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The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.

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.

This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of micro-rotational/stretch/shear degrees of freedom of material particles and nonlocality simultaneously.

To consider nonlocal influences, both integral (original) and differential versions of Eringen’s nonlocal theory are used. Accordingly, integral nonlocal-micromorphic and differential nonlocal-micromorphic beam models are formulated using matrix-vector relations, which are suitable for implementing in numerical approaches. A finite element (FE) formulation is also provided to solve the obtained equilibrium equations in the variational form. Timoshenko micro-/nano-beams with different boundary conditions are selected as the problem under study whose static bending is addressed.

It was shown that the paradox related to the clamped-free beam is resolved by the present integral nonlocal-micromorphic model. It was also indicated that the nonlocal effect captured by the integral model is more pronounced than that by its differential counterpart. Moreover, it was revealed that by the present approach, the softening and hardening effects, respectively, originated from the nonlocal and micromorphic theories can be considered simultaneously.

Developing a hybrid size-dependent Timoshenko beam model including micromorphic and nonlocal effects. Considering the nonlocal effect based on both Eringen’s integral and differential models proposing an FE approach to solve the bending problem, and resolving the paradox related to nanocantilever.

The dynamic characteristics prediction and frequency-modulation of pipeline was an important work for the design of aircraft hydraulic structure.

A complex pipeline was deemed as a combination of several segments of straight-pipe-element (SPE). The 3D vibration equations of each SPE were established in their local coordinate system based on Timoshenko-beam model and Euler-beam model, respectively. The dynamic-stiffness-matrixes were deduced from the dispersion relation of these equations. According to the complex pipeline layout in the global coordinate system, a multi dynamic stiffness matrixes assembling (MDSMA) algorithm was carried out to establish the characteristic equations of the whole complex pipeline. The MDSMA solutions were verified to be consistent with experimental results.

The MDSMA method based on Timoshenko-Beam model was more suitable for the short span aviation pipeline and the vibration at high frequency stage (>350 Hz). The layout affected the pipeline's in-plane stiffness and out-plane stiffness, for the Z-shaped pipe, each order natural mode took place on the ZP and NP alternately. Reasonable designs of bending position and bending radius were effective means for complex pipeline frequency-modulation.

A new dynamic modeling method of aircraft complex pipeline was proposed to obtain the influence of pipeline layout parameters on dynamic characteristics.

In this paper, the standard Peridynamic Timoshenko beam model accounting for the shear deformation is chosen to describe the thick beam kinematics. Unfortunately, when applied to very thin beam structures, the standard Peridynamics (PD) encounters the shear locking phenomenon, leading to incorrect solutions.

PD differs from classical continuum mechanics and other nonlocal theories that do not involve spatial derivatives of the displacement field. PD is based on the integral equation instead of differential equations to handle discontinuities and other singularities.

The shear locking can be successfully alleviated using the developed selective integration method. In particular, this technique has been implemented in the standard PD, which allows an accurate result for a wide range of slenderness from very thin to thick (10 < L/t < 10³) structures. It can also accelerate the computational time for particular dynamic problems using fewer neighboring integration particles. Several numerical examples are solved to demonstrate the effectiveness of the proposed method for modeling beam structures.

The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam available in the literature, especially for very thin structures. A new alternative for the alleviation of shear locking in the Peridynamic Timoshenko beam, using selective integration. Hence the developed Peridynamic Timoshenko beam model is effective for thin and thick structures. A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

1. The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam proposed in the literature, especially for very thin structures.

2. The developed Peridynamic Timoshenko beam model based on selective integration is effective for thin and thick structures.

3. A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam proposed in the literature, especially for very thin structures.

The developed Peridynamic Timoshenko beam model based on selective integration is effective for thin and thick structures.

A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

This study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.

Timoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.

The results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.

The combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks.

WE define as an open tube a thin‐walled structure, the cross‐section of which does not include any closed circuit. This property is common, for example, to the curved channel, the interspar wing cut‐out and the panel stiffened with Z‐sections, illustrated in FIG. 1 (a, b, c). But the interspar cut‐out with nose cell (FIG. 1d) is not an open tube in the present definition. All structures discussed in this paper are assumed to be cylindrical and to have a constant cross‐section. It is relatively simple to extend the results to conical taper and longitudinally varying thickness, but this would be beyond the scope and space of the present analysis (see, however, ref. 5).

As far as steel‐rod structures are concerned the yield‐hinge theory is a very efficient approach of the ultimate‐load theory. Unfortunately, most of the published strategies suffer from considerable deficiencies which depend on two main reasons: first, the yield condition is not approximated very well, and, second, a flow rule is not incorporated at all. This may significantly affect the calculated load‐carrying behaviour and as a consequence the elasto‐plastic failure prediction. In the present paper a consistent formulation of a refined numerical method based on the yield‐hinge theory is consistently developed from the theory of plasticity. The derivation is carried out in the framework of a geometrically nonlinear Timoshenko beam theory discretized for the displacement based finite element method. The plastic deformations can be interpreted as three‐dimensional eccentric yield‐hinges (generalized yield‐hinges). The presented numerical xamples show the efficiency of the proposed method.

Timoshenko deformation calculation theory is suited to open section beam, which is not suited to closed section beam due to the difference stress distribution between the open and the closed section beam. This study aims to modify the deflection formula for prestressed concrete hollow slab (closed section beam) based on the Timoshenko theory.

(1) The deflection curves of the prestressed concrete hollow slab beam were obtained under a single point force; (2) linear phases of the deflection values, which were calculated by Timoshenko theory and ABAQUS, were compared with the measured values; (3) a modified coefficient related to the loading location was obtained to modify the Timoshenko theoretical formula in calculating the deflection of the prestressed concrete hollow slab.

(1) There is a large difference between the calculated values and the measured values at 4.3 < a/H < 7.7, and the differences are between 24 and 33 percent; (2) the Timoshenko deflection formula has been modified to fit for the calculation of the prestressed concrete hollow slab. The mean of f/ft is 1.01, and the variation coefficient is 0.09 after modification. Therefore, the modified formula can be better applied in the deflection calculation of the prestressed concrete hollow slab.

The Timoshenko theory is the most classical theory, which is often used to calculate the deformation of beams. The modified deflection formula for prestressed concrete hollow slab based on the Timoshenko theory is reliable and convenient, which can help engineers to calculate the deflection for closed section beam quickly.

The purpose of this paper is to analyse the deflection of the flexible airship structure in a new way which can decrease the calculation amount and improve the calculation speed.

Infinitesimal method and tapered inflatable beam theory are combined to study the mechanics characteristics of the airship. Firstly, infinitesimal method is introduced into the airship structure analysis. The airship structure can be divided into several tapered inflatable beam elements. Then, tapered inflatable beam theory is improved and a developed model of the tapered inflatable beam under bending moment is presented. Besides, it is proved that deflection caused by pure load and pure moment can be linearly superimposed. Finally, the deflection of the airship structure is studied by means of tapered inflatable beam theory.

This paper improved the tapered inflatable beam theory. Besides, the proposed method for deflection analysis of the flexible airship in this paper can reach the same accuracy with traditional finite element method (FEM). However, the number of beam elements is much less than the one of FEM shell elements, which will decrease the calculation amount much and improve the calculation speed.

The flexible airship is a new and developing research area in engineering practice. The proposed method in this paper provides one precise and high-speed way to analyse the deformation of the airship.

The paper draws its value from the contributions to development of inflatable structure and the flexible airship mechanics research.