• Steel and Composite Structures
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• 제35권6호
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• pp.717-727
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• 2020

The homotopy perturbation method (HPM) to predict the pre- and post-buckling behaviour of simply supported steel beams with rectangular hollow section (RHS) is presented in this paper. The non-linear differential equations solved by HPM derive from a kinematics where large twist and cross-sections distortions are considered. The results (linear and non-linear paths) given by the present HPM are compared to those provided by the Newton-Raphson algorithm with arc length and by the commercial FEM code Abaqus. To investigate the effect of cross-sectional distortion of beams, some numerical examples are presented.

• Journal of Electrical Engineering and Technology
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• 제9권5호
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• pp.1577-1581
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• 2014

This paper presents a method to minimize torque ripple of a V-type IPMSM using the PSO (Particle Swarm Optimization) method with FEM. The proposed algorithm includes one objective function and three design variables for a notch on the surface of a rotor. The simulation model of the V-type IPMSM has 3-phases, 8-poles and 48 slots with 2 notches on the one-pole rotor surface. The arc-angle, length and width of the notch are optimized to minimize the torque ripple of the motor. The cogging torque of the model is reduced by 55.6% and the torque ripple is decreased by 15.5 %. Also, the efficiency of the motor is increased by 15.5 %.

• 대한토목학회논문집
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• 제4권4호
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• pp.127-135
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• 1984

본 연구는 실제 하중을 받는 강재 아치구조의 최적형상을 다루었다. 목적함수로는 아치의 중량을 취했으며, 제약조건으로는 단면력, 체적, 아치리브의 길이, 아치부채 단연적의 조합으로 구성된 웅력제약초건을 고려하였다. 형상최적화문제는 아치부재의 단면척이 설계변수의 항으로 형성되었으며, 첫단계로 구조해석의 정밀도가 최적 설계의 목적함수값에 미치는 영향을 분석하였다. 형상최적화 알고리즘은 Two-space System 으로 형성되었고, Space 1 에서는 Modified Newton-Raphson Method에 의한 단면최적화, Space 2 에서는 Powell Method 에 의한 형상최적화를 시도하여 형상최적화 알고리즘을 도출하였다. 본 연구에서 도출된 최적화 알고리즘을 이용하여 아치의 단면최적화와 최적 아치형상에 관한 연구가 수행되었다. 이 알고리즘에 의해 실제 조건하에서 아치의 최적 Span-Rise 비를 구할 수 있다.

• Smart Structures and Systems
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• 제15권5호
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• pp.1233-1252
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• 2015

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented method.

• Steel and Composite Structures
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• 제27권1호
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Composites Research
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• 제13권1호
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• pp.69-77
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• 2000

본 논문에서는 크기가 일정한 비증분 하중과 크기가 커서 증분이론을 사용해야만 하는 증분하중이 동시에 가해지는 구조물의 비선형 해석을 위한 수정 호길이법을 제시한다. 수정된 호길이법에서는 비선형 계산을 수행할 때 증분하중에 의한 변위와 비증분 하중에 의한 변위를 구분하여 처리하게 된다. 제안된 방법의 타당성은 내압, 외압 및 압축하중을 받는 쉘 구조물의 비선형 거동에 대한 기존 결과와의 비교를 통해 검토하였다. 또한 비증분 하중과 증분하중이 함께 가해지는 대표적인 경우로서, 일정 횡압력과 축방향 증분 압축하중을 동시에 받는 쉘 구조물의 비선형 좌굴거동에 대한 인자연구를 수행하였다.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• 대한전자공학회논문지
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• 제26권7호
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• pp.157-165
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• 1989

무늬로 부터의 3차원 정보의 복구에 있어서, 투영의 왜곡효과는 왜곡된 무늬로 부터 구별되어야 한다. 그래서 본 논문에서는 가우스 구상의 보이는 면, 즉 반구상에서 무늬의 국소 해석을 통하여 면방향을 구하는 근사화된 최대유사 추정법을 제시한다. 정사영과 원을 영상시스템과 무늬소로 가정하고 원의 호길이에 일정하게 존재하는 법선방향의 정사영을 통한 법선 분포의 변화로 부터 면방향을 구한다. 구해진 면의 방향은 그래디언트 공간상의 한점으로 표시한 슬랜트와 틸트로 나타낸다. 또 구해진 면방향은 바늘지도로 나타낸다. 입력 데이터로는 임의로 만든 제주도 지도와 원무늬를 사용하여 알고리듬을 적용하였다.