Optimization of cylindrical composite shells with regard to their critical mode of imperfections

This study deals with the optimum design of composite shells under external pressure with material strength and loss of stability according to the critical mode of imperfections taken as the failure criterion. The problem of optimum design is solved and the critical mode is obtained by nonlinear optimum programming for which the geometric and initial imperfection parameters are treated as variables. Numerical results are obtained for a cylindrical composite shell supported freely at its ends. The effect of shear forces between layers on the load-carrying capacity of the shell is also investigated.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 613–620, September–October, 1998.     

Mechanical properties of plasticized chlorinated-polymer film formers

It is shown with reference to three chlorinated polymers (CPVC, VKhVD-40, and PCN) that in the case of structural plasticization the optimum of the physico-mechanical properties corresponds to small amounts (0.02–0.04%) of structural plasticizer in the system. This is associated with the development of relaxation processes at the supermolecular level.State Scientific-Research and Planning Institute of the Paint Industry, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 945–948, September–October, 1968.     

Nonlinear moisture deformation of a composite with a densified reinforcement

Conclusion An analytical method is presented for estimation moisture deformation of densified in technological pressing wood-based composite material with nonlinear swelling properties. This includes modelling of the processing effects as well as interfacial bonding. By using the multilayer model supported on the laminate analogy the optimum particle alignment has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 314–320, May–June, 1994.     

Increasing the adhesion of polymers to metals by adding substances with conjugation systems

The electron-donor properties of polymers with conjugation systems (PCS) and their capability of forming -complexes with metals is of interest in relation to adhesion. Small amounts (0.01–0.1%) of substances with polyconjugation systems (polydiphenylbutadiene, polyphenylacetylene, and copolymers of naphthalene and anthracene with benzene) increase the adhesion between aluminum and polymers used as electrical insulation coatings (polyesters, polyimides, and their derivatives). With optimum PCS dosage, the resistance to peeling rises by 15–38%.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 365–367, March–April, 1974.     

Optimum stacking sequence of composite laminates for maximum strength

A method is presented for maximum strength optimum design of symmetric composite laminates subjected to in-plane and transverse loadings. The finite element method based on shear deformation theory is used for the analysis of composite laminates. Ply orientation angles are chosen as design variables. The quadratic failure criterion which is meant to predict fracture, is used as an object function for optimum stacking sequence design of a laminated plate. The Broydon-Fletcher-Goldfarb-Shanno optimization technique is employed to solve the optimization problem effectively. Numerical results are given for various loading conditions, boundary conditions, and aspect ratios. The results show that the quadratic failure criterion such as Tsai-Hill theory is effective for the optimum structural design of composite laminates.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 393–404, May–June, 1995.     

An optimal compressed circular cylindrical shell

The stability is considered for a shell of optimum weight. An isotropic shell is found to be suitable, and the bifurcation in the undeformed state can occur via an axially symmetric or other form. This explains the sensitivity of an isotropic shell to perturbation.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 944–947, September–October, 1973.     

Biaxial orientation of amorphous linear polymers

The mechanical properties of biaxially oriented polymethyl methacrylate, obtained on a broad range of stretch ratios and under a variety of orientation conditions, have been investigated. There is a fundamental difference between the variation of the forced elastic limit with increase in stretch ratio, which is monotone increasing, and the variation of such properties as the brittle strength, brittle temperature, true strength and elongation at break, which have an optimum at a certain stretch ratio. It is shown that the presence of an optimum is associated with the transformation of the supermolecular structures in the process of biaxial high-elastic deformation. A relation is established between the mechanical properties of biaxially oriented polymethyl methacrylate (orientation hardening) and the density of the molecular network.For communication 1 see [3].Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 586–593, July–August, 1971.     

Design of Steel-Composite Multirim Cylindrical Flywheels Manufactured by Winding with High Tensioning and in situ Curing. 2. Numerical Analysis

The possibility of using forced winding coupled with in situ curing to increase the energy storage capacity of hybrid steel-composite cylindrical flywheels is estimated and analyzed. Stress states for given loading conditions in two- and three-layered compound cylinders made from steel and four different types of unidirectional composites are calculated. For each of these combinations, optimum dimensions and the energy storage capacity of the flywheels are found.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 351–372, May–June, 2005.     

