Observation and evaluation of local buckling by photoelastic-strip method

A photoelastic measuring element, consisting chiefly of a strip of resin observed parallel to the surface to which it is attached, has been used in the analysis of a local-buckling problem. This strip method allows the determination of bending and membrane strain components along surface trajectories without the effect of transverse sensitivity. The method of measurement was verified for a hingedend Euler column, and then utilized in the analysis of a previously unsolved problem of local buckling—that of a sheet in tension with a rectangular opening.     

Conservation properties for plane deformations of anisotropic linearly elastic curved strips

Plane deformations of a curved strip, composed of an homogeneous cylindrically anisotropic linearly elastic material, are considered. The strip is in equilibrium under the action of end loads, with the lateral sides traction-free. Two conservation properties for certain cross-sectional stress measures are established, generalizing previously known results for the case of a rectangular strip. Such conservation properties are useful in assessing the influence of material anisotropy on Saint-Venant's principle, as well as in establishing convexity properties for cross-sectional stress measures. In particular, it is anticipated that the results should be useful in determining the extent of edge effects in the testing of anisotropic and composite curved strips.     

Functionally graded piezoelectric strip with a penny-shaped crack under electromechanical loadings

In this paper, the mixed-mode penny-shaped crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electromechanical loadings. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

A finite crack in a semi-infinite strip of a graded piezoelectric material under electric loading

In this paper, the mixed-mode crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electric loading. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

An anti-plane propagating crack in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric strip

Summary A finite crack propagating at constant speed in a functionally graded piezoelectric strip (FGPS) bonded to a homogeneous piezoelectric strip is considered. It is assumed that the electroelastic material properties of the FGPS vary exponentially across the thickness of the strip, and that the bimaterial strip is under combined anti-plane mechanical shear and in-plane electrical loads. The analysis is conducted for the electrically unified crack boundary condition, which includes both the traditional permeable and the impermeable ones. By using the Fourier transform, the problem is reduced to the solution of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and the crack sliding displacement are presented to show the influences of the crack propagation speed, electric loads, FGPS gradation, crack length, electromechanical coupling coefficient, properties of the bonded homogeneous piezoelectric strip and crack location.     

Determining Critical Stresses for Axially Compressed Cylindrical Shells from an Analysis of Response Characteristics

The stability of metallic and glass-reinforced plastic cylindrical shells is analyzed experimentally. It is established that if the equivalent stiffness is taken as an argument of the formula used to evaluate critical stresses in designing a shell, then the critical stresses depend linearly on its stiffness     

Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half plane

This paper studies the Mode III electric-elastic field of a cracked functionally graded piezoelectric strip bonded to a homogeneous piezoelectric half plane. The crack is oriented in arbitrary direction. The material properties of the strip vary along the strip thickness in exponential forms. By using the Fourier transform, the problem can be formulated to a system of singular integral equations and solved by applying the Gauss-Chebyshev integration formula. The effects come from the edge, crack orientations and the nonhomogeneous material parameter on intensity factors are discussed graphically.     

Electromechanical impact of an impermeable parallel crack in a functionally graded piezoelectric strip

The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under the in-plane mechanical and electric impact. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location, the material nonhomogeneity and the loading combination.     

Deflections and buckling of a bent elastica in contact with a flat surface

A straight elastica is bent until its ends are vertical and a fixed distance apart, and then it is pushed onto a flat rigid surface. The weight of the strip and friction between the strip and the surface are neglected. Planar equilibrium states of the strip are investigated, using either a shooting method or an integral formulation. Both symmetric and asymmetric configurations are possible. There may be a single point of contact, a flat region of contact, or two points of contact with a buckled section between them. Also, if the ends are pushed down sufficiently far, one or two loops may form when the upper portion of the strip makes contact with the lower portion on the surface. If the two ends are held together (vertically) and then pushed down, asymmetric configurations may occur in which there is a region of contact between the upper and lower portions of the strip near their ends. The properties of these various equilibrium shapes are investigated.     

A numerical approach for a crack problem by Gauss–Chebyshev quadrature

In this paper, a problem of a crack in an orthotropic strip is studied under plane strain conditions. It is assumed that normal displacements and shear stresses do not act on neither of the boundaries of the strip. Cauchy-type singular integral equation for the crack problem is derived by using the theory of plane elasticity and the Fourier transformation technique. A quadrature collocation approach is adopted for the numerical solutions of the singular integral equation. The effect of relative thickness and mechanical properties of strip on Mode I stress intensity factors (SIFs) are examined under different loading conditions. Some sample results are given for SIFs; also, material orthotropy and geometrical effects are discussed in detail.     

Transient thermal response of functionally graded piezoelectric laminates with an infinite row of parallel cracks normal to the bimaterial interface

In this paper, the problem of a functionally graded piezoelectric material strip(FGPM strip)containing an infinite row of parallel cracks perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Fourier transforms, the electro-thermoelastic problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.     

