Optimization of cyclindrical shells of fiber-reinforced composite materials

Problems of optimizing nonelastic circular shells are considered. The material of the shells is assumed to be a fiber-reinforced composite with fibers unidirectionally embedded in a relatively less stiff but ductile metallic matrix so that the material has the yield surface suggested by Lance and Robinson. The shell is subjected to an impulsive loading of short-time periods generating initial kinetic energy. During plastic deformation of the shell the initial kinetic energy is transformed into the plastic strain energy. The shell thickness is assumed to be piecewise constant. Various thicknesses and coordinates of the rings, where the thickness has jumps, are preliminarily unspecified. We look for a shell design for which the maximum residual deflection has a minimum value for the total weight given. The alternative problem of minimizing the shell weight for the maximum deflection given is also studied.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Octobe, 1995.Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 65–71, January–February, 1996.     

Fracture of fiber-reinforced materials

The fracture behaviour of fiber-reinforced materials is studied in this paper. Using a simple shear lag model, which includes friction at the debonded interface and the Poisson contraction of the fiber, the fiber-matrix debonding problem is solved. This gives the relationship between debonding load and debonded length. Interfacial friction is shown to have a significant effect on the debonding load. The fracture toughness of fiber-reinforced materials due to fiber debonding, frictional dissipation at fibre-matrix interface following debonding and other micro-fracture mechanisms is discussed with reference to strong and weak fibres. Finally, the strength and toughness of short fibre-reinforced materials are given.On leave from Harbin Shipbuilding Engineering Institute, Harbin, China     

Dynamic response of fiber-reinforced composite plates

The dynamic stability of orthotropic thick plates subjected to a periodic uniaxial stress and a bending stress is investigated. Both the rotary inertia and the transverse stress are considered in the investigation. The governing equations of motion of Mathieu type are established by applying the Galerkin method with reduced eigenfunction transforms. Based on Bolotin’s method, the dynamic instability regions of graphite- and glass-fiber-reinforced plates are evaluated by solving eigenvalue problems. A dynamic instability index is defined and used as an instability measure to study the influence of various parameters. The effects of material properties and load parameters on the instability region and on the index of dynamic instability of orthotropic plates are discussed.     

Some negative characteristics of fiber-reinforced materials

The effect of low resistance to shear and tension-compression at right angles to the layers of reinforcement on the state of stress and strain of elements composed of fiber-reinforced materials is analyzed. It is shown that to take these characteristics into account the calculations must be refined. In certain cases this leads to the appearance of qualitatively new effects. Typical problems in which the negative characteristics of the material must be allowed for are examined.Review of research conducted in the Polymer Structures Laboratory of the Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 140–149, January–February, 1969.     

Stability of members composed of fiber-reinforced materials

Equations for the stability of a centrally loaded compression member are derived from the general relations of the theory of elasticity of an anisotropic body. Other methods of deriving these equations are discussed and their accuracy evaluated. It is shown experimentally and theoretically that shears sharply reduce the critical load for members composed of fiber-reinforced materials. Limits beyond which increasing the stiffness in the axial direction ceases to be effective are established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 911–917, September–October, 1968.     

A fibre microbuckling model for predicting the notched compressive strength of composite sandwich panels

Cohesive-zone models have been successfully applied to predicting the damage from notches in engineering materials loaded intension. They have also been used to determine the growth of fibre microbuckling from a hole in a composite laminate under compression. The usual strategy is to replace the in elastic deformation associated with plasticity or microbuckling with a line crack and to assume some form of stress-displacement bridging law across the crack faces. This paper examines recent published experimental data for notched glass-fibre epoxy/honey comb sand wich panels loaded in uniaxial compression. A plastic fibre kinking analysis and a linear softening cohesive-zone model are used for the prediction of the unnotched and open-hole compressive strength and the theoretical results are found to be in a good agreement with experimental data. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 73–84, January–February, 2007.     

Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials

A method for calculating the elastic properties of fiber-reinforced composites is discussed. The method is based on the structural macroscopic theory for reinforced media [1, 2], which can be used for analysis of stiff and soft composites. As a measure of the elastic properties of composites, the parameters of macroscopic deformations of the base system of Cartesian coordinates are used, with the axes oriented in a certain direction relative to the general reinforcement and loading field. The corresponding macrostresses in the loaded composites are found by a solution of the microboundary problem for a composite macroelement with sides parallel to reinforcement planes of the system. The microboundary-value problem is multiply connected and is formulated based on the information about the homogeneous field of macroscopic displacements specified by the parameters of macroscopic deformation. The problem is solved using the local system of coordinates whose axes are directed along some of the reinforcement trajectories.State Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 733–745, November–December, 1998.     

