• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.21-29
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• 2001

The general topology optimization can be considered as optimal material distribution. Such an approach can be unstable, unless composite materials are introduced. In this research, a nodal volume fraction method is used to obtain the optimum topology of continuum structures. This method is conducted from a composite material model composed of isotropic matter and spherical void. Because the appearance of the chessboard patterns makes the interpretation of the optimal material layout very difficult, this method contains a chessboard prevention strategy. In this research, several topology optimization problems are presented to demonstrate the validity of the present method and the recursive quadratic programming algorithm is used to solve the topology optimization problems.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.703-723
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• 2015

In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.495-503
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• 2001

In a functionally graded materials(FGM), two constituent material particles are mixed up according to a specific volume fraction distribution so that its thermoelastic behavior is definitely characterized by such a material composition distribution. Therefore, the designer should determine the most suitable volume fraction distribution in order to design a FGM that optimally meets the desired performance against the given constraints. In this paper, we address a numerical optimization procedure, with employing interior penalty function method(IPFM) and FDM, for optimizing 2D volume fractions of heat-resisting FGMs composed of metal and ceramic. We discretize a FGM domain into finite number of homogenized rectangular cells of single design variable in order for the optimization efficiency. However, after the optimization process, we interpolate the discontinuous volume fraction with globally continuous bilinear function in order to enforce the continuity of volume fraction distributions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.6
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• pp.988-995
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• 2001

Functionally graded materials(FGMs) are highlighted to be suitable for high temperature engineering due to their continuous distribution of material properties. In this paper, an optimal design is executed for determining the optimal material volume distribution pattern that minimizes the steady-state thermal stress of FGM heat-resisting composites. The interior penalty function method and the golden section method are employed as optimization techniques while the finite element method is used for thermal stress analysis. Through numerical simulations we suggest the volume fraction distributions that considerably improve initial thermal stress distributions.

• Computers and Concrete
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• v.25 no.4
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• pp.303-310
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• 2020

In this research, a hybrid mathematical model is derived using the higher-order polynomial kinematic model in association with soft computing technique for the prediction of best fiber volume fractions and the minimal mass of the layered composite structure. The optimal values are predicted further by taking the frequency parameter as the constraint and the projected values utilized for the computation of the eigenvalue and deflections. The optimal mass of the total layered composite and the corresponding optimal volume fractions are evaluated using the particle swarm optimization by constraining the arbitrary frequency value as mass/volume minimization functions. The degree of accuracy of the optimal model has been proven through the comparison study with published well-known research data. Further, the predicted values of volume fractions are incurred for the evaluation of the eigenvalue and the deflection data of the composite structure. To obtain the structural responses i.e. vibrational frequency and the central deflections the proposed higher-order polynomial FE model adopted. Finally, a series of numerical experimentations are carried out using the optimal fibre volume fraction for the prediction of the optimal frequencies and deflections including associated structural parameter.

• Journal of Mechanical Science and Technology
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• v.14 no.3
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• pp.306-313
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• 2000

The homogenization method and the density function method are common approaches to evaluate the equivalent material properties for design cells composed of matter and void. In this research, using a new topology optimization method based on the homogenized material with a penalty factor and the chessboard prevention strategy, we obtain the optimal layout of a structure for the natural frequency of a designated mode. The volume fraction of nodes of each finite element is chosen as the design variable and a total material usage constraint is imposed. In this paper, the subspace method is used to evaluate the eigenvalue and its corresponding eigenvector of the structure for the designated mode and the recursive quadratic programming algorithm, PLBA algorithm, is used to solve the topology optimization problem.

• Steel and Composite Structures
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• v.48 no.5
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• pp.583-597
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• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• Journal of Powder Materials
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• v.6 no.1
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• pp.81-87
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• 1999

Based on the pore filling theory, the microstructure evolution during liquid-phase sintering has been analyzed in terms of interrelationship between average grain size and relative density. For constant liquid volume fraction, the microsturucture trajectories reduced to a single curve in a grain size(x)-density(y) map, regardless of grain growth constant. The slope of curves in the map was inversely proportional to average pore size, while it increased fapidly with liquid volume fraction. Increase in pore volume fraction retarded the densification considerably, but showed marginal effect on the slope. The activation energy of densification was predicted to be the same as that of grain growth as long as the liquid volume fraction is constant for any temperature range studied. The present analyses on microstricture evolution may demonstrate the usefulness of pore filling theory and provide a guideline for process optimization of liquid-phase sintering.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.68-72
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• 1999

In an effort to construct a structure under the design principle of minimal use of materials for maximum performances, a discrete gradient structure has been introduced in laminate composite systems. Using a sequential linear programming method, the gradient structure of composites to maximize the buckling load was optimized in terms of fiber volume fraction and thickness of each layer. Theoretical optimization results were then verified with experimental ones. The buckling load of laminate composite showed maximum value with the outmost [$0^{\circ}$] layer concentrated by almost all the fibers when the ratio of length to width(aspect ratio) was less than 1.0. But when the aspect ratio was 2.0, the optimum was determined in a structure where the thickness and fiber volume fraction were well balanced in each layer. From the optimization of gradient structure, the optimal fiber volume fraction and thickness of each layer were proposed. Experimental results agreed well with the theoretical ones. Gradient structures have also shown an advantage in the weight reduction of composites compared with the conventional homogeneous structures.

• Steel and Composite Structures
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• v.27 no.2
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• pp.177-184
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like structures on elastic foundations by using classic plate theory. Multi-material optimal topology and shape are produced as an alternative to provide reasonable material assignments based on stress distributions. Multi-material topology optimization problem is solved through an alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to thin plate potential strain energy are derived in terms of multiphase design variables and Winkler-Pasternak parameters considering elastic foundation to apply to the current topology optimization. Numerical examples verify efficiency and diversity of the present topology optimization method of elastic thin plates depending on multiple materials and Winkler-Pasternak parameters with the same amount of volume fraction and total structural volume.