• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• Composites Research
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• v.19 no.5
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• pp.1-6
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• 2006

In this study, a closed-form analysis has been developed for the transverse shear behavior of thin-walled composite beams with closed cross-sections. The shear flow distributions and cross-section stiffness coefficients are derived analytically by using a mixed beam approach. The theory has been applied to single-celled composite box-beams with elastic couplings. The location of the shear center and the effect of transverse shear deformation on the static behavior of composite beams are investigated in the framework of the analysis. The present results are validated against those of a two-dimensional finite element analysis and a good correlation has been obtained for box-beam cases considered in this study.

• Coupled systems mechanics
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• v.6 no.1
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• pp.97-111
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• 2017

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

• Steel and Composite Structures
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• v.5 no.4
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• pp.259-269
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• 2005

Many slab-on-girder bridges around the world are being assessed because they are approaching the end of their anticipated design lives or codes are permitting higher allowable loads. Current analytical techniques assume that the concrete and steel components act independently, typically requiring full-scale load testing to more accurately predict the remaining strength or endurance of the structure. However, many of the load tests carried out on these types of bridges would be unnecessary if the degree of interaction resulting from friction at the steel-concrete interface could be adequately modeled. Experimental testing confirmed that interface friction has a negligible effect on the flexural capacity of a slab-on-girder beam however, it also showed that interface friction is significant under serviceability loading. This has led to the development of an improved analytical technique which is presented in this paper and referred to as the slab-on-girder mixed analysis service load assessment approach.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.163-170
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• 2008

The aeroelastic stability analysis of a soft-in-plane, composite hingeless rotor blade in hover and in forward flight has been performed by combining the mixed beam method and the aeroelastic analysis system that is based on a moderate deflection beam approach. The aerodynamic forces and moments acting on the blade are obtained using the Leishman-Beddoes unsteady aerodynamic model. Hamilton's principle is used to derive the governing equations of composite helicopter blades undergoing extension, lag and flap bending, and torsion deflections. The influence of key structural modeling issues on the aeroelastic stability behavior of helicopter blades is studied. The issues include the shell wall thickness, elastic couplings and the correct treatment of constitutive assumptions in the section wall of the blade. It is found that the structural modeling effects are largely dependent on the layup geometries adopted in the section of the blade and these affect on the stability behavior in a large scale.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.163-168
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• 2000

Once the chip has developed a mixed mode of side-curl and up-curl, it would generally curl to strike the tool flank. The development of the bending stresses and sheat in the chip would ultimately lead to chip failure. This paper approach this problem from a mechanics-based approach, by treating the chip as a 3-D elastic curved beam, and applying appropriate constraints and forces. The expressions for bending, shear and direct stresses are developed through an energy-based criterion. The location of the maximum stresses is also identified and explained for simulated test conditions.

• Advances in nano research
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• v.6 no.2
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• pp.163-182
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• 2018

Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.730-734
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• 2000

Once the Chip has developed a mixed mode of side-curl and up-curl, it would generally curl to strike the too] flank. The development of the bending stresses and shear in the chip would ultimately lead to chip failure. This paper attacks this problem from a mechanics-based approach. by treating the chip as a 3-D elastic curved beam, and applying appropriate constraints and forces. The expressions for bending. shear and direct stresses are developed through an energy-based criterion. The location of the maximum stresses is also identified and explained for simulated test conditions.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.793-807
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• 2015

Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method.

• Steel and Composite Structures
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• v.30 no.6
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• pp.493-516
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• 2019

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.