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This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters.

Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time.

The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions.

The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to present the development and application of a numerical formulation for the structural dynamics and aeroelastic analysis of new generation helicopter and tiltrotor rotor blades. These are characterized by a curvilinear elastic axis, typically with the presence of tip sweep and anhedral angles.

The structural dynamics model implemented is based on nonlinear, flap‐lag‐torsion, rotating beam equations that are valid for slender, homogeneous, isotropic, non‐uniform, twisted blades undergoing moderate displacements. A second‐order approximation scheme for strain‐displacement is adopted. Aerodynamic contributions for aeroelastic applications are derived from sectional theories, with inclusion of wake inflow models to take into account three‐dimensional effects. The numerical integration is obtained through implementation within the COMSOL Multiphysics Finite‐Element‐Method (FEM) software code, considering the elastic axis of arbitrary curvilinear shape.

The computational tool developed is validated by comparisons with results available in the literature. These demonstrate the capability of the tool to accurately predict structural dynamics and aeroelastic behavior of curved‐axis rotor blades. In particular, the influence of sweep and anhedral angles at the blade tip is successfully captured.

The numerical tool developed is limited to the analysis of isotropic blades, with a simple sectional aerodynamic modeling for aeroelastic applications. However, the flexibility of the process through which the proposed tool has been developed is such that a moderate effort is required for its extension to composite blades and more accurate aerodynamic loads predictions.

The proposed computational solver is a reliable tool for preliminary design and optimal design processes of helicopter and tiltrotor rotor blades.

Computational tools for rotors with advanced‐geometry blades are not commonly available. Therefore, the presentation of a successful way to implement structural dynamics/aeroelastic mathematical formulations for rotor blades with curvilinear elastic axis in highly flexible, multiphysics, FEM‐based, commercial software may be of interest for designers and researchers.

This paper aims to present a new numerical model for the stability and load‐bearing capacity computation of space reinforced‐concrete (R/C) frame structures. Both material and geometric nonlinearities are taken into account. The R/C cross‐sections are assumed to undergo limited distortion under torsional action.

A simple, global discretization using beam‐column finite elements is preferred to a full, global discretization using 3D elements. This is more acceptable from a practical point of view. The composite cross‐section is discretized using 2D elements to apply the fiber decomposition procedure to solve the material and geometrical nonlinear behavior of the cross‐section under biaxial moments and axial forces. A local discretization of each beam element based on the comparative body model (i.e. a prismatic body discretized using brick elements, element by element, during the incremental‐iterative procedure) allows determining the torsional constant of the cross‐section under limited warping. The classical global iterative‐incremental procedure is then used to solve the resulting material and geometric nonlinear problem.

It has been noticed that, in case of a limited distortion of the cross‐section, the torsional constant of homogeneous (linear elastic) materials is greater than the one obtained from the Saint‐Venant theory. However, due to low‐tensile strength of concrete materials, the torsional constant decreases significantly after an early loading phase, primarily due to the lack of reinforcing flanges.

The current study does not cover the torsion analysis of R/C cross‐section with stirrups. Besides, the bond‐slip effect between concrete and steel reinforcement is not taken into account, nor is the local buckling of the beam flanges and rebar.

This new numerical model has been implemented in a computer program for effectively computing the nonlinear stability and load bearing capacity of space R/C frames.

The authors believe that the comparative body model should bring a new approach to the solution of torsion problems with limited distortion of cross‐sections in material and geometric nonlinear analysis of space R/C frames.

The purpose of this work is to perform the finite element analysis (FEA) for the numerical discretization of sections with different arrangements of Web openings to investigate the torsion behavior. Typical hexagonal and circular Web opening sections are extensively used in steel construction due to economic development in building design. However, the use of sections with different arrangements of Web opening had improved the performance of the section with Web opening in terms of structural behavior which leads to economic design compared to typical I-beam.

The accuracy of FE results allows extensive numerical analysis of stress concentration magnitude for sections with Web openings, concentrating on the sizes and positions of the Web opening. Five shapes and three sizes of Web opening are used in this work. The shapes involved are c-hexagon, hexagon, octagon, circular and square, whereas the sizes of the Web opening involved are 0.67 D, 0.75 D and 0.80 D where D is the height of the Web. Two types of models for 200 × 100 × 8×6 mm steel section involved which is Model 1, where the section with 50 mm edge and 150 mm center-to-center distance and Model 2, where the section with 100 mm edge and 200 mm center-to-center distance.

