• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.759-777
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• 2013

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.41-49
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• 2007

In density-based topology optimization, 0/1 solutions are sought. Discrete topological problems are often relaxed with continuous design variables so that they can be solved using continuous mathematical programming. Although the relaxed methods are practical, grey areas appear in the optimum topologies. SIMP (Solid Isotropic Microstructures with Penalization) employs penalty schemes to suppress the intermediate densities. SRV (the Sum of the Reciprocal Variables) drives the solution to a 0/1 layout with the SRV constraint. However, both methods cannot effectively remove all the grey areas. SRV has some numerical aspects. In this work, a new scheme SIMP-SRV is proposed by combining SIMP and SRV approaches, where SIMP is employed to generate an intermediate solution to initialize the design variables and SRV is then adopted to produce the final design. The new method turned out to be very effective in conjunction with the method of moving asymptotes (MMA) when using for the stiffness topology optimization of continuum structures for minimum compliance. The numerical examples show that the hybrid technique can effectively remove all grey areas and generate stiffer optimal designs characterized with a sharper boundary in contrast to SIMP and SRV.

• Quantitative Bio-Science
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• v.37 no.2
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• pp.133-141
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• 2018

Graphical lasso is one of the most popular methods to estimate a sparse precision matrix, which is an inverse of a covariance matrix. The objective function of graphical lasso imposes an ${\ell}_1$-penalty on the (vectorized) precision matrix, where a tuning parameter controls the strength of the penalization. The selection of the tuning parameter is practically and theoretically important since the performance of the estimation depends on an appropriate choice of tuning parameter. While information criteria (e.g. AIC, BIC, or extended BIC) have been widely used, they require an asymptotically unbiased estimator to select optimal tuning parameter. Thus, the biasedness of the ${\ell}_1$-regularized estimate in the graphical lasso may lead to a suboptimal tuning. In this paper, we propose a two-staged bias-correction procedure for the graphical lasso, where the first stage runs the usual graphical lasso and the second stage reruns the procedure with an additional constraint that zero estimates at the first stage remain zero. Our simulation and real data example show that the proposed bias correction improved on both edge recovery and estimation error compared to the single-staged graphical lasso.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.12
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• pp.5978-5999
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• 2018

Pedestrian detection is a challenging area in the intelligent vehicles domain. During the last years, many works have been proposed to efficiently detect motion in images. However, the problem becomes more complex when it comes to detecting moving areas while the vehicle is also moving. This paper presents a variational optical flow-based method for motion estimation in vehicular traffic scenarios. We introduce a framework for detecting motion areas with small and large displacements by computing optical flow using a multilevel architecture. The flow field is estimated at the shortest level and then successively computed until the largest level. We include a filtering parameter and a warping process using bicubic interpolation to combine the intermediate flow fields computed at each level during optimization to gain better performance. Furthermore, we find that by including a penalization function, our system is able to effectively reduce the presence of outliers and deal with all expected circumstances in real scenes. Experimental results are performed on various image sequences from Daimler Pedestrian Dataset that includes urban traffic scenarios. Our evaluation demonstrates that despite the complexity of the evaluated scenes, the motion areas with both moving and static camera can be effectively identified.

• Steel and Composite Structures
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• v.46 no.1
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• pp.33-51
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• 2023

This research presents a multi-material topology optimization for functionally graded material (FGM) and nonFGM with elastic buckling criteria. The elastic buckling based multi-material topology optimization of functionally graded steels (FGSs) uses a Jacobi scheme and a Method of Moving Asymptotes (MMA) as an expansion to revise the design variables shown first. Moreover, mathematical expressions for modified interpolation materials in the buckling framework are also described in detail. A Solid Isotropic Material with Penalization (SIMP) as well as a modified penalizing material model is utilized. Based on this investigation on the buckling constraint with homogenization material properties, this method for determining optimal shape is presented under buckling constraint parameters with non-homogenization material properties. For optimal problems, minimizing structural compliance like as an objective function is related to a given material volume and a buckling load factor. In this study, conflicts between structural stiffness and stability which cause an unfavorable effect on the performance of existing optimization procedures are reduced. A few structural design features illustrate the effectiveness and adjustability of an approach and provide some ideas for further expansions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.7
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• pp.4087-4092
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• 2014

