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The paper deals with the investigation of linear buckling and free vibration behavior of layered and multiphase magneto‐electro‐elastic (MEE) beam under thermal environment. The constitutive equations of magneto‐electro‐elastic materials are used to derive finite element equations involving the coupling between mechanical, electrical and magnetic fields. The finite element model has been verified with the commercial finite element package ANSYS. The influence of magneto electric coupling on critical buckling temperature is investigated between layered and multiphase magneto‐electro‐elastic beam. Furthermore, the influence of temperature rise on natural frequencies of magneto‐electro‐elastic beam with layered and different volume fraction is presented.

The stress recovery procedures discussed in the present paper refer to a multi‐layered element of assembled Timoshenko beam elements. Directly calculated stresses for a multi‐layered beam model strongly depend on properties of the approximation functions, and are unrealistic. Thus, an enhanced procedure which circumvents the limitations of the interface variables model, and hierarchical model is proposed. Each material layer of the beam element is covered by one quadrilateral 9‐node element, providing a parabolic approximation of displacements. The stresses are evaluated using 2 × 2 Gauss points, projected to corner nodes, and smoothed within material layers. Numerical calculations show very good accordance of stresses yielded by this procedure with 2D results.

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 study aims to conduct an experimental study and finite element model (FEM) to investigate the flexural behavior of heat-damaged beams strengthened/repaired by hybrid fiber-reinforced polymers (HFRP).

Two groups of beams of (150 × 250 × 1,200) mm were cast, strengthened and repaired using different configurations of HFRP and tested under four-point loadings. The first group was kept at room temperature, while the second group was exposed to a temperature of 400°C.

It was found that using multiple layers of carbon fiber-reinforced polymer (CFRP) and glass fiber-reinforced polymer (GFRP) enhanced the strength more than a single layer. Also, the order of two layers of FRP showed no effect on flexural behavior of beams. Using a three-layer scheme (attaching the GFRP first and followed by two layers of CFRP) exhibited increase in ultimate load more than the scheme attached by CFRP first. Furthermore, the scheme HGC (heated beam repaired with glass and carbon, in sequence) allowed to achieve residual flexural capacity of specimen exposed to 400°C. Typical flexural failure was observed in control and heat-damaged beams, whereas the strengthened/repaired beams failed by cover separation and FRP debonding, however, specimen repaired with two layers of GFRP failed by FRP rupture. The FEM results showed good agreement with experimental results.

Few researchers have studied the effects of HFRP on strengthening and repair of heated, damaged reinforced concrete (RC) beams. This paper investigates, both experimentally and analytically, the performance of externally strengthened and repaired RC beams, in flexure, with different FRP configurations of CFRP and GFRP.

This paper aims to analyze deeply the effect of surface roughness conditions of the common interface of the two-layered riveted cantilever beams on their frictional damping during free lateral vibration at first mode. Here, the product, (µ × α), and damping ratio, ξ, are the parameters whose variations are analyzed in this investigation. For this, the influencing parameters considered are the natural frequency of vibration, f; the amplitude of initial excitation, y; and surface roughness value, Ra.

For experimentally evaluating logarithmic damping decrement, d, the frequency response function analyzer for the case of free lateral vibrations was used. Later, for evaluating the product, µ × α (where µ is the kinematic coefficient of friction and α is the dynamic slip ratio), and then, the damping ratio, ξ, the empirical relation suggested for logarithmic damping decrement, d, of riveted cantilever beams was used. After this, the full and reduced quadratic models of the product, µ × α, ξ, response surface methodology (RSM) with the help of Design Expert 11 software was used. Corresponding main effects plots, surface plots and prediction comparison plots were obtained to observe the variations of the product, µ × α, ξ for the variations of influencing parameters: f, y and Ra. Finally, a machine learning technique such as artificial neural networks (ANNs) using “nntool” present in MATLAB R13a software was used to predict the ξ for the different combinations of f, y and Ra.

