Search results

In this study composite and sandwich beams with homogeneous core and homogeneous or Functional Graded Materials (FGM) faces under three point bending have been confronted. The purpose of this paper is to study numerically sandwich beams with homogeneous core and homogeneous or FGM faces under three point bending and to compare the results for the stress and displacement fields with those resulted of coating – substrate and homogeneous beams. Considering a crack in the lower face sheet to study the influence of the material gradation on the stress intensity factors.

At first a static finite element analysis is performed throughout the composite and sandwich beams, which is taking into account the graded character or not of the faces. For this reason five plane models are considered in order to have a comparable study for the stress and displacement fields of composite beams, which are subjected to three point bending. Second a crack in the lower face is considered parallel to the axis of gradation. When subjected to three point bending, this crack will propagate slowly perpendicular to the lower face.

Computed distributions of the stress fields across the core material and near the interfaces are given for different materials gradation of the faces; and possible crack-initiation positions have been identified. Stress intensity factors are calculated using finite element method, and assuming linear fracture mechanics and plane strain conditions.

The originality of the proposed analysis is to investigate for the first time numerically the influence of the FGMs or homogeneous faces in the core material of sandwich beams under three point bending relative to the coating – substrate and to the homogeneous beams. Second to study the influence of a crack in the lower graded face sheet on the overall behavior of the composite beam and to investigate the influence of the material gradation on the values of stress intensity factors.

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 investigate the thermoelastic functionally graded beam in a modified couple stress theory subjected to a dual-phase-lag model.

The governing equations are solved by using the Euler-Bernoulli beam assumption and the Laplace transform technique. The lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are obtained by ramp type heating in the transformed domain. A general algorithm of the inverse Laplace transform is developed to recover the results in a physical domain.

The lateral deflection, temperature change, displacement component, axial stress and thermal moment of the beam are computed numerically and presented graphically to show the effect of ramp time parameter and phase lags of heating.

Comparisons are made in the absence and presence of coupled dual-phase-lag thermoelastic and coupled thermoelastic L-S theories and also different values of ramp type parameter.

This paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.

The mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.

The analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.

Delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

The purpose of this paper is to present an analytical study of the delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam configuration. A delamination crack is located arbitrary along the height of the beam cross-section. The layers have different thicknesses and material properties. Perfect adhesion is assumed between layers. The material is functionally graded in both thickness and width directions in each layer. Besides, the material of the beam exhibits non-linear-elastic behaviour.

The delamination fracture behaviour is analysed in terms of the strain energy release rate. The J-integral approach is applied in order to verify the analysis of the strain energy release rate developed in the present paper.

The influence of material properties, the crack location along the height of the beam cross-section and the non-linear behaviour of the material on the delamination fracture is examined.

A non-linear delamination fracture analysis of multilayered two-dimensional non-symmetric functionally graded beam configuration is developed.

The purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration.

The fracture behaviour was studied analytically in terms of the strain energy release rate by applying methods of linear elastic fracture mechanics. It was assumed that the material is functionally graded along the beam width, height and length. The strain energy release rate was derived by analysing the stress and strain state in the beam cross-sections ahead and behind the crack front. An additional analysis of the strain energy release rate was performed by considering the beam strain energy for verification.

The influence of material gradient along the beam width, height and length on the delamination fracture behaviour was investigated. The effect of crack length was analysed too. The analytical approach developed is very useful for parametric fracture investigations. The results obtained in the present study can be applied for optimisation of three-dimensional functionally graded beam systems in their design with respect to delamination fracture behaviour.

An analytical approach for studying the delamination fracture in the SCB configuration that is functionally graded along the beam width, height and length was developed.

The purpose of this paper is to perform an analytical study of non-linear elastic delamination fracture in the multilayered functionally graded split cantilever beam (SCB) configuration. The SCB studied may have an arbitrary number of vertical layers. The material in each layer is functionally graded along the layer thickness. Also, the material properties may be different in each layer. The analytical solution derived was applied for parametric investigations in order to evaluate the effects of material properties and delamination crack location on the non-linear fracture behaviour.

The delamination fracture was studied in terms of the strain energy release rate. The SCB mechanical response was described by using a power-law stress-strain relation. A non-linear analytical solution for the strain energy release rate was derived by considering the SCB complementary strain energy. In order to verify the solution, an additional analysis of the strain energy release rate was developed by considering the complementary strain energy in the beam cross-sections ahead and behind the crack front.

The effects of material gradient, crack location along the beam width and non-linear material behaviour on the delamination fracture were evaluated. The analytical solution derived is useful for parametric studies of non-linear fracture in multilayered functionally graded beams.

Delamination fracture in the multilayered functionally graded SCB configuration was analysed with considering the non-linear material behaviour.

The purpose of this paper is to analyze and control the flutter vibrations of a thermoelastic functionally graded material (FGM) beam subjected to follower force using the piezoelectric sensors/actuators.

The beam is made of FGM properties which are functionally graded in the thickness direction according to the volume fraction power law distribution and change with temperature. As the two sides of the beam are located in two different temperatures, the thermoelastic effects are considered in the governing equation of motion. The beam is fixed from one end and a follower force is applied to the free end of it. An active control is applied to the system to suppress the flutter vibration of the beam.

After the simulation, the effects of the temperature gradient, magnitude of the follower force and piezoelectric lengths on the dynamic stability and the response of the system are studied. Simulation results show that the vibration of the system has been damped rapidly by applying the controller to the system.

Stability analysis and robust control of a thermoelastic FGM beam subjected to a follower force using piezoelectric sensors and actuators is the novelty of this study.

This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered.

Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions.

The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed.

The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. This formulation guarantees a zero transverse shear stress on the top and bottom surfaces of the shell and the shear correction factors is no longer needed.

The purpose of this paper is to define and solve the problem of an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling achievement of a maximum buckling load.

Two kinds of inclusions are considered: regular distribution of inclusions of different rigidities and non-uniform distribution of identical inclusions. It is shown that the optimal conditions are similar for both structural designs. The optimization problems are solved by using the homogenization method, and the target functions belong to the class of piece-wise continuous functions. Both optimized structures exhibit border zones free of any inclusions, and the largest amount of inclusions is localized in the central zone of the beams.

It has been shown that the final result of the carried out optimization of the internal structure for both studied types of FGM are similar. The relative increase in the buckling force of the FG beam with the optimized internal structure is on amount of 20 per cent while comparing it with the regular structure beam.

In contrary to a standard approach, this paper is aimed to detect and study a scenario of transition from heterogeneous to its counterpart homogeneous beam structure based on the consideration of the FGM inclusions. In addition, the problem of inversed transition from the optimized homogeneous structure to the optimal heterogeneous one is solved.