Optimal reinforcement schemes for cylindrical glass-plastic shells subjected to a temperature field

Conclusions In the design of shells with an optimum structure one must take into account the variation of the winding angle over the thickness as a result of nonuniform heating of the shell and temperature-dependent changes in the elastic properties. The changes in this angle due to heating are appreciable (up to 12% in our example shown here).Translated from Mekhanika Polimerov, No. 4, pp. 681–686, July–August, 1976.     

Equilibrium glass-plastic pressure vessels of minimum mass with a nongeodesic winding

A lens-shaped vessel having various central apertures made by a continuous winding process is considered. Using the methods of variational calculus, the optimum winding trajectory (yielding a structure of minimum mass) is established, subject to certain limitations regarding the angle of geodesic deviation and the stress level in the filaments. The shape of the base is determined with due allowance for the trajectory found in this way, which comprises sections of geodesic lines and lines of limiting deviation.Translated from Mekhanika Polimerov, No. 6, pp. 983–987, November–December, 1975.     

Fatigue strength at subzero temperature of films made of polymer mixtures based on thermoplastic polyurethane

Conclusions The investigations show that the flexing resistance of the films of thermoplastic polyurethane at the subzero temperatures can be increased several times by mixing polyurethane with rubber with a low glass transition temperature. As a result of the heterogeneity of the structure in the mixtures containing the optimum or almost optimum amount of rubber, cyclic bending is accompanied by the formation of a large number of microdefects but the conditions for formation of a macrocrack are less favorable, whilst in pure polyurethane the main crack can form and propagate in the presence of far less extensive volume damage. The design of the small-angle light diffractometer proposed in this work can be used successfully for examining fatigue damage in nonuniformly loaded specimens. The quality of the resultant mixtures can be inspected by measuring the integral optical properties or light scattering indicatrices.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 977–984, November–December, 1987.     

Synthesis of optimum cylindrical shells of reinforced plastics for an external pressure and axial compression

The synthesis of anisotropic cylindrical shells of minimum weight is considered; the initial data relate to the characteristics of the reinforcing filaments and binder. The optimum case satisfying the requirements of stability, strength, and geometrical limitations is found by the method of projective gradients.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Kaunass Polytechnic Institute. Translated from Mekhanika Polimerov, No. 2, pp. 301–309, March–April, 1972.     

Posted price profit maximization for multicast by approximating fixed points

We describe an iterative fixed point approach for the following stochastic optimization problem: given a multicast tree and probability distributions of user utilities, find an optimal posted price mechanism—i.e., compute prices to offer the users in order to maximize the expected profit of the service provider. We show that any optimum pricing is a fixed point of an efficiently computable function. We can then apply the non-linear Jacobi and Gauss–Seidel methods of coordinate descent. We provide proof of convergence to the optimum prices for special cases of utility distributions and tree edge costs.     

Multicriterion optimization of strengthened hybrid composite panels

A multicriterion model has been developed for the optimum design of a carbon fiber panel with strengthening ribs under both normal and tangential stress relative to minimalization of both mass and cost. The panel packet consists of elementary layers reinforced in two, three, or four directions with several types of reinforcement filaments for models both homogeneous and heterogeneous over their thickness. A modified intermittently active procedure based on the successive compliance principle was used for optimization.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 370–377, May–June, 1995.     

Variation in angles between fibers in forming articles from unhardened composite materials

Conclusion The Gaussian curvature of the surface and the geodesic curvatures of the reference filaments of the fabric exerts a significant influence on the interfilament angles of the base fabric of composites formed to a surface. It is demonstrated that the lines of constant grid angle in the coordinates of the plane fabric are close to hyperbolas, while the optimum layout of the base fabric of the composite material in the sense of least fiber disorientation is that layout for which the lines of the seams intersect the fibers of the fabric at an angle of 45 °.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 138–142, January–February, 1991.     

