• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.

• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.239-245
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• 2015

In this paper, to examine the difference between the linear and non-linear static, dynamic analysis for a structure, a cantilevered beam was used. Then, an external transverse static and dynamic loads were applied at the free end of the beam. Classical theories were used for the linear analysis and the EDISON CSD solver, co-rotational dynamic FEM program, was used for nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in the linear and nonlinear analysis. Then, normalized displacement of tip of the beam was predicted for different frequency ration and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.04a
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• pp.149-154
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• 2001

This paper presents the experimental study of the static stiffness for the BT Shank(7/24 Long Taper) and the HSK Tool Shank(1/10 Short taper). The static stiffness test was performed under different experimental conditions. The results obtained are as follows ; As known in the analysis results of the Load-Deflection diagram of the 7/24 Test tool shank, it is turned out that the diagram is a linear characteristics without regard to axial drawing force and according as the axial drawing force get to the 6kN, the static stiffness of the shank increase linearly. Thus the effective axial drawing force which maintains the static stiffness of the Main spindle taper of Machine Tool is larger than 6kN. It is found that the Load-Deflection diagram with 6kN of drawing force in the 1/10 Test tool shank is characterized by non-linear. But according as the axial drawing force is increasing by the 8kN, the diagram is characterized by linear. And increasing amount of deflection is about 60%. Therefore commendable axial drawing force is larger than 8kN. As a result, considering that the actual drawing force of the Machining Center is about 1300kgf and axial drawing force 12kN is equivalent amount as a 1220kgf, it is turned out that 1/10 Test tool shank superior to 7/24 Test tool shank in the static stiffness.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.467-475
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• 2015

In this paper, the behaviour of a cantilevered beam was predicted to examine the difference between linear and non-linear static, dynamic analysis for a structure by using CR nonlinear formulation. Then, external transverse static and dynamic loads were applied at the free tip of the beam. Classical theories were used for the present linear analysis and co-rotational dynamic FEM program was used for the present nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in both linear and nonlinear analysis. Then, normalized displacement at the tip of the beam was predicted for different frequency ratio and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.644-650
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• 1998

In this paper , a state space model for flexible beam is presented using the assumed-modes approach. The state space equation is derived for a flexible beam in which one end is connected to a motor and is driven by a torque equation and the other end is free. Many of the transfer function proposed thus far use the torque to the flexible beam as the input and the tip deflection of the flexible beam as the output. The Technique for the analysis and synthesis of the dual-input describing function(DIDF) is introduced here and the construction of a non-linear compensator, based on this technique, is proposed. This non-linear compensator, properly connected in the direct path of a closed-loop linear or non-linear control system. The above non-linear network is used to compensate linear and non-linear systems for instability, limit cycles, low speed of response and static accuracy. The effectiveness of the proposed scheme is demonstrated through computer simulation and experimental results.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.240-244
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• 2005

In this study a simple model is developed that predicts impact damage in a composite laminate using an analytical model. The model uses a non-linear approximation method (Rayleigh-Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point impact load at its centre. It is assumed that the deformation due to a static transverse load is similar to that occurred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with FEM predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture mechanics model developed by the second investigator and co-workers to calculate the compression after impact strength of such laminates. This approach could save significant running time when compared to FEM solutions.

• Journal of Mechanical Science and Technology
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• v.19 no.4
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• pp.947-957
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• 2005

In this study a simple model is developed that predicts impact damage in a composite laminate avoiding the need of the time-consuming dynamic finite element method (FEM). The analytical model uses a non-linear approximation method (Rayleigh-Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point impact load at its centre. It is assumed that the deformation due to a static transverse load is similar to that oc curred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with FEM predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture mechanics model developed by the second investigator and co-workers to calculate the compression after impact strength of such laminates. This approach could save significant running time when compared to FEM solutions.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.751-763
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• 2017

This article deals with the buckling behaviour of multilayered magneto-electro-elastic (MEE) plate subjected to uniaxial and biaxial compressive (in-plane) loads. The constitutive equations of MEE material are used to derive a finite element (FE) formulation involving the coupling between electric, magnetic and elastic fields. The displacement field corresponding to first order shear deformation theory (FSDT) has been employed. The in-plane stress distribution within the MEE plate existing due to the enacted force is considered to be equivalent to the applied in-plane compressive load in the pre-buckling range. The same stress distribution is used to derive the potential energy functional. The non-dimensional critical buckling load is accomplished from the solution of allied linear eigenvalue problem. Influence of stacking sequence, span to thickness ratio, aspect ratio, load factor and boundary condition on critical buckling load and their corresponding mode shape is investigated. In addition, static deflection of MEE plate under the sinusoidal and the uniformly distributed load has been studied for different stacking sequences and boundary conditions.