• Coupled systems mechanics
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• 제13권1호
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• pp.73-93
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• 2024

In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology.

• 항공우주시스템공학회지
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• 제17권1호
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• pp.24-32
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• 2023

본 논문에서는 기 개발된 로터 블레이드 해석 모델 중 구조 모델을 보완하여 기존에 수행한 HART II의 연구결과와 비교하였다. 구조 모델은 혼합변분 정식화 기반의 기하학적 정밀 보 모델이며, 블레이드의 기하학적 비선형 거동을 정밀하게 예측할 수 있다. 기존 해석 결과에서는 비틀림 변형과 구조하중 결과에서 실험결과 대비 위상차가 발생하였는데 본 연구에서는 기존 결과 대비 위상차가 현저히 감소한 결과를 도출하였다.

• Coupled systems mechanics
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• 제8권6호
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• pp.537-553
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• 2019

In this paper we present geometrically exact Kirchhoff's initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner's geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff's constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite's polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.

• Coupled systems mechanics
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• 제11권6호
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• pp.525-542
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• 2022

In this work we present an advanced approach to the design of small wind turbine support steel structures. To this end we use an improved version of previously developed geometrically exact beam models. Namely, three different geometrically exact beam models are used, the first two are the Reissner and the Kirchhoff beam models implementing bi-linear hardening response and the third is the Reissner beam capable of also representing connections response. All models were validated in our previous research for a static response, and in this work they are extended to dynamic response. With these advanced models, we can perform analysis of four practical solutions for the installation of small wind turbines in new or existing buildings including effects of elastoplastic response to vibration problems. The numerical simulations confirm the robustness of numerical models in analyzing vibration problems and the crucial effects of elastoplastic response in avoiding resonance phenomena.

• 한국전산구조공학회논문집
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• 제31권4호
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• pp.183-190
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• 2018

본 논문에서는 보의 대변형 및 비틀림 변형을 고려한 인간동력항공기 주익 main spar 질량 최적화 과정을 소개한다. 순차적 이차 프로그래밍 기법(sequential quadratic programming)을 최적화 기법으로 선정해 구조 최적설계에 적절한 최적화 알고리즘을 수행하였다. Main spar 내부 직경, 적층 두께 등을 설계변수로 설정하였다. 목적함수에는 질량 최소화, 굽힘 변형 변위 일정, 그리고 비틀림 변형 각도 일정 등의 요소를 포함하였다. 굽힘과 비틀림 변형 계산엔 대변형 해석에 적합한 기하학적 정밀 보 모델을 도입하였으며, 기하학적 정밀 보 모델에 필요한 단면 물성은 Variational Asymptotic Beam Sectional Analysis(VABS) 단면 해석프로그램를 통해 계산하였다. 그 결과 main spar의 굽힘 변형 및 비틀림 변형을 최대 1.45% 이내로 유지한 채로 7.88%의 질량 감소를 이루는 최적설계를 도출하였다, 이후 응력복원 및 변형률 복원을 통해 최적설계의 구조적 안정성과 최적화 과정의 타당성을 검증하였다.

• Structural Engineering and Mechanics
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• 제22권3호
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• pp.263-278
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• 2006

Starting with the geometrically non-linear formulation and the subsequent linearization, this paper presents a consistent formulation of the exact mechanical analysis of geometrically and materially linear three-layer continuous planar beams. Each layer of the beam is described by the geometrically linear beam theory. Constitutive laws of layer materials and relationships between interlayer slips and shear stresses at the interface are assumed to be linear elastic. The formulation is first applied in the analysis of a three-layer simply supported beam. The results are compared to those of Goodman and Popov (1968) and to those obtained from the formulation of the European code for timber structures, Eurocode 5 (1993). Comparisons show that the present and the Goodman and Popov (1968) results agree completely, while the Eurocode 5 (1993) results differ to a certain degree. Next, the analytical solution is used in formulating a general procedure for the analysis of layered continuous beams. The applications show the qualitative and quantitative effects of the layer and the interlayer slip stiffnesses on internal forces, stresses and deflections of composite continuous beams.

• 한국항공우주학회지
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• 제47권2호
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• pp.98-106
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• 2019

인간동력항공기의 날개는 고세장비의 형상을 가지고 있어 큰 굽힘변위가 발생한다. 본 논문에서는 고세장비 형상의 날개가 가지는 구조적인 한계를 붙임각을 변경함으로써 개선하고자 하였다. 날개의 익형 및 단면형상을 고정시킨 후 동일 수준의 양력 발생을 만족시킨다는 전제하에 붙임각의 변경에 따른 날개 끝단의 굽힘변위 변화 경향을 관측하였다. 이를 위해 유한날개의 양력, 항력, 모멘트 하중을 날개의 각 섹션에 분포시켰다. 그리고 EDISON의 "geometrically exact beam (GEB)" 프로그램과 "Variational Asymptotic Beam Sectional Analysis (VABS)" 단면해석 프로그램을 사용하여 변경된 설계안의 구조 안전도를 평가하였다. 또한, 다물체 동역학 해석 프로그램 DYMORE를 이용하여 본 논문에서 예측한 날개의 끝단 변위 예측값을 비교 검증하였다.

• 한국해양공학회지
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• 제11권4호
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• pp.7-22
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• 1997

A finite element analysis is performed for lateral buckling problems on the basis of a geometrically nonlinear formulation for a beam with small elastic strain but with possibly large rotations. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformations in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement. This is illustrated through several numerical examples and followed by appropriate discussion.

• Coupled systems mechanics
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• 제11권2호
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• 한국전산구조공학회논문집
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• 제34권5호
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• pp.287-292
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• 2021

본 논문에서는 CAD 시스템에서 사용하는 NURBS 기저함수를 사용하는 아이소-지오메트릭 해석(Isogeometric analysis) 방법과 기하학적으로 엄밀한 빔 모델링(geometrically exact beam model)을 활용하여 회전과 병진 운동이 결합된 새로운 형태의 메타물질(metamaterial)에 대한 해석을 진행하였다. 이차원 셀 구조는 자유형상변환(Free-form deformation) 법과 적절한 내삽법(Interpolation)을 통해 원통 위에 입혀졌다. 원통의 치수와 셀 개수가 비틀림 각도에 미치는 영향이 매개변수 연구(parametric study)를 통해 확인되었다. 비틀림과 병진 운동이 결합된 구조의 메커니즘에 대해 수치 예제를 통해 알아보았다.