Multicriteria optimization of a composite cylindrical shell subjected to thermal and dynamic actions

Multicriteria optimization of the structure and geometry of a laminated anisotropic composite shell subjected to thermal and dynamic actions is considered. From the known properties of monolayers and the given values of variable structural and geometric parameters, the thermoelastic properties of the layered anisotropic composite are determined. The criteria to be optimized—the natural frequency and the thermal stresses—depend on two variable design parameters, stochastic properties of the composite, and temperature. In the space of the optimization criteria, the domain of allowable solutions and the Pareto-optimal region are found.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 753–760, November–December, 2004.     

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.     

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.     

Design of two-way glass-reinforced plastics with high compressive strength

The conditions determining the design of two-way glass-reinforced plastics with high compressive strength are investigated. The relations between the physicomechanical and geometric parameters of the composite are obtained in the form of a system of inequalities, satisfaction of which ensures the obtaining of a high-strength material with a given utilization factor. It has been shown experimentally that these inequalities can be used as a first approximation for the optimal design of a two-way reinforced composite with high compressive strength.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 4, pp. 655–660, July–August, 1973.     

Asymptotic Gauss–Jacobi quadrature error estimation for Schwarz–Christoffel integrals

Numerical conformal mapping packages based on the Schwarz–Christoffel formula have been in existence for a number of years. Various authors, for good reasons of practical efficiency, have chosen to use composite n-point Gauss–Jacobi rules for the estimation of the Schwarz–Christoffel path integrals. These implementations rely on an ad hoc, but experimentally well-founded, heuristic for selecting the spacing of the integration end-points relative to the position of the nearby integrand singularities. In the present paper we derive an explicitly computable estimate, asymptotic as n→∞, for the relevant Gauss–Jacobi quadrature error. A numerical example illustrates the potential accuracy of the estimate even at low values of n. It is apparent that the error estimate will allow the adaptive construction of composite rules in a manner that is more efficient than has been possible hitherto.     

Frequency response analysis of laminated composite beams

Conclusions The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 5, pp. 664–674, September–October, 1994.     

Some problems in the application of statistical dynamics to shells manufactured from fibrous composites

On the basis of a statistical approach presupposing direct utilization of experimental data produced in modelling operations, a procedure is proposed for computational estimates on composite materials in which allowance is made for the initial defects, the variable properties of the material, and the conditions of use (physical medium). Experimental data on Plexiglas shells which confirm the practical applicability of the procedure are given. Questions relating to the design of tests on composite shells are discussed.Translated from Mekhanika Polimerov, No. 4, pp. 743–745, July–August, 1972.     

Evaluating the feasibility of using composites in ship shafting 1. Analysis of the loads and stress state of a composite shaft

Literature data is used to analyze the theoretical loads that develop in ship shafting. A study is made of the stress state of different thicknesses of shafts made of glass- and carbon-fiber-reinforced plastics loaded with an axial force, torque, and bending by a concentrated force. The results contain information needed for optimizing the design of composite ship shafting.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31. No. 6, pp. 797–807. November–December, 1995.     

A measure of rotatability for second order response surface designs

The concept of rotatability introduced by Box and Hunter (1957,Ann. Math. Statist.,28, 195–241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3 ^k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.     

Measuring the stresses in fibers of a loaded composite material by the method of infrared spectroscopy

Conclusions 1. Actual stresses in reinforcement fibers of a loaded composite have been measured by infrared spectroscopy.2. It has been shown that the plain rule of mixtures, not accounting for changes in mechanical properties of the matrix during processing of a composite, does not apply to a hot molded polyethylene-polypropylene composite.3. It is suggested that around the reinforcement fibers there exists an ordered layer of the matrix material capable of carrying a heavy load. A method is proposed, furthermore, for calculating the mechanical characteristics of the composite with such a layer. The volume fraction and the thickness of this hardened layer have been estimated from experimental data.Paper presented at the Third All-Union Conference on Polymer Mechanics in Riga, 1976.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 832–837, September–October, 1977.     