It was found that these configurations affect the section with various shapes of Web openings sizes (0.67 D, 0.75 D, and 0.80 D). This also includes the spacing distances, with 50 mm edge and 150 mm center-to-center distance and also a section with 100 mm edge and 200 mm center-to-center distance. Through the FEA results of Model 1 and Model 2, it is found that 50% reduction in horizontal member length in hexagon Web opening, from 50 mm to 20 mm, caused increment about 30%–53% stress concentration in Web for c-hexagon. However, for a stress analysis of c-hexagon, geometry resulted in a lower stress concentration in the Web than other Web opening.

Additionally, the work emphasized the efficiency of Web opening shapes by using an appropriate Web opening radius in section with c-hexagon, hexagon, octagon, square and circular shapes. The final results show the contribution of appropriate Web opening radius to increase the section torsional capacity. It is observed that the torsional capacity at certain loading condition and its angle of twist is analysed.

The purpose of this paper is to get a more consistent finite element description for three-dimensional (3D) Timoshenko beam elements. It extends the common description of beam elements by modifying the shape functions and considers the warping of the cross-section due to torsion.

The paper builds mainly on a finite element description of 3D Timoshenko beam elements. The implementation of high-order shape functions for torsion is done by adding a seventh degree of freedom to the system.

The results reveal that for some beams, depending on their physical dimensions, the warping of the cross-section has large influence. In comparison to a conventional FE program, the extended finite element description considers the warping and yields more accurate results.

An application of the extended finite element description is done with an implementation of the code in MATLAB. The static and dynamic behavior of a rotor in an electrical machine is investigated.

This paper presents a more consistent finite element description of 3D Timoshenko beam elements considering the warping. A comparison to conventional finite element descriptions is given.

The paper reports experiments carried out on beams in pure bending. The material used was a cast magnesium alloy AZ855. The beam sections were rectangular, circular, I‐section, T‐scction and diamond. One series of tests was carried out up to 1 per cent fibre strain. A second series of tests was carried out up to fracture. Tension and compression tests were also made on the material. The experimental results show conclusively that the usual theory of plastic bending is correct and that the tension‐compression stress‐strain curve of the material may be used to determine the bending moment‐curvature relationships, etc., for a beam. Measurements of neutral axis shift also confirm the predictions of plastic bending theory.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

THE kinetic heating associated with supersonic flight produces temperature gradients within the aircraft structure. These in their turn are responsible for so‐called ‘thermal stresses’ in the components. The calculation of these effects falls into two stages. The first stage consists in the application of the theory of heat transfer to obtain the history of the temperature distribution in the structure. The second stage uses this data to obtain distributions of stress within the structure, resulting from these imposed temperature gradients and proceeds to assess their influence on strength and stiffness. The present paper is concerned entirely with this second stage of the problem and derives basic formulae for the analysis of beam‐like structures and components. The results can be applied to wings, fuselages, etc., on the one hand, and to linear reinforcing members like stringers and longerons on the other, in the same way as the usual theories of bending and torsion are applied in the isothermal case.

Due to the enormous increase in economic development, structural steel material gives an advantage for the construction of stadiums, factories, bridges and cities building design. The purpose of this study is to investigate the behaviour of bending, buckling and torsion for I-beam steel section with and without web opening using non-linear finite element analysis.

The control model was simulated via LUSAS software with the four main parameters which included opening size, layout, shape and orientation. The analysis used a constant beam span which is 3.5 m while the edge distance from the centre of the opening to the edge of the beam is kept constant at 250 mm at each end.

The analysis results show that the optimum opening size obtained is 0.65 D while optimum layout of opening is Layout 1 with nine web openings. Under bending behaviour, steel section with octagon shapes of web opening shows the highest yield load, yield moment and thus highest structural efficiency as compared to other shapes of openings. Besides, square shape of web opening has the highest structural efficiency under buckling behaviour. The lower buckling load and buckling moment contribute to the higher structural efficiency.

Further, the square web opening with counter clockwise has the highest structural efficiency under torsion behaviour.