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

• Structural Engineering and Mechanics
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• 제35권1호
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• pp.83-98
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• 2010

In this paper, the mass optimization of four bar linkages is carried out using genetic algorithms (GA) with single and dual constraints. The single constraint of bending stress and the dual constraints of bending and buckling stresses are imposed. From the movement response of the bar linkage mechanism, the analysis of the mechanism is developed using the combination of kinematics, kinetics, and finite element analysis (FEA). A penalty-based transformation technique is used to convert the constrained problem into an unconstrained one. Lastly, a detailed comparison on the effect of single constraint and of dual constraints is presented.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1995년도 가을 학술발표회 논문집
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• pp.1-8
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• 1995

This work presents a new method to deal with buckling constraints. The mathematical optimization process of truss structures proposed earlier by the author has been proved to be the most rigorous method. The inclusion of buckling constraints, however, gives rise to a new problem The allowable compression stress of a member changes from one design iteration to another. This changing stress limit creates a good deal of noise in selecting active constraints and makes the solution process unstable. This problem can be overcome by introducing relaxation parameters. This work, however, aims at establishing a more rigorous method by containing the allowable compression stress in the left hand side of the associated constraint.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.725-740
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• 2015

This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

• 대한기계학회논문집
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• 제16권4호
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• pp.630-648
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• 1992

본 연구에서는 여러가지 하중조건하에서 단순지지된 보강원통셸의 최소중량화 설계문제를 CONMIN을 사용하여 해석하고, 일반적인 대칭적층[0/.+-..theta./90]$_{s}$ 의 복합 적층원통셸, 복합적층honeycomb sandwich원통셸, 그리고 보강된 복합적층원통셸의 최 소중량화 설계문제에도 확장 적용한다. 설계변수(design variable)로는 등방성재료 인 경우와 복합적층인 경우 최대 9개, 부등제한조건으로는 전체좌굴(general buckling ), 준전체좌굴(panel buckling), 판 및 보강재의 국부좌굴(local cripping), 로링모드 (rolling mode), 그리고 응력과 변형률제한 등의 성질제한조건(behavior constraints) 과 설계변수의 상, 하한을 나타내는 기하학적 제한(side constraints)등 최대 32개를 설정한다. 본 최소중량화 설계예에서는 보강재의 최적단면형상을 검토하기 위하여 직사각형(R)형, I형, 그리고 T형 단면 등의 보강재들을 사용한다.

• 대한기계학회논문집A
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• 제25권9호
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• pp.1483-1492
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• 2001

A robust optimization procedure is applied to determine the design of the laminated composite plates with buckling constraints. In order to investigate the variation effect to the whole performance of a structure, both design variables and system parameters are assumed as random variables about their nominal values. The robust optimization method has advantages that the mean value and the variation of the performance function are controlled simultaneously and the second order sensitivity information is not required. Considering the information of uncertainty, robust optima for the buckling load of the laminated composite plates with cut-out is obtained. The robustness of the structures is compared to that of the deterministic optimization using scaling factors.

• Structural Engineering and Mechanics
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• 제16권3호
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
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• pp.80-84
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• 2000

A mesh superposition technique is presented for an efficient analysis of structural behavior. Refined child mesh is superimposed over parent elements for the region of interest. It is a kind of adaptive mesh refinement, which allows locally refined mesh without introducing transition region or multipoint constraints. Proper boundary condition is necessary to avoid redundant rigid body motion and kinematic compatibility between neighbor elements. Delamination buckling analysis is conducted to demonstrate accuracy and efficiency of the present method.

• 한국생산제조학회지
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• 제7권6호
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• pp.12-18
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• 1998

The optimal design for stiffened laminate composite cylindrical shells under combined loads is studied by a nonlinear mathematical search algorithm. The optimal design is accomplished with the CONMIN. several types of buckling modes with maximum allowable stresses and strains are included as constraints in the optimal design process, such as general buckling, panel buckling with either stringers or rings smeared out, local skin buckling, local crippling of stiffener segments. Rectangular or T type stringers and rectangular rings are used for stiffened laminate composite cylindrical shells.

• 한국강구조학회 논문집
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• 제27권2호
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• pp.131-142
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• 2015

트러스구조는 대형구조물의 설계 및 시공에 편리하며, 부재의 경량화에 따른 비용의 절검 효과를 얻을 수 있는 구조물로 최근 다양한 형태의 구조물건설에 많이 사용되고 있다. 본 연구에서는 응력, 좌굴 그리고 구조물의 고유진동수 제약조건을 고려한 트러스 구조물의 단면과 형상에 대해 최적설계를 하였다. 최적설계에서 최적화기법으로 HA-SA방법을 제시하였으며, HA-SA방법은 HA 초기메모리에서 최상의 설계를 SA의 초기 설계로 하여 최적화 하는 방법이다. 예제에 사용된 트러스 구조물은 고유진동수 제약조건으로 10-bar, 72-bar, 52-bar 트러스와 응력 및 좌굴응력 제약조건으로 18-bar, 47-bar 트러스를 사용하였다. 그리고 52-bar, 18-bar, 47-bar의 경우는 트러스의 형상을 최적설계 하였다. 예제로부터 다양한 설계 제약조건하에서 여러 연구결과와 HA, SA, GA, HA-SA방법에 의한 결과를 서로 비교하여 HA-SA방법의 적용성을 입증하였다.