Evaluating the potential use of composites in ship shafting 3. Efficient design of the intermediate shaft of ship shafting

This report examines the problems associated with the design of a composite intermediate shaft for a ship shaftline. A comparison is made between shafts of carbon- and glass-fiber-reinforced plastics made by winding with different laws governing the change in winding angle through the thickness of the shaft. An analysis and comparison of results obtained for a specific example show that the use of a composite significantly reduces the weight and stiffness of the shaft compared to steel shafts and thus appreciably reduces all of the additional loads on the bearings and other shafts.See [2] for Report No. 2.Institute of Polymer Mechanics, Latvian Academy of Sciences (Riga, LV-1006 Latvia). Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 66–81, January–February, 1997.     

Minimum weight design of sandwich and laminated composite structures

Conclusions The illustrative examples presented above show that the proposed optimum design method based on planning of experiments is an efficient method for the minimum weight design of sandwich and laminated composite plates. Vibration and damping constraints can be modeled using simple mathematical expressions. These expressions are obtained using the finite element solution in the experiment points. Reference points in the search domain are determined from plans of experiment. The advantage of the proposed method is its minimum computational effort for repeated finite element solutions. The major advantage of the method is the possibility of using the data not only from the computer solution, but also the data obtained experimentally in the reference points. In this case, simple mathematical models represent both theoretical and experimental data.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 51–64, January–February, 1995.     

Composite generalized Laguerre–Legendre pseudospectral method for Fokker–Planck equation in an infinite channel

In this paper, we propose a composite generalized Laguerre–Legendre pseudospectral method for the Fokker–Planck equation in an infinite channel, which behaves like a parabolic equation in one direction, and behaves like a hyperbolic equation in other direction. We establish some approximation results on the composite generalized Laguerre–Legendre–Gauss–Radau interpolation, with which the convergence of proposed composite scheme follows. An efficient implementation is provided. Numerical results show the spectral accuracy in space of this approach and coincide well with theoretical analysis. The approximation results and techniques developed in this paper are also very appropriate for many other problems on multiple-dimensional unbounded domains, which are not of standard types.     

Multi-objective optimization of composite structures. A review

Studies performed on the optimization of composite structures by coworkers of the Institute of Polymers Mechanics of the Latvian Academy of Sciences in recent years are reviewed. The possibility of controlling the geometry and anisotropy of laminar composite structures will make it possible to design articles that best satisfy the requirements established for them. Conflicting requirements such as maximum bearing capacity, minimum weight and/or cost, prescribed thermal conductivity and thermal expansion, etc. usually exist for optimal design. This results in the multi-objective compromise optimization of structures. Numerical methods have been developed for solution of problems of multi-objective optimization of composite structures; parameters of the structure of the reinforcement and the geometry of the design are assigned as controlling parameters. Programs designed to run on personal computers have been compiled for multi-objective optimization of the properties of composite materials, plates, and shells. Solutions are obtained for both linear and nonlinear models. The programs make it possible to establish the Pareto compromise region and special multicriterial solutions. The problem of the multi-objective optimization of the elastic moduli of a spatially reinforced fiberglass with stochastic stiffness parameters has been solved.The region of permissible solutions and the Pareto region have been found for the elastic moduli. The dimensions of the scatter ellipse have been determined for a multidimensional Gaussian probability distribution where correlation between the composite's properties being optimized are accounted for. Two types of problems involving the optimization of a laminar rectangular composite plate are considered: the plate is considered elastic and anisotropic in the first case, and viscoelastic properties are accounted for in the second. The angle of reinforcement and the relative amount of fibers in the longitudinal direction are controlling parameters. The optimized properties are the critical stresses, thermal conductivity, and thermal expansion. The properties of a plate are determined by the properties of the components in the composite, eight of which are stochastic. The region of multi-objective compromise solutions is presented, and the parameters of the scatter ellipses of the properties are given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 363–376, May–June, 1996. Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga.     

Optimization of a cylindrical composite shell with a viscoelastic core in axial compression

The problem of the optimal design of a composite shell in creep is formulated. The progressive buckling of a cross-wound reinforced cylindrical shell supported on a viscoelastic core is considered as a particular case. The reinforcement structure and shell thickness corresponding to minimum weight for a given load and service life are found.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 442–446, May–June, 1975.     