The influence of epoxy resin on the morphological and rheological properties of PET/PA66 blend

Interfacial reactions have dominant effects on the morphological and rheological properties of compatibilized polymer blends. This work aims to investigate the effect of epoxy resin, as a coupling agent, on the interface properties and subsequent influences on the morphological and rheological properties of polyethylene terephthalate/polyamide66 (PET/PA66) blend. PET/PA66 70/30 blends with different amount of bisphenol A epoxy resin (0, 1, 3, and 5 wt.%) were prepared. SEM micrographs show reduction in droplet size with increasing epoxy resin concentration, confirming the reactive compatibilizing effect of the epoxy resin. Reactions at the interface of the PET-EP-PA66 blend are confirmed by FTIR spectra. Shear viscosity results demonstrates that adding epoxy resin could suppress the interfacial slip at the blend interphase. Obtained results from storage modulus (G′) curves show the presence of one plateau for the blends at low frequency region; nevertheless, relaxation spectra indicate the presence of two more relaxation mechanisms than precursors which are related to the shape relaxation of droplets and the interface relaxation. The presence of the interface relaxation time in the blend without epoxy resin can prove the presence of reactions between two condensation polymers; however, adding the epoxy resin results in reducing both relaxation time and interfacial tension and increasing interfacial shear modulus. These observations indicate that the epoxy resin has been successful to boost the reactions at the interface between two polymers. Fitting the obtained experimental data using Palierne model indicates that the general Palierne model could describe rheological properties of the blends very well.     

Stress analysis for an infinite strip weakned by periodic cracks

Stress analysis for an infinite stripcracks were assumed in a horizontal position,weakened by periodic cracks is studied. The and the strip was applied by tension “p“ in y-direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T-stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.     

Conservation properties for plane deformations of isotropic and anisotropic linearly elastic strips

Plane deformations of a rectangular strip, composed of an homogeneous fully anisotropic linearly elastic material, are considered. The strip is in equilibrium under the action of end loads, with the lateral sides traction-free. Two conservation properties for certain cross-sectional stress measures are established, generalizing previously known results for the isotropic case. It is noteworthy that in the first of these conservation laws only one of the off-axis elastic constants appears explicitly while in the second only the opposite off-axis constant appears explicitly. Such conservation properties are useful in assessing the influence of material anisotropy on Saint-Venant's principle, as well as in establishing convexity properties for cross-sectional stress measures. In particular, it is anticipated that the results should be useful in determining the extent of edge effects in the off-axis testing of anisotropic and composite materials.     

DYNAMIC BEHAVIOR OF SEVERAL CRACKS IN FUNCTIONALLY GRADED STRIP SUBJECTED TO ANTI-PLANE TIME-HARMONIC CONCENTRATED LOADS

This paper contains a theoretical formulations and solutions of multiple cracks sub- jected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors （SEDFs） for multiple cracks with differ- ent configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.     

Calculating creep strains in linear viscoelastic materials under nonstationary uniaxial loading

The creep strains in linear viscoelastic materials under nonstationary loading of various types (incremental loading, complete unloading, and cyclic loading) are determined. Boltzmann–Volterra hereditary theory with fractional exponential kernel is used. Nonstationary loads are specified by Heaviside functions. The calculated results are validated by experimentally determining nonstationary creep strains of glass-reinforced plastic, plastic laminate, polymer concrete, duralumin, and nylon     

Anti-plane stress intensity, energy release and energy density at crack tips in a functionally graded strip with linearly varying properties

The fracture problem of a crack in a functionally graded strip with its properties varying in a linear form along the strip thickness under an anti-plane load is considered. The embedded anti-plane crack is located in the middle of strip half way through the thickness. The third mode stress intensity factor is derived using two different methods. In the first method, by employing Fourier integral transforms, the governing equation is converted to a singular integral equation, which is subsequently solved numerically by the collocation method based on Chebyshev polynomials. Then, the problem is solved by means of finite element method in which quadrilateral 8-node singular elements around each crack tip are used. After inspecting the validity of the solution technique, effects of crack geometry and non-homogeneous material parameter on the stress intensity, energy release and energy density are studied and the results of analytical and FEM solutions are compared.     

Propagation of flexural waves and localized vibrations in the strip plate with a layer using Hamilton system

Based on the theory of laminated plates and applying the method in Hamiltonian state space, the propagation of flexural waves and vibrations in the strip plate covered with a layer are investigated. The boundaries at the two lateral sides are free of traction. According to the character of solar panel, the existence of all kinds of localized vibration modes and wave propagation modes is analyzed. By using eigenfunction expansion method, the dispersion relations of waveguide modes in the strip plate covered with a layer are derived. Through the numerical examples of solar panel, the existence of all kinds of vibration modes and propagating modes is analyzed. The dispersion curves of the strip plate covered with a layer under different parameters are presented and analyzed. The effects of the properties of the covering layer on the propagation of flexural waves are also examined.     

The strain rate intensity factor in the plane strain compression of thin anisotropic metal strip

Using an available analytic solution for instantaneous plane strain compression of a plastically anisotropic strip between two parallel plates the strain rate intensity factor is found assuming Hill’s quadratic yield criterion. The distribution of material properties is uniform. The effect of parameters characterizing plastic anisotropy of the strip on the magnitude of the strain rate intensity factor is demonstrated. A possibility to replace the strain rate intensity factor with the plastic work rate intensity factor is discussed. Singular behavior of the plastic spin in the vicinity of the friction surface is revealed and discussed.     

Mode III crack problem in a functionally graded magneto-electro-elastic strip

Considering the material properties to be one-dimensionally dependent, this paper studied an anti-plane problem for an embedded crack and edge crack perpendicular to the boundary of a functionally graded magneto-electro-elastic strip. The crack is assumed to be either magneto-electrically impermeable or permeable. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. Numerical results show the effects of the loading combination parameter, material gradient parameter and crack configuration on the field intensity factors and the energy release rates of the functionally graded magneto-electro-elastic strip.