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## An accurate stress analysis model for angle-ply laminates with weakly bonded layers

### Acta Mechanica (2001-09-01) 150: 161-178 , September 01, 2001

### Summary

This paper presents a shear slip model suitable for the analysis of angle-ply composite laminated plates with weakly bonded layers. Being an extension of a relevant model that deals with perfectly bonded laminates, this study accounts further for the effects of shear slip by introducing appropriate interfacial bonding conditions. Accordingly, the model is based on a general five-degrees-of-freedom displacement field which includes certain general shape functions of the transverse co-ordinate. These are determined by means of appropriate three-dimensional elasticity considerations and include information relevant to the interfacial constitutive relations that account for weak bonding between layers. In dealing with weakly bonded angle-ply laminated plates in cylindrical bending, a closed form solution which is independent of the imposed boundary edge conditions is obtained. As a special case, the corresponding cross-ply laminated, weakly bonded plates solution is obtained by letting all the lamination angles involved to take 0° or 90° values. The high accuracy of the present model is shown by means of numerical comparisons with corresponding results based on an exact elasticity solution obtained for simply supported laminates. The effects of shear slip on the response of angle- and cross-ply laminated plates subjected to different edge boundary conditions are finally studied by means of corresponding numerical results that are obtained, presented and discussed.

## Chaotic motion analysis of a rigid spacecraft dragging a satellite by an elastic tether

### Acta Mechanica (2015-08-01) 226: 2761-2771 , August 01, 2015

An analytic method studying the in-plane chaotic motion of an asymmetric rigid spacecraft with a tethered body is presented. Starting with the lumped masses modeling the viscoelastic tether, a numerical simulation of pitch motion of the tether is made. According to the configurations of the tether during the pitch motion, a simplified rod model is served as the ideal mechanics model for the tether. Near local equilibrium position, the equations of pitch motion of the system are uncoupled, so that their solutions can be expressed with elliptic functions. Furthermore, by using the Melnikov method, the threshold borders for the chaotic motion of the rigid spacecraft are obtained. The results show that the chaotic motion of a tethered rigid spacecraft would occur within threshold borders and can be suppressed by adding system damping.

## Scattering of the SH wave from a crack in a piezoelectric substrate bonded to a half-space of functionally graded materials

### Acta Mechanica (2009-08-29) 208: 299-308 , August 29, 2009

The scattering of the SH wave from a crack in a piezoelectric substrate which is bonded to a half-space of functionally graded materials (FGM) is studied. The governing equations along with permeable crack boundary, regularity and continuity conditions across the interface are reduced to a coupled set of Cauchy singular integral equations which are solved approximately by applying Chebyshev polynomials. Numerical results for the normalized dynamic stress intensity factors (NDSIF) and the normalized electric displacement intensity factors (NEDIF) are presented. The effects of the geometric and physical parameters, and the effects of the frequency and the angle of incidence on NDSIF and NEDIF are discussed.

## Interaction of a cylindrical cavity with a periodically supported thin shell liner

### Acta Mechanica (1981-09-01) 38: 199-208 , September 01, 1981

### Summary

The coupled axisymmetric problem of a periodically supported circular cylindrical shell bonded to a cylindrical cavity in an infinite isotropic, homogeneous elastic body is investigated. Explicit expressions for the resulting Fourier coefficients are obtained and convergence of the solution is established. Numerical results for two different shell materials in contact with a typical geologic formation are presented.

## Laminar flow in an annulus between two concentric rotating porous spheres

### Acta Mechanica (1993-09-01) 97: 215-228 , September 01, 1993

### Summary

An analysis is presented for the steady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric porous spheres with injection/suction at their boundaries. The inner sphere rotates with constant angular velocity about its own fixed axis, while the outer sphere is stationary. A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique. The solution obtained is in the form of a power series expansion in terms of the rotational Reynolds number Re, and an injection/suction Reynolds number Re_{w}, and is valid for small values of these parameters. Results for the velocity distributions, streamlines, and viscous torques for various values of the flow parameters Re, Re_{w}, and radius ratios λ are presented. Viscous torques at the inner and outer spheres are compared with those obtained from the numerical solution of the Navier-Stokes equations, in order to find the range of Re and Re_{w} for which this solution is accurate.

## Laminar heat transfer to power law fluids in tubes with variable wall heat flux

### Acta Mechanica (1981-03-01) 41: 129-141 , March 01, 1981

### Summary

The present paper deals with laminar heat transfer to non-Newtonian power law fluids in circular tubes with boundary condition of variable, wall heat flux. The differential equations of motion, energy and continuity governing the problem discussed have been solved numerically by means of finite-difference scheme. The results of numerical computations are presented graphically and their physical meaning is given. A special attention has been paid to the effects of temperature dependent rheological fluid properties and viscous energy dissipation on temperature, velocity and pressure-drops distributions in heated (cooled) tubes section as well as on mean Nusselt number. In some special cases a comparison with the empirical formulae encountered in literature is presented. This work is intended to be an extension of the previous paper by Forrest and Wilkinson [1] in which the boundary condition of constant wall heat flux was considered.

## Generalized Ilyushin's spaces for a more adequate description of plastic hardening

### Acta Mechanica (1984-07-01) 52: 1-13 , July 01, 1984

### Summary

Generalized Ilyushin's deviatoric stress and strain spaces are introduced, which make it possible to apply directly the postulate of isotropy to initially isotropic materials with plastic properties influenced by the third deviatoric stress invariant and to a certain class of initially anisotropic materials. The generalizations proposed are connected with a new concept of description of plastic hardening, the main idea of which is also briefly presented.

## Eccentric crack in a rectangular piezoelectric medium under electromechanical loadings

### Acta Mechanica (2001-03-01) 148: 239-248 , March 01, 2001

### Summary

The solutions of an eccentric crack problem in a rectangular piezoelectric ceramic medium under combined anti-plane shear and in-plane electrical loadings are obtained by the continuous electric crack face condition. Fourier transforms and Fourier series are used to reduce the problem to two pairs of dual integral equations, which are then expressed by a Fredholm integral equation of the second kind. Numerical values of the stress intensity factor and the energy release rate are obtained to show the influence of the electric field.

## Chemically reactive solute transfer in a moving fluid over a moving surface

### Acta Mechanica (2013-03-01) 224: 513-523 , March 01, 2013

The distribution of a solute, undergoing a chemical reaction, between a moving surface and a moving stream is analyzed in this paper: uniform concentration at the boundary is assumed. The governing nonlinear partial differential equations are first transformed into nonlinear ordinary differential equations (ODEs) by a similarity transform, and then the ODEs are solved numerically by a shooting method. The obtained numerical results are compared with the known results in the literature in order to demonstrate the validity of the solutions. Furthermore, analytical results are provided for some parameter regimes. The effects of the governing parameters on the flow and chemical fields are examined. The numerical results indicate that dual solutions exist when the sheet and the free stream move in the opposite directions. These results are in agreement with Ishak et al. (Chem Eng J 148:63–67, 2009), where the results were obtained without chemical reaction. The concentration boundary layer thickness decreases with an increase in the Schmidt number and reaction rate parameter. Moreover, mass absorption at the plate is noted in the case of a constructive chemical reaction.