Load-absorption by a discontinuous filament in a fiber-reinforced composite

Zusammenfassung Diese Arbeit befasst sich analytisch mit der statischen Kraftübertragung auf eine einzelne unendliche, elastische Faser, die an einem Querschnitt unterbroche ist. Die Faser ist vollständig in einem unendlich ausgedehnten Körper von anderen elastischen Eigenschaften eingebettet. Der Körper selbst ist im Unendlichen einer einachsigen Zugspannung parallel zur Faser ausgesetzt. Die Charakterisierung der gesuchten Faserkraft wird durch eine schon früher erprobte Annäherungsmethode auf eine Fredholmsche Integralgleichung zweiter Art zurückgeführt und die letztere wird auf numerischem Wege gelöst. Die Verteilung der Faserkraft ist für verschiedene Werte des Verhältnisses der beiden Elastizitätsmodulen dargestellt.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contract N00014-67-A-0094-0020 with the Office of Naval Research in Washington, D.C.     

Damping by dry friction of dynamic loads in a fiber-reinforced composite

Conclusions The accurate analytical solutions of a number of nonlinear problems of impacts on semiinfinite and finite fibers, interacting with the matrix in accordance with the dry friction law, were obtained. We examined the cases of both unidirectional motions and reversed motions caused by unloading, and also oscillatory motions. The results can be used to calculate the energy dissipated in the separating sections of the composite in shock effects. It was shown that the amount of energy dissipated in the dynamic effect is considerably greater than in the quasistatic effect. Thus, dissipation in the system with friction depends strongly on the nature of load application with time.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 28–37, January–February, 1986.     

Markov model for analyzing the residual static strength of a fiber-reinforced composite

The possibility of using a unified mathematical model, based on the theory of Markov chains, to describe the distribution of the conditional fatigue limit at a fixed number of loading cycles and the residual strength of a specimen after cyclic loading is demonstrated. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 559–568, July–August, 2008.     

Effect of interlaminar stiffness and strength of fiber-reinforced materials in plane stress

The distortion of the strains associated with a difference in the influence coefficients of the reinforcing layers is considered. The effect of the compliance of the intermediate resin layers on the average stiffness of composites is estimated. An attempt is made to explain in these terms the experimentally established deformation characteristics of three-dimensionally reinforced materials [12, 13] and laminated plastics loaded at an angle to the direction of reinforcement [11].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 876–883, September–October, 1970.     

Heat-conduction theory for composite materials

The problem of the macroscopic conduction of heat in a composite medium is considered. The medium consists of inclusions of arbitrary geometry embedded in a matrix. Starting with an analysis of the micro-conduction in a suitably defined representative volume, a fourth order equation governing the macro-conduction is deduced together with appropriate boundary conditions. The theory closely resembles the mechanical theory of non-simple materials of grade 2 developed by Toupin [2]. In particular, the well known characteristic material length encountered in stress-gradient theories is evaluated in terms of constituent material properties. It is further shown, as a basis of the theory, that anatural ratio exists between the dimensions of a local representative volume and those of a unit-cell given by the ratio of the classical Voigt and Reuss bounds on the effective diffusivities. In consequence, application of the theory hinges on the evaluation of certain material constants from given information on the inclusion arrangement in a representative volume of specific dimensions. Differences in the behaviour of media with different inclusion distributions depend entirely on the magnitude of such constants.

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Zusammenfassung Aus der Variationsgleichung für die Mikroleitung wird eine Beziehung für Makroleitung mit mikrostrukturellen Einflüssen hergeleitet. Bei diesem Herleitungsprozess entsteht ein natürliches Verhältnis zwischen den Dimensionen eines representativen Volumens und jenen der Einheitszelle. Das Verhältnis drückt sich durch die effektiven Voigt und Reuss Diffusionskoeffizienten aus. Daraus ergeben sich eine natürliche Materiallänge und eine Zeitskala, welche sich explizit in Funktion der Materialgrössen darstellen lassen. Man kann schliesslich bemerken, dass wegen der mathematischen Aehnlichkeiten die vorliegende Theorie auf alle physikalischen Prozesse mit der Diffusionsgleichung anwendbar ist.

     

On the stressed state in a fiber-reinforced composite material with twisted filaments

Using the model of a piecewise-homogeneous body in the framework of the linear theory of elasticity we study the distribution of internal stresses in a fiber-reinforced composite material with twisted filaments under loading at infinity by uniformly distributed normal strains in the direction of the filaments. It is assumed that the concentration of filaments is rather sparse and their interaction is not taken into account.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 74–79.