• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.93-107
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• 2023

In this paper, a density based topology optimization is proposed for generating of supports required in additive manufacturing to maintain the overhanging regions of main structures during layer by layer fabrication process. For this purpose, isogeometric analysis method is employed to model geometry and structural analysis of main and support structures. In order to model the problem two cases are investigated. In the first case, design domain of supports can easily be separated from the main structure by using distinct isogeometric patches. The second case happens when the main structure itself is optimized by using topology optimization and the supports should be designed in the voids of optimum layout. In this case, in order to avoid boundary identification and re-meshing process for separating design domain of supports from main structure, a parameterization technique is proposed to identify the design domain of supports. To achieve this, two density functions are defined over the entire domain to describe the main structure and supporting areas. On the other hand, since supports are under gravity loads while main structure and its stiffness is not completed during manufacturing process, in the proposed method, stiffness of the main structure is considered to be trivial and the gravity loads are also naturally applied to design support structures. By doing so, the results show reasonable supports are created to protect, continuously, overhanging surfaces of the main structure. Several examples are presented to demonstrate the efficiency of the proposed method and compare the results with literature.

• Proceedings of the KIEE Conference
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• 2002.07b
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• pp.726-728
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• 2002

The topology optimization of electromagnetic systems with two materials is investigated using the FEM. The design sensitivity equation for topology optimization is derived using the adjoint variable method and the continuum approach. The proposed method is applied to the topology optimization of C-core and compared to previous study with one material.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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• pp.164-170
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• 2006

To prevent the numerical instabilities in topology optimization, continuous approximation of material distribution (CAMD) is proposed to the homogenization design method (HDM) and the simple isotropic material with penalization (SIMP) method. The continuous FE approximation of design variables including high order elements is applied to the formulation of SIMP method. Numerical examples are presented to compare the efficiency of CAMD both in HDM and SIMP.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.6
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• pp.367-374
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• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1194-1202
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• 2002

A study on the topology optimization of a multi-spectral camera for space-use is presented. The optimization is carried out under self-weight and polishing pressure loading. A multi-spectral camera for space-use experiences degradation of optical image in the space, which can not be detected on the optical test bench on the earth. An optical surface deformation of a primary mirror, which is a principal component of the camera system, is an important factor affecting the optical performance of the whole camera system. In this study, topology optimization of the primary mirror of the camera is presented. As an objective function, a measure of Strehl ratio is used. Total mass of the primary mirror is given as a constraint to the optimization problem. The sensitivities of the objective function and constraint are calculated by direct differentiation method. Optimization procedure is carried out by an optimality criteria method. For the light-weight primary mirror design, a three dimensional model is treated. As a preliminary example, topology optimization considering a self-weight loading is treated. In the second example, the polishing pressure is also included as a loading in the topology optimization of the mirror. Results of the optimized design topology for the mirror with various mass constraints are presented.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1157-1176
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• 2015

This study presents optimizing structural topology patterns using regularization of Heaviside function. The present method needs not filtering process to typical SIMP method. Using the penalty formulation of the SIMP approach, a topology optimization problem is formulated in co-operation, i.e., couple-signals, with design variable values of discrete elements and a regularized Heaviside step function. The regularization of discontinuous material distributions is a key scheme in order to improve the numerical problems of material topology optimization with 0 (void)-1 (solid) solutions. The weak forms of an equilibrium equation are expressed using a coupled regularized Heaviside function to evaluate sensitivity analysis. Numerical results show that the incorporation of the regularized Heaviside function and the SIMP leads to convergent solutions. This method is tested using several examples of a linear elastostatic structure. It demonstrates that improved optimal solutions can be obtained without the additional use of sensitivity filtering to improve the discontinuous 0-1 solutions, which have generally been used in material topology optimization problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.281-290
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• 2003

Co Evolutionary Structural Design(CESD) Framework is presented, which can deal with the load design and structural topology design simultaneously. The load design here is the exploration algorithm that finds the critical load patterns of the given structure. In general, the load pattern is a crucial factor in determining the structural topology and being selected from the experts어 intuition and experience. However, if any of the critical load patterns would be excluded during the process of problem formation, the solution structure might show inadequate performance under the load pattern. Otherwise if some reinforcement method such as safety factor method would be utilized, the solution structure could result in inefficient conservativeness. On the other hand, the CESD has the ability of automatically finding the most critical load patterns and can help the structural solution evolve into the robust design. The CESD is made up of a load design discipline and a structural topology design discipline both of which have the fully coupled relation each other. This coupling is resolved iteratively until the resultant solution can resist against all the possible load patterns and both disciplines evolve into the solution structure with the mutual help or competition. To verify the usefulness of this approach, the 10 bar truss and the jacket type offshore structure are presented. SORA(Sequential Optimization & Reliability Assessment) is adopted in CESD as a probabilistic optimization methodology, and its usefulness in decreasing the computational cost is verified also.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1102-1109
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• 2006

In this paper, the polarization of piezoelectric materials is considered to improve actuation since the piezoelectric polarization has influences on the performance of the actuator. The topology design of compliant mechanism can be formulated as an optimization problem of material distribution in a fixed design domain and continuous approximation of material distribution (CAMD) method has demonstrated its effectiveness to prevent the numerical instabilities in topology optimization. The optimization problem is formulated to maximize the mean transduction ratio subject to the total volume constraints and solved using a sequential linear programming algorithm. The effect of CAMD and the performance improvement of actuator are confirmed through Moonie actuator and PZT suspension design.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.5
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• pp.1149-1160
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• 2005

Generally, the network topology design problem, which is difficult to solve with the classical method because it has exponentially increasing complexity with the augmented network size, is characterized as a kind of NP-hard combinatorial optimization problem. The problem of this research is to design the highly reliable network topology considering the connection cost and all-terminal network reliability, which can be defined as the probability that every pair of nodes can communicate with each other. In order to solve the highly reliable network topology design problem minimizing the construction cost subject to network reliability, we proposes an efficient two phase approach to design reliable network topology, i.e., the first phase employs, a genetic algorithm (GA) which uses $Pr\ddot{u}fer$ number for encoding method and backtracking Algorithm for network reliability calculation, to find the spanning tree; the second phase is a greedy method which searches the optimal network topology based on the spanning ree obtained in the first phase, with considering 2-connectivity. finally, we show some experiments to demonstrate the effectiveness and efficiency of our two phase approach.