• Coupled systems mechanics
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• v.7 no.5
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• pp.583-610
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• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

• Journal of Biomedical Engineering Research
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• v.36 no.5
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• pp.211-220
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• 2015

Recently, model-based iterative reconstruction (MBIR) has played an important role in transmission tomography by significantly improving the quality of reconstructed images for low-dose scans. MBIR is based on the penalized-likelihood (PL) approach, where the penalty term (also known as the regularizer) stabilizes the unstable likelihood term, thereby suppressing the noise. In this work we further improve MBIR by using a more expressive regularizer which can restore the underlying image more accurately. Here we used a spline regularizer derived from a linear combination of the two-dimensional splines with first- and second-order spatial derivatives and applied it to a non-quadratic convex penalty function. To derive a PL algorithm with the spline regularizer, we used a separable paraboloidal surrogates algorithm for convex optimization. The experimental results demonstrate that our regularization method improves reconstruction accuracy in terms of both regional percentage error and contrast recovery coefficient by restoring smooth edges as well as sharp edges more accurately.

• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.359-370
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• 2017

This study presents a particle swarm optimization algorithm integrated with weighted particle concept and improved fly-back technique. The rationale behind this integration is to utilize the affirmative properties of these new terms to improve the search capability of the standard particle swarm optimizer. Improved fly-back technique introduced in this study can be a proper alternative for widely used penalty functions to handle existing constraints. This technique emphasizes the role of the weighted particle on escaping from trapping into local optimum(s) by utilizing a recursive procedure. On the other hand, it guaranties the feasibility of the final solution by rejecting infeasible solutions throughout the optimization process. Additionally, in contrast with penalty method, the improved fly-back technique does not contain any adjustable terms, thus it does not inflict any extra ad hoc parameters to the main optimizer algorithm. The improved fly-back approach, as independent unit, can easily be integrated with other optimizers to handle the constraints. Consequently, to evaluate the performance of the proposed method on solving the truss weight minimization problems with discrete variables, several benchmark examples taken from the technical literature are examined using the presented method. The results obtained are comparatively reported through proper graphs and tables. Based on the results acquired in this study, it can be stated that the proposed method (integrated particle swarm optimizer, iPSO) is competitive with other metaheuristic algorithms in solving this class of truss optimization problems.

• Journal of the Korea Society of Computer and Information
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• v.23 no.3
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• pp.85-92
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• 2018

We consider a project scheduling problem in which the jobs can be compressed by using additional resource to meet the corresponding due dates, referred to as a time-cost tradeoff problem. The project consists of two independent subprojects of which precedence graph is a chain. The due dates of jobs constituting the project can be interpreted as the multiple assessments in the life of project. The penalty cost occurs from the tardiness of the job, while it may be avoided through the compression of some jobs which requires an additional cost. The objective is to find the amount of compression that minimizes the total tardy penalty and compression costs. Firstly, we show that the problem can be decomposed into several subproblems whose number is bounded by the polynomial function in n, where n is the total number of jobs. Then, we prove that the problem can be solved in polynomial time by developing the efficient approach to obtain an optimal schedule for each subproblem.

• Management Science and Financial Engineering
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• v.22 no.1
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.2 s.107
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• pp.115-123
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• 2006

A feasibility of using the topology optimization method for structural damage identification is investigated for the first time. The frequency response functions (FRFs) are assumed to be constructed by the finite element models of damaged and undamaged structures. In addition to commonly used resonances, antiresonances are employed as the damage identifying modal parameters. For the topology optimization formulation, the modal parameters of the undamaged structure are made to approach those of the damaged structure by means of the constraint equations, while the objective function is an explicit penalty function requiring clear black-and-white images. The developed formulation is especially suitable for damage identification problems dealing with many modal parameters. Although relatively simple numerical problems were considered in this investigation, the possibility of using the topology optimization method for structural damage identification is suggested through this research.

• Journal of KSNVE
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• v.6 no.1
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• pp.65-70
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• 1996

The sensor response of a piezoelectric transducer embedded in a fluid loaded structure is modeled using a hybrid numerical approach. The structure is excited by an obliquely incident acoustic wave. Finite element modeling in the structure and fluid surrounding the transducer region, is used and a plane wave representation is exploited to match the displacement field at the mathematical boundary. On this boundary, continuity of field derivatives is enforced by using a penalty factor and to further achieve transparency at the mathematical boundary, drilling degrees of freedom (d.o.f.) are introduced to ensure continuity of all derivatives. Numerical results are presented for the sensor response and it is found that the sensor at that location is not only non-intrusive but also sensitive to the characteristic of the structure.

• The Transactions of the Korea Information Processing Society
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• v.2 no.3
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• pp.417-424
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• 1995

This paper describes MFT(Mean Field Theory) neural network with continuous with continuous variables is applied to quantification analysis problem. A quantification analysis problem, one of the important problems in statistics, is NP complete and arises in the optimal location of objects in the design space according to the given similarities only. This paper presents a MFT neural network with continuous variables for the quantification problem. Starting with reformulation of the quantification problem to the penalty problem, this paper propose a "one-variable stochastic simulated annealing(one-variable SSA)" based on the mean field approximation. This makes it possible to evaluate of the spin average faster than real value calculating in the MFT neural network with continuous variables. Consequently, some experimental results show the feasibility of this approach to overcome the difficulties to evaluate the spin average value expressed by the integral in such models.ch models.

• Steel and Composite Structures
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• v.34 no.2
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• pp.227-239
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• 2020

The aim of this study is to obtain the nonlinear and post-buckling responses of relatively thick functionally graded plates with oblique elliptical cutouts using a new semi-analytical approach. To model the oblique elliptical hole in a FGM plate, six plate-elements are used and the connection between these elements is provided by the well-known Penalty method. Therefore, the semi-analytical technique used in this paper is known as the plate assembly technique. In order to take into account for functionality of the material in a perforated plate, the volume fraction of the material constituents follows a simple power law distribution. Since the FGM perforated plates are relatively thick in this research, the structural model is assumed to be the first order shear deformation theory and Von-Karman's assumptions are used to incorporate geometric nonlinearity. The equilibrium equations for FGM plates containing elliptical holes are obtained by the principle of minimum of total potential energy. The obtained nonlinear equilibrium equations are solved numerically using the quadratic extrapolation technique. Various sets of boundary conditions for FGM plates and different cutout sizes and orientations are assumed here and their effects on nonlinear response of plates under compressive loads are examined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.