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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.

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.

The dynamic stability of nano-tubes is an important issue in engineering applications. Dynamic stability of anti-symmetric coupled-carbon nanotubes (C-CNTs)-systems in thermal environment is presented in this paper. In this system, the top and bottom CNTs are subjected to axial harmonic load and action of the viscous fluid, respectively.

The coupling and surrounding mediums of the CNTs are simulated by visco-Pasternak foundation containing the spring, shear and damper coefficients. Based on the Timoshenko beam theory and Hamilton’s principle, the coupled motion equations are derived considering size effects using Eringen’s nonlocal theory. Using the exact solution in conjunction with Bolotin’s method, the dynamic instability region (DIR) of the coupled structure is obtained. The effects of various parameters such as small scale parameter, Knudsen number, fluid velocity, static load factor, temperature change, surrounding medium and nanotubes aspect ratio are shown on the DIR of the coupled system.

Results indicate that considering parameters such as small scale effects, static load factor, Knudsen number and fluid velocity shifts the DIR of C-CNTs to a lower frequency zone.

To the best of our knowledge, analyses of anti-symmetric coupled CNTs have not received enough attentions so far. In order to optimize the nanostructures designing, the main purpose of the present paper is to investigate nonlocal dynamic stability of CNTs subjected to axial harmonic load coupled with CNTs conveying fluid.

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.

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 work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.

Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.

The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.

A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

Fracture characterization of human cortical bone under pure mode I loading was performed in this work. The purpose of this paper is to validate the proposed test and procedure concerning fracture characterization of human cortical bone under pure mode I loading.

A miniaturized version of the double cantilever beam (DCB) test was used for the experimental tests. A data reduction scheme based on crack equivalent concept and Timoshenko beam theory is proposed to overcome difficulties inherent to crack length monitoring during the test. The application of the method propitiates an easy determination of the Resistance-curves (R-curves) that allow to define the fracture energy under mode I loading from the plateau region. The average value of fracture energy was subsequently used in a numerical analysis with element method involving cohesive zone modelling.

The excellent agreement obtained reveals that the proposed test and associated methodology is quite effective concerning fracture characterization of human cortical bone under pure mode I loading.

A miniaturized version of traditional DCB test was proposed for cortical human bone fracture characterization under mode I loading owing to size restrictions imposed by human femur. In fact, DCB specimen propitiates a longer length for self-similar crack propagation without undertaking spurious effects. As a consequence, a R-curve was obtained allowing an adequate characterization of cortical bone fracture under mode I loading.

The aim of this paper is to study the dynamic vibrations of embedded double‐walled carbon nanotubes (DWCNTs) subjected to a moving harmonic load with simply supported boundary conditions.

The model of DWCNTs is considered as an Euler‐Bernoulli beam with waviness along the length, which is more accurate than the straight beam in previous works. Based on the nonlocal beam theory, the governing equations of motion are derived by using the Hamilton's principle, and then the separation of variables is carried out by the Galerkin approach, leading to two second‐order ordinary differential equations (ODEs).

The influences of the nonlocal parameter, the amplitude of the waviness, the surrounding elastic medium, the material length scale, load velocity and van der Waals force on the nonlinear vibration of DWCNTs are important.

The dynamic responses of DWCNTs are obtained by using the precise integrator method to ordinary differential equations.

Hoping to uncover the physical principles of the vibration of the functionally graded material (FGM) microplate, by which the authors can make contributions to the design and manufacturing process in factories like micro-electro-mechanical system (MEMS) and other industries.

The authors design a method by establishing a reasonable mathematical model of the physical microplate composed of a porous FGM.

The authors discover that the porosity, the distributions of porosity, the power law of the FGM and the length-to-thickness ratio all affect the natural frequency of the vibration of the microplate, but in different ways.

Originally proposed a model of the micro FGM plate considering the different distributions of the porosity and scale effect and analyzed the vibration frequency of it.

This paper aims to develop a new multi-fiber element for predicting the structural behavior of planar-reinforced concrete (RC) members.

In this work, an exact multi-directional stiffness matrix is analytically derived based on the post-cracking bond-slip interaction between concrete and steel bars. The approach is also extended for large displacement analysis using Green–Lagrange finite strain tensor. In the proposed formulation, the weak form of governed differential equations is approximated by a trial-function expansion based on a finite strain-description and an additional degree of freedom for steel bars.

The findings provide a realistic description of cracking in the concrete structure. Numerical studies are conducted to examine the accuracy of the suggested approach and its capability to predict fairly complex responses of RC models. The findings prove that the proposed element can evaluate local and global responses of RC members, and it can be used as a reliable tool to reflect bond-slip effects in large displacement level. This leads to a robust and precise model for non-linear analysis of RC structures.

The methodology is capable of simulating coupled inelastic shear-flexural behavior of RC members through local stress field theory and Timoshenko beam model.