The full and reduced quadratic regression models for the product, (µ × α) and the damping ratio, ξ of riveted cantilever beams for free lateral vibrations of the first mode in terms of the parameters: f, y and Ra were obtained. In addition, the main effects plots, surface plots and prediction comparison plots for the product, µ × α, ξ, with the corresponding experimental values of the product, µ × α, ξ, were obtained. Also, the execution of ANNs using MATLAB R13a software is proved to be the more accurate tool for the prediction of damping ratios in comparison to quadratic regression equations obtained from Design Expert 11 software. In the end, the assumption that the effect of surface roughness value on the product, (µ × α), and the damping ratio, ξ, is negligible is proved to be true using the main effects plots for the product, (µ × α) and ξ obtained from the Design Expert 11 software.

Obtaining the full and reduced quadratic regression equations for the product, (µ × α), and ξ of the two-layered riveted cantilever beams in terms of parameters: f, y and Ra was done. In addition, the conditions for the corresponding minimum and maximum values of the product, (µ × α), and ξ were obtained. Later, the main effects plots, surface plots and comparison plots of the predicted product, (µ × α), and ξ versus experimental product, (µ × α), and ξ were also obtained. Finally, the predicted values of the product, (µ × α), and ξ using the ANNs tool are observed to be the more accurate values in comparison to that obtained from RSM using the Design Expert 11 software.

This paper aims to present development of a layer‐wise (LW) beam model for geometric nonlinear finite element analysis of laminated beams with partial layer interaction.

The model is built assuming first order shear deformation theory (FSDT) at layer level and moderate interlayer slips. LW kinematic, strain and stress fields are established in view of co‐rotational finite element formulation. Laminated beam equilibrium relations are developed in strong, weak and matrix form. A notion of interface shear stress is used to define layer interactions.

Through suitable choice of kinematic model the co‐rotational approach is shown to provide means of obtaining robust finite element formulation for geometric nonlinear analysis of laminated structures with interlayer slips.

The proposed model is dedicated to geometric nonlinear finite element analysis of laminated beams undergoing large planar displacements, subject to small strains and moderate interlayer slips.

Novelty of the proposed approach is based on encompassing shear deformations in geometric nonlinear analysis of laminated beams with interlayer slips. Arbitrary number of layers is considered.

The purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.

The FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.

A series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.

This paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

The purpose of this paper is to deal with an analytical investigation of delamination fracture in the mixed-mode bending (MMB) multilayer beam configurations taking into account the material non-linearity.

The J-integral approach was applied in fracture analysis. The beam layers non-linear mechanical response was described by using a power-law stress-strain relation with four material constants. Analytical solutions of the J-integral were derived by using the technical beam theory. The fracture analysis developed is valid for MMB beams whose layers may have different thicknesses. Also, the values of material constants in the non-linear stress-strain equation may be different for each layer.

The effect of material constants, crack location and layer thicknesses on the non-linear fracture was evaluated. The analytical solutions obtained are very suitable for parametric studies of non-linear fracture behaviour. The approach developed here can be used for optimization of multilayered beam structures with respect to the delamination fracture performance. The present study can also be useful for the understanding of fracture in multilayered beams exhibiting material non-linearity.

For the first time, an analytical study was performed of the delamination fracture behaviour of the MMB multilayered beam configuration taking into account the material non-linearity.

This paper aims to present the potential of using aligned single-layer graphene sheets to reinforce the methyl methacrylate cantilever beam in low-velocity impact problem.

The Halpin–Tsai law is applied to compute the mechanical properties of isotropic polymer beam reinforced by aligned graphene sheet. Using both longitudinal and lateral displacements in composite beam, all components of the stress and strain fields are written. The equations of motion are derived by applying energy method, generalized Lagrange equations and Ritz method.

The analytical formulation accuracy is corroborated by comparing the present results with those available in the literature. Numerical examples indicate that the contact duration is decreased with increasing of graphene volume fraction, whereas the values of peak contact force, shear strain and shear stress at peak contact force tend to be vice versa. Also, among the results, shear stress at the peak contact force has the most effect with graphene volume fraction changes.

This research fulfils an identified need to investigate how graphene-reinforced beam behavior subjected to low-velocity impact can be enabled.

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.