Archive of Applied Mechanics

An approximate analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear is presented. The solution based on the classical Vlasov’s thin-walled beam theory is modified for thin-walled laminated composite beams with orthotropic and symmetrical lay-up. It is shown that the beam subjected to torsion with influence of shear, caused by couples in the cross section planes, is also subjected to bending due to shear in the plane orthogonal to the plane of symmetry. If the cross section has two axes of symmetry, the beam will be subjected only to torsion with influence of shear. The expressions for the displacements and normal stresses are derived in closed analytic form. The material influence on shear is defined by factor that depends on the fibre orientations. Simply supported and clamped beams subjected to distributed couples are considered. Illustrative examples are provided, and the results for the displacements and stresses show very good agreement between analytical ones and numerically obtained results utilizing three-dimensional shell finite elements.

A semi-infinite plate with an oblique edge crack is analyzed as a thin plate bending problem and a plane elastic problem. The rational mapping function of the sum of fractional expressions and the complex variable method are used. Closed solutions are obtained for these respective problems. Stress distributions, stress intensity factors are investigated for loads causing transverse bending, twisting and uniform tension. The relations between the stress intensity factors and the angle of the oblique edge crack are also investigated.

Residual stresses in composite constructions are created because of non-uniform contraction of layers during cooling from curing to ambient temperature. The aim of this study is to investigate the feasibility of incremental ring-core method to estimate non-uniform residual stresses in various laminates of polymer matrix composites. To carry out this test, glass/epoxy specimens were selected in two different types of symmetric cross-ply laminate $$\left( \left[ 0^{\circ }_{4}/90^{\circ }_{4}\right] _{S}\right) $$ and symmetric quasi-isotropic laminate $$\left( \left[ 0^{\circ }_{2}/\pm 45^{\circ }/90^{\circ }_{2}\right] _{S}\right) $$ . The samples were created using hand layup and vacuum bagging. By experimental tests, released strains measured during milling process and coefficient factors for every annular groove machining operations were obtained by finite element modeling. As well, residual stresses were calculated by classical lamination plate theory. For symmetric cross-ply, the maximum difference between experimental and theoretical results was about 16%, which was observed in the first and eighth layers. Symmetric quasi-isotropic specimen showed also good agreement between the results and the maximum measurement error of 8% was observed. For the mentioned two cases, summation of components of the residual stress in all directions is near to zero. The results of this study show that in the ring-core method, because of the nature and higher volume of material removal than other methods, values of residual stress released are higher and the results have a good consistency compared with the theoretical values.

A dimensional analysis is reported for the dynamic plastic response and failure of structural members, which includes material strain hardening, strain rate and temperature effects. Critical shear failure conditions are also discussed based on the dimensional analysis results. It is shown that the response number R n proposed in [3], is an important independent dimensionless number for the dynamic plastic bending and membrane response of structural members. However, additional dimensionless numbers are necessary when transverse shear, strain hardening, strain rate, and temperature effects are important.

The Stroh sextic formalism, together with Fourier analysis and the singular integral equation technique, is used to study the propagation of a possible slip pulse in the presence of local separation at the interface between two contact anisotropic solids. The existence of such a pulse is discussed in detail. It is found that the pulse may exist if at least one medium admits Rayleigh wave below the minimum limiting speed of the two media. The pulse-propagating speed is not fixed; it can be of any value in some regions between the lower Rayleigh wave speed and minimum limiting speed. These speed regions depend on the existence of the first and second slip-wave solutions without interfacial separation studied by Barnett, Gavazza and Lothe (Proc. R. Soc. Lond. 1988, A415, 389–419). The pulse has no free amplitude directly but involves the arbitrary size of the separation zone that depends on the intensity of the motion. The interface normal traction and the particle velocities involve a square-root singularity at both ends of the separation zones that act as energy source and sink.

Heat transfer from a sheet and a cylinder (at constant temperature) moving in a fluid at rest is examined. Asymptotic expressions for the Nusselt number are found for very small and very large Prandtl numbers.

The effect of small imperfections on the stability behaviour of an N-degree-of-freedom system exhibiting 2-fold coincident critical points is investigated. The analysis is based on equilibrium surfaces and the multiple-parameter perturbation technique. The relationship between certain forms of the equilibrium surface and the Catastrophe theory is discussed. An illustrative structural model is analyzed.