• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2000년도 추계학술대회논문집A
• /
• pp.345-350
• /
• 2000

In this paper, we introduce a new artificial material model for topology optimization. The present material model, named S-shape material model, accelerates topology optimization process especially in mathematical programming. We overcome the instability and the flatness in heuristic optimization process. Numerical examples show the superiority of the proposed material.

• Structural Engineering and Mechanics
• /
• 제33권3호
• /
• pp.285-306
• /
• 2009

In the literature the problem of the topology optimization of the structure is usually solved for one, clearly described from the mechanical point of view material. Generally the topology optimization answers the question of the distribution of this mentioned above material within the design domain. Finally, material-voids distribution it is obtained. In this paper, for the structure mainly strengthened or sometimes weakened by the inclusions, the variation approach of the topology optimization problem is formulated. This multi material approach may be useful for the design process of various mechanical or civil engineering structures which need to be more "refined" and more "optimal" than they can be using previous topology optimization procedures of optimization one material structures.

• Steel and Composite Structures
• /
• 제51권2호
• /
• pp.203-223
• /
• 2024

This study shows functionally graded material structural topology optimization under buckling constraints. The SIMP (Solid Isotropic Material with Penalization) material model is used and a method of moving asymptotes is also employed to update topology design variables. In this study, the quadrilateral element is applied to compute buckling load factors. Instead of artificial density properties, functionally graded materials are newly assigned to distribute optimal topology materials depending on the buckling load factors in a given design domain. Buckling load factor formulations are derived and confirmed by the resistance of functionally graded material properties. However, buckling constraints for functionally graded material topology optimization have not been dealt with in single material. Therefore, this study aims to find the minimum compliance topology optimization and the buckling load factor in designing the structures under buckling constraints and generate the functionally graded material distribution with asymmetric stiffness properties that minimize the compliance. Numerical examples verify the superiority and reliability of the present method.

• Steel and Composite Structures
• /
• 제27권1호
• /
• pp.27-33
• /
• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Steel and Composite Structures
• /
• 제27권2호
• /
• pp.177-184
• /
• 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.

• 한국전산구조공학회논문집
• /
• 제20권1호
• /
• pp.19-28
• /
• 2007

이산화 된 구조물의 위상최적화 과정은 균일하게 분포된 재료 밀도의 위상으로 표현되는 초기 설계영역을 시발점으로 한다. 최적화 과정 동안 구조물의 위상은 고정된 설계영역 내에 주어진 최적화 문제를 만족시키는 방향으로 변화하면서, 최종적으로 최적 위상의 재료 밀도 분포를 생산한다. Eschenauer et al.에 의해 제안되었던 설계영역 안에 구멍을 도입하는 개념은 원래 경계면의 최적화 문제에 대해 설계변수의 유한적인 변화를 촉진시켜 최적화의 수렴성 개선을 도모하기 위함이었으나, 위상최적화의 관점에서는 초기 위상의 정의에 따라 다양한 최적 위상이 생산되는 것을 의미한다. 본 연구에서는 초기 설계영역 안에 국소적인 솔리드 상을 도입해 초기 위상에 변화를 주었을 때, 한정된 재료 하에 구조물에 배치 가능한 다양한 최적 위상을 산출할 수 있음을 검증하였다. 수치 예제로서 초기 설계영역 내에 다양한 치수를 가지는 국부적인 원형 솔리드의 고정된 개수를 투입하여 간단한 MBB-보의 위상최적 설계를 수행하였다.

• 한국정밀공학회지
• /
• 제20권6호
• /
• pp.113-122
• /
• 2003

Topology optimization is begun with layout optimization that is attributed to Rozvany and Prager of the 1960's. They claimed that structure was transformed into truss connecting all the nodes of finite element and optimized by control of its sectional modulus. But, this method is partial topology optimization. General layout optimal design appliable to continum structure was proposed by Bendsoe and Kikuchi in 1988. Topology optimization expresses material stiffness of structure into function of arbitrary variable. If this variable is 1, material exists but if this variable is 0, material doesn't exist. Therefore, topology optimization searches the distribution function of material stiffness for structure. There are a few researchs for simple engineering problem such as topology optimization of square plane structure or truss structure. So, This study applied to topology optimization of table liner for vertical roller mill that is the largest scale in the world. After table liner decreased by 20% of original weight, the structure analysis for first optimized model was performed.

• 한국공작기계학회논문집
• /
• 제16권1호
• /
• pp.47-52
• /
• 2007

A material mixing method to obtain an optimal topology for a structure in a thermal environment was suggested. This method is based on Evolutionary Structural Optimization(ESO). The proposed material mixing method extends the ESO method to a mixing several materials for a structure in the multicriteria optimization of thermal flux and thermal stress. To do this, the multiobjective optimization technique was implemented. The overall efficiency of material usage was measured in terms of the combination of thermal stress levels and heat flux densities by using a combination strategy with weighting factors. Also, a smoothing scheme was implemented to suppress the checkerboard pattern in the procedure of topology optimization. It is concluded that ESO method with a smoothing scheme is effectively applied to topology optimization. Optimal topologies having multiple thermal criteria for a printed circuit board(PCB) substrate were presented to illustrate validity of the suggested material mixing method. It was found that the suggested method works very well for the multicriteria topology optimization.

• Structural Engineering and Mechanics
• /
• 제55권5호
• /
• pp.901-911
• /
• 2015

The goal of this study is to investigate computational convergence of optimal solutions, with respect to optimality criteria (OC) method and methods of moving asymptotes (MMA) as optimization model for non-linear programming of material topology optimization using an acceleration method that makes design variables rapidly move toward almost 0 and 1 values. 99 line topology optimization MATLAB code uses loop vectorization and memory pre-allocation as properly exploiting the strengths of MATLAB and moves portions of code out of the optimization loop so that they are only executed once as restructuring the program. Numerical examples of a simple beam under a lateral load and a given material density limitation provide merits and demerits of the present OC and MMA for 99 line topology optimization code of continuous material topology optimization design.

• Structural Engineering and Mechanics
• /
• 제51권5호
• /
• pp.793-808
• /
• 2014

The goal of this study is to evaluate and design steel plates with optimal material distributions achieved through a specific material topology optimization by using a CCARAT (Computer Aided Research Analysis Tool) as an optimizer, topologically optimally updating node densities as design variables. In typical material topology optimization, optimal topology and layouts are described by distributing element densities (from almost 0 to 1), which are arithmetic means of node densities. The average element densities are employed as material properties of each element in finite element analysis. CCARAT may deal with material topology optimization to address the mean compliance problem of structural mechanical problems. This consists of three computational steps: finite element analysis, sensitivity analysis, and optimality criteria optimizer updating node densities. The present node density based design via CCARAT using node densities as design variables removes jagged optimal layouts and checkerboard patterns, which are disadvantages of classical material topology optimization using element densities as design variables. Numerical applications that topologically optimize reinforcement material distribution of steel plates of a cantilever type are studied to verify the numerical superiority of the present node density based design via CCARAT.