Theory Of Orthotropic Elasticity Research Articles

Analysis of a shear fracture in unidirectional fiber-reinforced composites.

A semi-infinite shear fracture initiated from notch roots and the other stress concentrators in unidirectional fiber-reinforced composites is considered on the basis of the two-dimensional theory of orthotropic elasticity. By use of the Wiener-Hopf technique, simultaneous Wiener-Hopf equations are derived for the semi-infinite shear fracture in an infinite strip of the composites under tensile loading at infinity. The stress intensity factors at the tip of the shear fracture are obtained through asymptotic properties of the equations with the aid of some numerical computations. As a consequence, it is revealed that the considerably large stress intensity factor for the opening mode appears in addition to the stress intensity factor for the in-plane-shear mode. Furthermore, when the results for the stress intensity factors is compared with one obtained by the well-known method of energy balance, it is found that the results do not coincide and the latter is inappropriate to estimate the stress intensity factors.

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. By the use of Green's functions and the complex variable theory of orthotropic elasticity developed by Lekhnitskii, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. With these adhesive stresses, the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive did not have a significant effect on the stress-intensity factor unless the near crack tip was beneath the stringer. The present investigation assumes that the adhesive bond remains intact. Onset of adhesive failure is predicted to occur at decreasing levels of applied stress as the crack propagates beneath the stringer.

On the effect of boundary conditions on finite deflections of heated annuli exhibiting temperature-dependent properties

The present study concerns nonlinear deflection analyses of axisymmetrically heated annular plates for several boundary conditions at the outer radius. Temperature-dependent mechanical and thermal properties of plates are considered within the frame of orthotropic elasticity theory. It is pointed out by numerical calculations that the temperature-dependent effect on finite deflections differs markedly for distinct boundary conditions.

Stability of multilayered composite plates

Quantitative assessment is made of the accuracy and range of validity of the classical and shear-deformation plate theories when applied to the stability analysis of multi-layered composite plates with large numbers of layers. The standard of comparison is taken to be the linear three-dimensional theory of orthotropic elasticity. In the shear-deformation theory, the composite correction are included and are shown to result in close agreement with three-dimensional elasticity solutions for a wide range of lamination and geometric parameters.

Three-dimensional solutions of laminated cylinders

A mixed finite-difference scheme is presented for the free vibration analysis of simply supported laminated orthotropic circular cylinders. The study is based on the linear three-dimensional theory of orthotropic elasticity, and the governing equations are reduced to six first-order ordinary differential equations in the thickness coordinate. In the finite-difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented of the effects of variations in the lamination and geometric characteristics of circular cylinders on their vibration characteristics. Also, the accuracy and range of validity of two-dimensional Sanders—Budiansky type shell theories are investigated.

Mixed finite-difference scheme for analysis of simply supported thick plates

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Multiaxial-stress studies on rigid polyurethane foam

Thin-walled tubes of rigid polyurethane foam, at 5 lb/cu ft and 4 lb/cu ft nominal density, were subjected to combined stresses. A universal-test machine applied the axial tensile or compressive stress; an independent pressurization system supplied the internal pressure to the specimen. Changes in diameter, length and wall thickness were measured at room temperature and at −50°F. Failure envelopes in 2-dimensional stress space were obtained for the two densities at room temperature and for the greater density at −50°F. For the wall-thickness range investigated (0.15≤t≤0.25 in.), no effect on the failure envelope was observed. Material constants were obtained in terms of orthotropic elastic theory (at 5 lb/cu ft and room temperature) to describe the material in terms of structure.

Pressurization of two layered incompressible orthotropic tubes

The effect of internal pressure an a closed tube of incompressible orthotropic material is analyzed. The cross section of the tube consists of two regions each having a different set of material properties. An exact solution for the stresses, strains and radial displacement is obtained based on the theory of orthotropic elasticity. The exact solution is simplified for thin walled tubes. The presence of a second layer is shown to reduce the stress in the original layer by more than the ratio of wall thickness. In general, the stresses in each layer are unequal. A relation is presented which assures the existence of equal circumferential stress in each layer

Asymptotic Theory for the Vibrations of Elastic Plates

Differential equations governing the vibrations of plates are established in a systematic and consistent manner without making any of the usual a priori assumptions regarding the distribution of stresses and displacements over the thickness of the plate. The analysis consists of the application of the boundary-layer technique to the equations of the three-dimensional theory of orthotropic elasticity. After suitably nondimensionalizing these equations, an asymptotic expansion of both the stress and displacement variables and length scales in terms of a small plate parameter is performed. By equating corresponding powers of the parameter, successive systems of differential equations are obtained. The lowest-order system in each case yields the different classical thin-plate equations. The higher-order systems yield the corresponding higher-order terms in the expansions and constitute thickness corrections associated with the effects of transverse shear, normal stress, and rotatory inertia.