Adhesion bond and temperature stresses at the polymer - filler interface in polyethylene composites

The temperature stresses in polyethylene composites with fibrous fillers have been estimated. It is shown that they do not represent a threat to the adhesion bond or the cohesion strength of the components of the systems investigated. Model experiments have revealed the presence of an adhesion interaction between the filler and the matrix in the composite itself and have made it possible to estimate the actual threat posed by the temperature stresses. The mechanism of action of the filler particles on the thermal expansion of the composite is explained.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1049–1056, November–December, 1970.     

Structural approach to calculation of the effect of moisture on elastic characteristics of organoplastics

Data have been obtained for the structural calculation of the effect of moisture on the elastic characteristics of organoplastics from the properties of components. The distribution of moisture between the fiber and matrix — the components of a unidirectional composite — is considered. The elastic properties of the fiber are determined by an inverse calculation using the experimental dependences of the composite and matrix on moisture. The moisture effect on the properties of the materials is taken into account with influence functions, which differ by more than 25% for various characteristics. The results can be used for calculating the elastic properties of composites with various reinforcement schemes and at the nonequilibrium distribution of the moisture concentration in an actual environment.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 525–530, July–August, 1998.     

Thermal deformation of unidirectionally reinforced hybrid composites. Report no. 1

Conclusion We conducted a dilatometric study of three types of hybrid unidirectionally reinforced composites (organic-glass-, organic-carbon-, and carbon-glass-fiber plastics), each of which was represented by several batches differing in the relative content of the two types of fibers. The tests were performed on a specially-designed laboratory prototype. It was shown that, for the materials studied, the coefficient of linear expansion can be controlled by means of hybridization — by combining several types of fibers with positive and negative values of the coefficient of linear expansion in one composite. Analytic expressions for the coefficient that were obtained by generalizing a three-phase model of a two-component composite with isotropic fibers to the case of a hybrid composite with anisotropic fibers satisfactorily describe the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 229–236, March–April, 1989.     

Elastic blade root connection in wind turbine using flexible elements from composites

The aim of an elastic blade root connection with a hub is to decrease loads in the blade root section during wind gusts. Two designs of connection were considered: for the load reduction on the blade in operating regime and for stopped blade unloading under storm wind. In the first case two versions of joint were discussed: the first one — with hinges and U-shaped composite beams, the second one — formed with straight beams oriented in different directions. Both joints have low torsional stiffness in wind direction and much higher stiffnesses around two other axes. Formulas for angular stiffnesses and the methods of obtaining the nonlinear behavior of the joint are presented. The objective of the flexible spar was to allow the blades to bend back out of the wind to reduce loads when the wind turbine was stationary in storm conditions. Calculations supported the feasibility of such a design. With a low torsional stiffness, spar (which can be rigidly connected to the blade) acts as a pitching beam for turbine control. A compound spar design consisting of pultruded bars clamped through specified distance was proposed. Torsional stiffnesses of different types of spars with equal specified bending rigidity were compared.Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 388–400, May–June, 1996.     

On the three-dimensional stability loss problems of elements of structures of viscoelastic composite materials

Up to now, numerous problems of the stability loss for elements of structures made from composite materials have been investigated in the framework of the three-dimensional linearized theory of stability (TDLTS). It follows from the analysis of these investigations that the TDLTS was mainly applied to the design of elements of structures made from time-independent materials. For the solution of these problems for viscoelastic materials in the framework of the TDLTS, the dynamic investigation method and the critical deformation method are recommended in many references. However, it is known that a very reliable and frequently used approach for viscoelastic materials is the approach based on the study of the growth of insignificant initial imperfections in elements of structures with time. Taking into account the above-mentioned, an approach based on the growth of the initial imperfection for the investigation of the stability loss problems of elements of structures made from viscoelastic composite materials in the framework of TDLTS is proposed in the present paper. The composite material is modeled as an anisotropic, viscoelastic solid with averaged mechanical properties and all investigations are made on the strip simply supported at the ends.Yildiz Technical University, Dept. Math. Eng., 80750, Besiktas-Yildiz, Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 761–770, November–December, 1998.