• Smart Structures and Systems
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• v.22 no.6
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• pp.689-697
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• 2018

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear 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 lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• 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.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.27-36
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• 2018

The objective of this work is to analyze geometrically nonlinear static analysis a simply supported laminated composite beam subjected to a non-follower transversal point load at the midpoint of the beam. In the nonlinear model of the laminated beam, total Lagrangian finite element model of is used in conjunction with the Timoshenko beam theory. The considered non-linear 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. In the numerical results, the effects of the fiber orientation angles and the stacking sequence of laminates on the nonlinear deflections and stresses of the composite laminated beam are examined and discussed. Convergence study is performed. Also, the difference between the geometrically linear and nonlinear analysis of laminated beam is investigated in detail.

• Steel and Composite Structures
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• v.26 no.6
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• pp.733-743
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• 2018

This paper presents post-buckling responses of a simply supported laminated composite beam subjected to a non-follower axially compression loads. In the nonlinear kinematic model of the laminated beam, total Lagrangian approach is used in conjunction with the Timoshenko beam theory. In the solution of the nonlinear problem, incremental displacement-based finite element method is used 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 distinctive feature of this study is post-buckling analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. The effects of the fibber orientation angles and the stacking sequence of laminates on the post-buckling deflections, configurations and stresses of the composite laminated beam are illustrated and discussed in the numerical results. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the laminated composite beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1222-1227
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• 2000

The optimization study are carried out for helicopter rotor blades with composite box-beam spar. The objective function is to minimize the weight of rotor blades subject to frequency, aeroelastic stability and failure constraints. Design variables include the number of ply and ply angles of the laminated walls. The beam model of a hinge less rotor blade is based on a large deflection beam theory to describe the arbitrary large deflections and rotations. The p-k method and unsteady two dimensional strip theory are used to calculate aeroelastic stability boundary.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Steel and Composite Structures
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• v.53 no.2
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• pp.169-194
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• 2024

Although the excellent characteristics of functionally graded materials (FGMs) cracks could be found due to manufacturing defects or extreme working conditions. The existence of these cracks may threaten the material or structural strength, reliability, and lifetime. Due to high cost and restrictions offered by practical operational features these cracked components couldn't be replaced immediately. Such circumstances lead to the requirement of assessing the dynamic performance of cracked functionally graded structural components especially under moving objects. The present study aims to comprehensively investigate the dynamic behavior of functionally graded cracked Timoshenko beams (FGCTBs) resting on Winkler foundation and subjected to moving load through shear locking free finite elements methodology. The through thickness material distribution is simulated by the exponential gradation law. The geometric discontinuity due to cracks is represented using the massless rotational spring approach. The shear locking phenomena is avoided by using the different interpolation functions orders for both deflections and rotations. Based on Timoshenko beam element, a shear locking free finite elements methodology is developed. The unconditionally stable Newmark procedure is employed to solve the forced vibration problem. Accuracy of the developed procedure is verified by comparing the obtained results with the available results and an excellent agreement is found. Parametric studies are conducted to explore effects of the geometrical, material characteristics, crack geometrical characteristics, the elastic foundation parameter, and the moving load speed on the dynamic behavior for different boundary conditions. Obtained results revealed the significant effect these parameters on the dynamic performance of FGCTBs.