Recommendations for the optimum design of pultruded frameworks

Conclusions For the optimum choice of pultruded beam members in frameworks there is a need to have a greater understanding of framework behavior under load. Research on the lateral-torsional buckling of a symmetric I-section has shown how much the resistance may be affected by the loading position and the support boundary conditions. By changing the warping at the connections from free, as assumed in the USA design manual, to fixed, as may be achieved with practical connection designs it is shown that there is a potential doubling in the buckling resistance. In addition, practical connections have some initial stiffness and moment resistance, thus the connections behave in a semirigid manner. This connection behavior makes inappropriate the present procedure for choosing beam sections on the basis of limiting deflection for a simply supported member. It is proposed that research be conducted to establish the potential of semirigid design, as now being used with structural steelwork. Results from such research should provide the first stage in the process for the optimum design of frameworks.Published in Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 675–682, September–October, 1993.     

Asymptotic expansion for an optimal control system with two small singularly perturbing parameters

An asymptotic approximation of control is derived in feedback form. While not uniform over the entire definition domain of the system, the asymptotic control produces slow motions that are uniformly close to the optimum.Simferopol' Instrument-Building Institute. Translated from Dinamicheskie Sistemy, No. 10, pp. 57–63, 1992.     

Guidance strategies for near-optimum take-off performance in a windshear

This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-off problem is considered with reference to flight in a vertical plane.First, trajectories for optimum performance in a windshear are determined for different windshear models and different windshear intensities. Use is made of the methods of optimal control theory in conjunction with the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. In this approach, global information on the wind flow field is needed.Then, guidance strategies for near-optimum performance in a wind-shear are developed, starting from the optimal trajectories. Specifically, three guidance schemes are presented: (A) gamma guidance, based on the relative path inclination; (B) theta guidance, based on the pitch attitude angle; and (C) acceleration guidance, based on the relative acceleration. In this approach, local information on the wind flow field is needed.Next, several alternative schemes are investigated for the sake of completeness, more specifically: (D) constant alpha guidance; (E) constant velocity guidance; (F) constant theta guidance; (G) constant relative path inclination guidance; (H) constant absolute path inclination guidance; and (I) linear altitude distribution guidance.Numerical experiments show that guidance schemes (A)–(C) produce trajectories which are quite close to the optimum trajectories. In addition, the near-optimum trajectories associated with guidance schemes (A)–(C) are considerably superior to the trajectories arising from the alternative guidance schemes (D)–(I).An important characteristic of guidance schemes (A)–(C) is their simplicity. Indeed, these guidance schemes are implementable using available instrumentation and/or modification of available instrumentation.Portions of this were presented at the AIAA 24th Aerospace Sciences Meeting, Reno, Nevada, January 6–9, 1986. The authors are indebted to Boeing Commercial Aircraft Company, Seattle, Washington and to Pratt and Whittney Aircraft, East Hartford, Connecticut for supplying some of the technical data pertaining to this study.The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, Hampton, Virginia for helpful discussions. They are also indebted to Mr. Z. G. Zhao, Aero-Astronautics Group, Rice University, Houston, Texas for analytical and computational assistance.This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516. This paper, a continuation of Ref.1, is based in part on Refs. 2–3.     

Optimal designing of orthotropic cylindrical shells fastened to elastic filler

Conclusions A method has been proposed for optimally designing an orthotropic cylindrical shell rigidly fastened to an elastic and isotropic filler of finite dimensions. The design takes into account simultaneous action of pressure, body forces, and heat on the structure. The optimum design has been calculated for the case of temperature-dependent elastic properties and strength characteristics of the tape. The method allows also for limitation on the strength of the filler. The convergence of the iteration process schematically shown in Fig. 2 is quite fast. Indeed, for the given design variant, the condition of manufacturability (1) is satisfied with a sixfold margin in the third approximation (n=3) already.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 91–94, January–February, 1984.