which are in the core of SDM process. But quite often, non-matching nodes problem occurs in the process of synthesizing substructures. The reason is that, in general, each substructure is modelled separately, then later combined together to form a entire structure model under interface constraint conditions. Without solving the non-matching nodes problem, the substructure based SDM can not be processed. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalues of whole structure are calculated using determinant search method. The number of degrees of freedom of the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Thus, the eigenvalue sensitivities can be easily calculated, and further SDM can be efficiently performed. Some numerical problems are tested to show the effectiveness of handling non-matching nodes.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11a
• /
• pp.155-160
• /
• 2001

Actual engineering structure is frequently very complex, and parts of structure are designed independently by different engineers. Also each structure contains so many degree of freedom. For these reason, methods have been developed which permits the structure to be divided into components or substructures, with analysis being done on a small substructure in order to obtain a full structural system. In such case, because of different mesh size among finite element model (FEM) or different matching points among FEM models and experimentally obtained models, their interfacing points may be non-matching. Solving this non-matching problem is useful to other application such as structural dynamic modification or model updating. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint, and interface displacement is approximated by polynomial presentation. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalue of whole structure are calculated using the determinant search method. The number of degree of freedom in the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Some numerical simulation is performed to show usefulness of synthesis method.

• The Journal of the Korea Contents Association
• /
• v.9 no.4
• /
• pp.27-33
• /
• 2009

Selection of the Lagrangian multiplier is a key factor to determine the performance of Rate-Distortion Optimization (RDO) in video coding. JM, reference S/W of H.264, employs only one RDO model for all macroblock. However, since the characteristics of macroblocks are different, RDO model adaptive to their characteristics can give some performance improvement. In this paper, we propose an RDO algorithm adaptive to characteristics of macroblocks. We empirically obtain the optimal Lagrangian multipliers considering characteristics of macroblocks. For performance evaluation, the proposed method is applied to JM10.2 and, as a result, we have PSNR gain of 0.2dB on average.

• The Korean Journal of Applied Statistics
• /
• v.17 no.3
• /
• pp.489-498
• /
• 2004

In this paper, a new form of linear models referred to as generalized weighted linear models is proposed. The proposed models assume that the relationship between the response variable and explanatory variables can be modelled by a distribution function of the response mean and a weighted linear combination of distribution functions of covariates. This form addresses a structural problem of the link function in the generalized linear models in which the parameter space may not be consistent with the space derived from linear predictors. The maximum likelihood estimation with Lagrange's undetermined multipliers is used to estimate the parameters and resampling method is applied to compute confidence intervals and to test hypotheses.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.23 no.4
• /
• pp.369-378
• /
• 2010

The mixed finite element analysis is the most widely used method for saturated porous media. Generally, in this method, direct method and iterative method are proposed to obtain unknown variable, however, the iterative method is recommended because the method provide numerical stability and accuracy under the material properties for solid and fluid are different. In this paper, we introduce staggered method which has strong numerical stability, and FETI(Finite Element Tearing and Interconnecting) which is one of decomposition methods are applied into the method in order to obtain numerical efficiency. In which, Lagrange Multipliers and conjugated gradient method to solve decomposed domain are proposed, and then, the proposed method is verified numerical efficiency by point to point MPI(Message Passing Interface) library.

• Structural Engineering and Mechanics
• /
• v.56 no.6
• /
• pp.959-982
• /
• 2015

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.32 no.4
• /
• pp.249-256
• /
• 2019

This paper presents an optimization framework of electrical impedance tomography for characterizing electrical conductivity profiles of concrete structures in two dimensions. The framework utilizes a partial-differential-equation(PDE)-constrained optimization approach that can obtain the spatial distribution of electrical conductivity using measured electrical potentials from several electrodes located on the boundary of the concrete domain. The forward problem is formulated based on a complete electrode model(CEM) for the electrical potential of a medium due to current input. The CEM consists of a Laplace equation for electrical potential and boundary conditions to represent the current inputs to the electrodes on the surface. To validate the forward solution, electrical potential calculated by the finite element method is compared with that obtained using TCAD software. The PDE-constrained optimization approach seeks the optimal values of electrical conductivity on the domain of investigation while minimizing the Lagrangian function. The Lagrangian consists of least-squares objective functional and regularization terms augmented by the weak imposition of the governing equation and boundary conditions via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to the Karush-Kuhn-Tucker condition to obtain an optimal solution for electrical conductivity within the target medium. Numerical inversion results are reported showing the reconstruction of the electrical conductivity profile of a concrete specimen in two dimensions.