Design of closed thin-walled composite shapes for bending

A study is made of the possibility of dividing the complex bending of a structure into elementary components, and an examination is made of closed wing-type monocoque structures with a rigid contour. The structures studied are asymmetric with respect to their geometric and stiffness characteristics. They are subjected to bending without torsion and are referred to a cylindrical coordinate system (Z, S). The longitudinal displacements are determined on the basis of the method of conjugate displacements by integrating the Cauchy equation and circulation equation, with the displacement along the contour (due to its stiffness) being represented in the form of a series containing terms describing the bending of the structure. The shear strains are similarly represented. The resolvent equations are obtained by using the principle of the minimum potential strain energy of the contour.Deceased.Moscow State Aviation Institute (Technical University). Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 82–89, January–February, 1997.     

Calculation of thin-wall closed profiles of composite materials under a complex loading

Uniclosed caisson structures with deformable perimeters, which are asymmetric in terms of geometry and stiffness and which are subjected to a complex loading (bending in two planes and torsion with respect to the longitudinal axis) are examined in terms of a cylindrical coordinate system Z, S. The possibility of partitioning the general problem of the stress and strain state into elementary problems by fulfilling conditions of orthogonality is demonstrated. The coordinates of the center of rotation are determined. The need for consideration of the deformation of the cross-sectional perimeter, which defines the warping function and normal bitorque stresses under torsion is indicated. The law governing the distribution of tangential stresses, which contains both a constant component that corresponds to Bredt's theory, and also a part corresponding to Vlasov's theory, is derived.Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 349–359, May–June, 1997.     

Calculation of effective moduli of composite materials

Effective properties of composite and porous materials are determined by using an approach based on two-scale asymptotic expansions. Explicit approximate formulas are derived for the effective moduli of composite and porous materials of elongated structures. A numerical method is proposed for finding solutions to cell problems, which are used to determine “exact” effective moduli. Examples are computed for a two-dimensional porous medium with variously shaped pores and various degrees of “elongation.” The effective moduli produced by the explicit approximate formulas prove to be similar to those found by numerically solving cell problems.     

Limiting loads of thin-walled glass-reinforced plastic cylinders in torsion

The article presents the results of an experimental investigation of the regularities of the change of the load-bearing capacity and deformation properties of smooth thin-walled cylinders of glass-reinforced plastic on a phenol formaldehyde binder loaded on the ends by twisting moments at normal and elevated temperature. Integral methods are used for calculating the limiting loads in the case of a temperature field varying over the thickness of the wall. The calculation results are compared with the experimental data.N. E. Joukowski Central Aerohydrodynamic Institute, Moscow Oblast. Translated from Mekhanika Polimerov, No. 3, pp. 502–508, May–June, 1970.     

Bending and torsion of anisotropic thin-walled open sections

A theory of thin-walled open sections, based on Vlasov's assumptions, is proposed. The section is assumed to be composed of rectangular strips whose cross section remains constant in the z-direction. The material is homogeneous and anisotropic with a single plane of elastic symmetry parallel to the middle surface of the strip. The general case of loading-tension, unsymmetrical bending, and constrained torision-is considered.Mekhanika Polimerov, Vol. 3, No. 5, pp. 900–905, 1967     

Mathematical modeling of processes of devising fibrous composite materials and thin-walled structural elements by forced winding

Conclusions With the aid of the method of averaging processes in regular media, on the assumption that the temperature field in the semiproduct of PM is homogeneous at all stages of the production of thin-walled articles of CM, we suggested averaged equations of equilibrium, and also constructive algorithms for calculating the effective moduli and defining relations of the material of the semiproduct of CM. On the basis of these equations and the boundary conditions corresponding to them, we showed that it is possible to determine the RTS in a finished product of CM, and also to predict the change of its shape after removal from the mandrel and cutting it up into separate elements. To determine the above-mentioned technological characteristics of thin-walled elements made of fibrous CM, it is necessary to know the physicomechanical characteristics of the fibers and of the PM before and after polymerization; the volume fraction of the reinforcing filler and of the PM during winding, and also the orientation of the reinforcement; the relative change of volume of the PM after heat treatment and cooling; the prestresses in the fibers in the process of winding. It should be noted that the obtained averaged equations make it possible to calculate only the components of the averaged RTS in products of CM. To determine the local stresses in PM and fibers at all stages of making the product, it would be necessary to investigate in detail the rheology of PM at different temperatures.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 513–527, May–June, 1990.     

SBFEM elements for thin-walled composite beams with arbitrary layup

The scaled boundary finite element method (SBFEM) is a semi-analytical method in which only the boundary is discretized. The results on the boundary are scaled into the domain with respect to a scaling center which must be “visible” from the whole boundary. For beam-like problems the scaling center can be selected at infinity and only the cross-section is discretized. Two new elements for thin-walled beams have been developed on the basis of the first order shear deformation theory. The beam sections are considered to be multilayered laminate plates with arbitrary layup. The arbitrary cross-section is discretized with beam elements of Timoshenko type. Using the virtual work principle gives the SBFEM equation, which is a system of differential equations of a gyroscopic type. The solution is calculated using the matrix exponential function. The elements have been tested and compared with a finite element model and they give good results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)