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Here the healing process of glass/epoxy composites is studied experimentally. The healing agent is composed of ML506 epoxy resin and HA-11 hardner which is charged into microtubes. The microtubes are interleaved between the first and the second and the fifth and the sixth layers. The initial damage is introduced to the samples by drop weight impact tests and the recovery percentage of the tensile strength due to healing process is measured by tensile test. The effects of healing time (without thermal cycles), number of healing units and thermal cycles are investigated on the recovery of the tensile strength. Composite samples containing 8, 16 and 32 healing units are studied in the periods of 1, 6 and 12 days after the initial damage. Also, some damaged samples are set to 1, 3, 5 and 7 thermal cycles and after one day, tensile tests are carried out. The results show that without thermal cycles the healing process is almost completed after 6 days with an 83% recovery. In addition, the maximum amount of tensile strength recovery is equal to 86% which is related to the samples with 32 healing units after 12 days. This amount of healing efficiency can also be achieved by means of 5 thermal cycles. This is also true for thermal cycles where the effect of thermal cycles is tangible up to 5 cycles.

In this study, the vibration of a composite cylindrical shell in the presence of a longitudinal and circumferential crack was investigated. The governing equations were derived based on the first-order shear deformation theory and could be converted to Donnell’s, Love’s, and Sanders’ theories by selecting proper parameters. A multi-domain generalized differential quadrature method was used to solve the problem. In this technique, a physical domain was decomposed into several elements. Then, a generalized differential quadrature method was employed to discretize the governing equations, boundary conditions at shell edges, and the compatibility conditions at the interface boundaries of adjacent elements in both longitudinal and circumferential directions. Assembling these discretized equations led to a system of algebraic equations, which could be solved through an eigenvalue solution to calculate the natural frequency of the shell. This procedure was coded in Matlab environment. Numerical results obtained by the presented method were compared with Abaqus results and those available in the literature. After verifying the accuracy and precision of the proposed method, it was employed to study the effect of different parameters on the vibrational behavior of cracked composite shells. The obtained results can be used as a benchmark for further studies.

In this paper, the free vibration of a composite shell with and without a rectangular cutout was studied based on the first-order shear deformation theory. The equations were derived in a general form and can be converted to Donnell`s, Love`s, and Sanders` theories. To investigate the perforated shell a physical domain was decomposed into several elements with uniform boundary and loading conditions in each element edges. In each element, the governing equations were discretized in both longitudinal and circumferential directions by the use of generalized differential quadrature method (GDQM) as well as the boundary conditions at the cutout edges, and the compatibility conditions at the interface boundaries of adjacent elements. Assembling these discretized relations, a system of algebraic equations was generated. Finally, the natural frequencies were calculated by an eigenvalue solution. To validate the presented method, the results of GDQM were compared with the available ones in the literature and also with the ABAQUS finite element model. Then a parametric analysis was performed to investigate the effects of different parameters on the vibrational behavior of the shells with and without cutouts. This study illustrated that small cutouts (c/L<0.3) had no significant effect on the natural frequency of the shell. This was independent of both shell material and layup. In addition, decreasing the length to radius ratio or increasing the shell thickness decreased the effect of cutout on natural frequency. Moreover, circumferential cutouts had less effect than longitudinal ones.

In this paper, axial buckling of a composite cylindrical shell with and without a rectangular cutout is studied based on the first-order shear deformation theory. The equations are derived in a general form and can be converted to Donnell`s, Love`s, and Sanders` theories. To investigate the perforated shell, a physical domain is decomposed into several elements with uniform boundary and loading conditions in each element edges. In each element, the governing equations are discretized in both longitudinal and circumferential directions by the use of generalized differential quadrature method (GDQM). By assembling these discretized relations, a system of algebraic equations is generated. The boundary conditions at the shell and cutout edges, and the compatibility conditions at the interface boundaries of adjacent elements are also discretized by GDQM. Finally, the buckling load is calculated by an eigenvalue solution. To validate the presented method, the results of GDQM are compared with the available ones in the literature and also with ABAQUS finite element model. Then a parametric analysis is performed to investigate the effects of different parameters on the buckling behavior of the shells with and without cutouts. This study illustrates that the shell layup has a great effect on the buckling load of a shell. In addition, the influence of increasing the cutout size is not identical for different layups. However, the buckling behavior is independent of the shell material. Moreover, it was concluded that the shell with a square cutout has higher critical load than the one with a rectangular opening.

Although many researchers investigated the effect of geometrical imperfection on the buckling load of unstiffened shells, the stiffened shells were not studied yet. In this paper, the effects of geometrical imperfection the buckling load of unstiffened and stiffened composite shell with and without cutout are investigated. For this goal, several specimens are manufactured and tested. The mechanical properties of fibers and resin matrix and volume fraction of fibers in the shell and the stiffeners are determined based on the standard tests. Finally, the mechanical properties of each component are calculated by micromechanical relations. These properties are used for finite element modeling by ABAQUS package. Linear eigen value analysis and nonlinear RIKS method -which can consider the geometrical imperfection- are used. FE results are validated in comparison with experimental tests. Using FE model, the effects of imperfection amplitude on the buckling behavior of unstiffened and stiffened shell with and without cutout are studied. The results show that geometrical imperfections have more effect on the buckling load of unstiffened shells in comparison with stiffened ones. Nevertheless, ignoring these imperfections and using eigen value analysis overestimate the buckling load. This fact is more evidence for shells without an opening. In perforated shells, the cutout itself represents an imperfection that is much more significant than geometric imperfections.

Due to high strength and stiffness-to-weight ratio of composite cylindrical shells, they are increasingly being used in different industries. Applying different types of stiffeners is one of the ways to improve the buckling resistance of these structures. In this paper new analytical method based on smear method is developed to analyze the stiffened composite shells. The main difference of this method and previous methods is on technique of combination of shell`s and stiffeners` stiffness parameters, and calculating the equivalent stiffness parameters. In the suggested method a three layered shell is designed in such a way that this shell and stiffeners have the same volume and stiffness. Putting these layers under the main layers of shell, the equivalent stiffness parameters could be calculated easily. Using the Ritz energy method the critical load of axial buckling of shell is calculated. The method is verified using finite element ABAQUS package. The results show that the proposed method has less difference from finite element`s results compare to previous methods. In addition, the effects of different parameters on buckling load and special buckling load of stiffened shell is investigated. The results show that in order to have efficient stiffened structure; there must be an adequate number of ribs and unit cells. It also shows that, although adding stiffening ribs increase the buckling load of the shell, the special buckling load does not increase necessarily. The optimum angle for helical ribs is 30 to 40 degrees respect to axis of the cylindrical shell.

In this article two dimensional sliding contact of a rigid cylindrical punch on a functionally graded (FG) semi-infinite medium is studied. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions between the constituting phases. The governing equations are solved by finite difference (FD) method by means of MATLAB software. The effects of different parameters such as non-homogeneity­, q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction are investigated on the force-displacement diagram of the punch, stress distribution and modes I and II stress intensify factors (KI and KII). The results show that the contact force and the stress distribution under the punch are affected by the thickness of the graded layer, radius of the punch and the non-homogeneity­ coefficient. But the variation of q has no effects on the contact force and the stress distribution under the punch. In the absence of the friction, KI is always non-positive and the crack has no tendency to grow under this mode. Increasing the friction coefficient, increases KI but decreases KII.

Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.