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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.

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.

The purpose of this paper is to discuss about evaluating the integrals involving B-spline wavelet on the interval (BSWI), in wavelet finite element formulations, using Gauss Quadrature.

In the proposed scheme, background cells are placed over each BSWI element and Gauss quadrature rule is defined for each of these cells. The nodal discretization used for BSWI WFEM element is independent to the selection of number of background cells used for the integration process. During the analysis, background cells of various lengths are used for evaluating the integrals for various combination of order and resolution of BSWI scaling functions. Numerical examples based on one-dimensional (1D) and two-dimensional (2D) plane elasto-statics are solved. Problems on beams based on Euler Bernoulli and Timoshenko beam theory under different boundary conditions are also examined. The condition number and sparseness of the formulated stiffness matrices are analyzed.

It is found that to form a well-conditioned stiffness matrix, the support domain of every wavelet scaling function should possess sufficient number of integration points. The results are analyzed and validated against the existing analytical solutions. Numerical examples demonstrate that the accuracy of displacements and stresses is dependent on the size of the background cell and number of Gauss points considered per background cell during the analysis.

The current paper gives the details on implementation of Gauss Quadrature scheme, using a background cell-based approach, for evaluating the integrals involved in BSWI-based wavelet finite element method, which is missing in the existing literature.

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.

The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications.

In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code.

First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios.

A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.

A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.

First, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.

The proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.

This work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.

This paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.

The governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.

The results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.

The results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

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.

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.

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.