The gangway connection of the articulated high speed railway vehicles (HSRV) is a double wrinkled rubber component to seal the air of the corridor under a range of angular deviations between the carriage end parts. From the results of non-linear structural analysis, one of the severe loading conditions for the connection is mixed mode (rolling+yawing) angular displacements while passing through the small-radius curved siding track of the HSRV depot. In this study, to ensure the safety enhancement of the component, the optimal design for the cross section of that was performed using the Solid Isotropic Material with Penalization (SIMP) method. Nonlinear finite element analysis confirmed that the decreases in the maximum principal strain of the optimized design under rolling and mixed modes are 68% and 39%, respectively, compared to the initial design.

• Earthquakes and Structures
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• v.12 no.3
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• pp.349-357
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• 2017

The design of reinforced concrete structures strongly depends on the value of the compression concrete strength used for the structural components. Given the uncertainties involved on the materials quality provided by concrete manufacturers, in the construction stage, these components may be either over or under-reinforced respect to the nominal condition. If the structure is under reinforced, and the deficit on safety level is not as large to require the structure demolition, someone should assume the consequences, and pay for the under standard condition by means of a penalty. If the structure is over reinforced, and other failure modes are not induced, the builder may receive a bonus, as a consequence of the higher, although unrequested, building resistance. The change on the building safety level is even more critical when the structure is under a seismic environment. In this research, a reliability-based criteria, including the consideration of expected losses, is proposed for bonification/penalization, when there are moderated differences between the supplied and specified reinforced concrete strength for the buildings. The formulation is applied to two hypothetical, with regular structural type, 3 and 10 levels reinforced concrete buildings, located on the soft soil zone of Mexico City. They were designed under the current Mexican code regulations, and their responses for typical spectral pseudoaccelerations, combined with their respective occurrence probabilities, are used to calculate the building failure probability. The results are aimed at providing objective basis to start a negotiation towards a satisfactory agreement between the involved parts. The main contribution resides on the explicit consideration of potential losses, including the building and contents losses and the business interruption due to the reconstruction period.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.197-205
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• 2017

We investigate the slat noise generation mechanism by using large-eddy simulation (LES) and simple source modeling based on linearized Euler equations. An incompressible LES of an MD 30P30N three-element airfoil in the high-lift configuration is conducted at $Re_c=1.7{\times}10^6$. Using the total derivative of the hydrodynamic pressure (DP/Dt) acquired from the incompressible LES, representative noise sources in the slat cove region are characterized in terms of simple sources such as frequency-specific monopoles and dipoles. Acoustic radiation around the 30P30N multi-element airfoil is effectively computed using the Brinkman penalization method incorporated with the linearized Euler equation. The directivity pattern of $p^{\prime}_{rms}$ at $r=20c_{slat}$ in the multiple sources is closely compared to that obtained by the application of the LES/Ffowcs-Williams and Hawking's methods to the entire flow field. The power spectrum of p' at ${\theta}=290^{\circ}$ is in good agreement with the data reported in BANC-III, especially the broadband part of the spectrum with a decaying slope ${\propto}f^{-3}$.

• Journal of Ocean Engineering and Technology
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• v.34 no.4
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• pp.263-271
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• 2020

In this study, we performed a three-dimensional (3D) topology optimization of a fixed offshore structure to enhance its structural stiffness. The proposed topology optimization is based on the solid isotropic material with penalization (SIMP) method, where a volume constraint is applied to utilize an equivalent amount of material as that used for the rule-based scantling design. To investigate the effects of the main legs of the fixed offshore structure on its structural stiffness, the leg region is selectively considered in the design domain of the topology optimization problem. The obtained optimal designs and the rule-based scantling design of the structure are manufactured by 3D metal printing technology to experimentally validate the topology optimization. The behaviors under compressive loading of the obtained optimal designs are compared with those of the rule-based scantling design using a universal testing machine (UTM). Based on the structural experiments, we concluded that by employing the topology optimization method, the structural stiffness of the structure was enhanced compared to that of the rule-based scantling design for an equal amount of the fabrication material. Furthermore, by effectively combining the topology optimization and rule-based scantling methods, we succeeded in enhancing the structural stiffness and improving the breaking load of the fixed offshore structure.