• Structural Engineering and Mechanics
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• 제30권4호
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• pp.427-444
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• 2008

A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

• Steel and Composite Structures
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• 제22권5호
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• pp.1163-1192
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• 2016

This paper presents the cost optimization of a composite I beam floor system, designed to be made from a reinforced concrete slab and steel I sections. The optimization was performed by the mixed-integer non-linear programming (MINLP) approach. For this purpose, a number of different optimization models were developed that enable different design possibilities such as welded or standard steel I sections, plastic or elastic cross-section resistances, and different positions of the neutral axes. An accurate economic objective function of the self-manufacturing costs was developed and subjected to design, resistance and deflection (in)equality constraints. Dimensioning constraints were defined in accordance with Eurocode 4. The Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm was applied together with a two-phase MINLP strategy. A numerical example of the optimization of a composite I beam floor system, as presented at the end of this paper, demonstrates the applicability of the proposed approach. The optimal result includes the minimal produced costs of the structure, the optimal concrete and steel strengths, and dimensions.

• Steel and Composite Structures
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• 제1권2호
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• pp.245-268
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• 2001

The analysis of steel-concrete composite joints presents some particular aspects that increase their complexity when compared to bare steel joints. In particular, the influence of slab reinforcement and column concrete encasement clearly change the moment-rotation response of the joint. Starting from an energy approach developed in the context of steel joints, an extension to composite joints is presented in this paper that is able to provide closed-form analytical solutions. In addition, the possibility of tri-linear or non-linear component behaviour is also incorporated in the model, enabling adequate treatment of the influence of cracked concrete in tension and the softening response of the column web in compression. This methodology is validated through comparison with experimental tests carried out at the University of Coimbra.

• International Journal of Concrete Structures and Materials
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• 제11권2호
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• pp.261-273
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• 2017

The control of the deformative behaviour of pre-stressed concrete roof elements for a satisfactory service performance is a main issue of their structural design. Slender light-weight wing-shaped roof elements, typical of the European heritage, are particularly sensitive to this problem. The paper presents the results of deformation measurements during storage and of both torsional-flexural and purely flexural load tests carried out on a full-scale 40.5 m long innovative wing-shaped roof element. An element-based simplified integral procedure that de-couples the evolution of the deflection profile with the progressive shortening of the beam is adopted to catch the experimental visco-elastic behaviour of the element and the predictions are compared with normative close-form solutions. A linear 3D fem model is developed to investigate the torsional-flexural behaviour of the member. A mechanical non-linear beam model is used to predict the purely flexural behaviour of the roof member in the pre- and post-cracking phases and to validate the loss prediction of the adopted procedure. Both experimental and numerical results highlight that the adopted analysis method is viable and sound for an accurate simulation of the service behaviour of precast roof elements.

• 한국전산구조공학회논문집
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• 제32권6호
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• pp.359-366
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• 2019

PS 강거더의 비선형, 비탄성 거동에 대한 편향부 효과를 조사하기 위하여 PS 시스템의 거동특성에 대한 실험적 및 이론적 연구를 수행한다. 이를 위하여 H빔, 편심을 갖는 직선 케이블, 정착부, 그리고 편향부를 갖는 4개의 시험체를 제작하여 2점 하중에 의한 파괴거동시험을 수행한다. 또한, 편향부가 없는 경우와 등간격으로 3개의 편향부가 설치된 경우의 PS 시스템에 대하여 면내 변형이론을 새로이 정식화하고 symbolic 연산을 수행할 수 있는 메스메티카를 이용하여 비선형해를 구한다. 실험 및 이론적 연구의 타당성을 검증하기 위하여 박벽보요소, 강성이 매우 큰 보요소, 그리고 케이블-트러스요소로 구성되는 유한요소모델을 구축하고 비탄성해석을 수행하여 그 결과를 실험결과 및 해석해와 비교한다. 결과적으로 외부에 설치된 비부착 편향부로 인하여 H빔의 횡변위가 강하게 구속되어 PS 시스템의 강성 및 파괴강도는 편향부가 없는 경우와 비교할 때 크게 증가한다.

• Smart Structures and Systems
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• 제18권2호
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• pp.335-354
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• 2016

This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• 한국해양공학회지
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• 제9권1호
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• pp.22-35
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• 1995

A simplified numerical procedure have proposed to trace the dynamic behaviour of offshore tubulars subjected to lateral collision impacts. The local denting and overall bending deformation of the struck tubular are represented by a non-linear spring and an elastic visco-plastic beam respectively. In this method a temporal finite difference method and a spacial finite element method are employed. Using this method various boundary conditions are able to considered and their effects on the extent of damage can be quantified. The extent of damage due to collision can be obtained as results of the dynamic analysis. The predictions using the proposed method have been correlated with existing test results and then the reliability of the procedure has been substantiated. The characteristics of the dynamic response of tubulars under lateral impacts are compared for simply supported roller and fixed end conditions and their effects on the extent of damage are specfied.

• Structural Engineering and Mechanics
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• 제89권1호
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• pp.23-31
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• 2024

Ratcheting is the cyclic buildup of inelastic strain on a structure resulting from a combination of primary and secondary cyclic stress. It can lead to excessive plastic deformation, incremental collapse, or fatigue. Ratcheting has been numerically investigated on a cantilever beam, considering the current study's primary and secondary bending loads. In addition, the effect of input frequency on the onset of ratcheting has been investigated. The non-linear dynamic elastic-plastic approach has been utilized. Analogous to Yamashita's bending-bending ratchet diagram, a non-dimensional ratchet diagram with a frequency effect is proposed. The result presents that the secondary stress values fall sequentially with the increase of primary stress values. Moreover, a displacement amplification factor graph is also established to explain the effect of frequency on ratchet occurrence conditions. In terms of frequency effect, it has been observed that the lower frequency (0.25 times the natural frequency) was more detrimental for ratchet occurrence conditions than the higher frequency (2 times the natural frequency) due to the effect of dynamic displacement. Finally, the effect of material modeling of ratcheting behavior on a beam is shown using different hardening coefficients of kinematic hardening material modeling.

• Computers and Concrete
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• 제30권6호
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• pp.433-443
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• 2022

In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FG-GPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.