• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.423-435
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• 2022

In this article, we present torsion-bending analysis of a composite FGM beam with an open section, according to the advanced and refined theory of 1D / 3D beams based on the 3D Saint-Venant's solution and taking into account the edge effects. The (initially one-dimensional) model contains a set of three-dimensional (3D) displacement modes of the cross section, reflecting its 3D mechanical behaviour. The modes are taken into account depending on the mechanical characteristics and the geometrical form of the cross-section of the composite FGM beam. The model considered is implemented on the CSB (Cross-Section and Beam Analysis) software package. It is based on the RBT/SV theory (Refined Beam Theory on Saint-Venant principle) of FGM beams. The mechanical and physical characteristics of the FGM beam continuously vary, depending on a power-law distribution, across the thickness of the beam. We compare the numerical results obtained by the three-beam theories, namely: The Classical Beam Theory of Saint-Venant (Classical Beam Theory CBT), the theory of refined beams (Refined Beam Theory RBT), and the theory of refined beams, using the higher (high) modes of distortion of the cross-section (Refined Beam Theory using distorted modes RBTd). The results obtained confirm a clear difference between those obtained by the three models at the level of the supports. Further from the support, the results of RBT and RBTd are of the same order, whereas those of CBT remains far from those of higher-order theories. The 3D stresses, strains and displacements, obtained by the present study, reflect the 3D behaviour of FGM beams well, despite the initially 1D nature of the problem. A validation example also shows a very good agreement of the proposed models with other models (classical or higher-order beam theory) and Carrera Unified Formulation 1D-beam model with Lagrange Expansion functions (CUF-LE).

• Journal of Aerospace System Engineering
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• v.1 no.3
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• pp.26-31
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• 2007

This paper addresses a method for structural optimum design of composite rotor blade. The basic model of a composite helicopter main rotor blade is designed and its parameters determining the structural/dynamic properties are studied. Through the investigation of flap/lag/torsional stiffness, the structural properties of the model are analyzed. In this study, helicopter rotor blades are analyzed by using VABS. The computer program VABS (Variational Asymptotic Beam Section Analysis) uses the variational asymptotic method to split a three-dimensional nonlinear elasticity problem into a two dimensional cross-sectional analysis and a one-dimensional nonlinear beam problem. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. In addition, the rotational stability of the blade is estimated by the frequency diagram from FE analysis(MSC.Patran/Nastran) to understand its vibrational property. From the result, design parameters to determine and optimize the properties of the model are presented.

• Journal of KSNVE
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• v.5 no.3
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• pp.327-335
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• 1995

The study deals with the vibration of a beam whose flexural and centroidal axes are not coincident. The elementary bending-twisting theory is employed to derive the equation of motion, in which the effects of rotary inertia are added to the bending displacements and the effects of warping are added to the twist. Bending translation is restricted to one direction so that one bending equation is used instead of two. The equations of motion are solved by using the boundary value problem. The exact natural frequencies are fund from the frequency equation, which is obtained from the condition that the homogeneous system of algebraic equations representing the spatial solution shall not yield a trivial solution. The orthogonal conditions are established, and the principal mode equations of forced vibration are derived. As an example, the cantilevered beam is chosen and the first some natural frequencies and their modal shapes are found.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.33-49
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• 1997

A method of analysis is proposed for curved multicell box girder grillages. The method can be used to analyze box girder grillages comprising straight and/or curved segments. Each segment can be modelled by a number of beam elements. Each element has three nodes and the nodal degrees of freedom (DOF) consist of the six DOF for a conventional beam plus DOF to account for torsional warping, distortion, distortional warping, and shear lag. This element is an extension of a straight element that was developed earlier. For a more realistic analysis of the intersection regions of non-colinear box girder segments, the concept of a rigid connector is introduced, and the compatibility requirements between adjoining elements in those regions are discussed. The results of the analysis showed good agreement with the shell finite element results, but the proposed method of analysis needs a fraction of the time and effort compared to the shell finite element analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Steel and Composite Structures
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• v.10 no.3
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• pp.223-243
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• 2010

This paper reports recent developments concerning the application of Generalised Beam Theory (GBT) to the structural analysis of steel-concrete composite bridges. The potential of GBT-based semi-analytical or finite element-based analyses in this field is illustrated/demonstrated by showing that both accurate and computationally efficient solutions may be achieved for a wide range of structural problems, namely those associated with the bridge (i) linear (first-order) static, (ii) vibration and (iii) lateral-torsional-distortional buckling behaviours. Several illustrative examples are presented, which concern bridges with two distinct cross-sections: (i) twin box girder and (ii) twin I-girder. Allowance is also made for the presence of discrete box diaphragms and both shear lag and shear connection flexibility effects.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.709-712
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• 2004

A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Computers and Concrete
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• v.11 no.5
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• pp.399-410
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• 2013

A nonlinear finite element analysis of R/C hybrid deep T-beam with web opening subjected to pure torsion is presented. Hexahedral 8-nodes and space truss element were used for modeling concrete and reinforcement. The reinforcement was assumed perfectly bonded to the corresponding nodes of the concrete element. The constitutive relations for concrete and reinforcement are based on the modified field theory and elastic perfectly plastic. The smear crack approach was adopted for modeling the crack. The torque-twist angle relationship curve based on the finite element analysis was compared to the experimental results. The comparison shows that the curve of torque-twist angle predicted by the nonlinear finite element analysis is linear before cracking and close to the experimental result. After cracking, the curve becomes nonlinear and stiffer compared to the experimental result.

• Journal of Korean Society of Steel Construction
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• v.17 no.1 s.74
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• pp.45-52
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• 2005

The object of this study was a cold-formed steel wall stud panel sheathed by gypsum boards. In the beam-analysis, the panel was treated as a simple beam with a uniform lateral loading. The deflections were calculated by considering the primary factors that reduced the stiffness of the panel. In the column-analysis, the panel was treated as a bearing wall with an axial load. By using an energy method, nominal axial strength could be evaluated by considering both flexural buckling and torsional-flexural buckling. All calculations were programmed and compared with the results of the experiment. In the beam-analysis, experimental deflections were close to theoretical deflections. In the column-analysis, the experimental values were also close to theoretical values in axial strength.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.759-769
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• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.