Multicriteria optimization of a rectangular composite plate subjected to longitudinal thermal stresses and buckling in shear loading

The multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to thermal and shear loading is considered. From the known properties of the monolayer and given values of variable structural parameters, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 85–92, January–February, 2007.     

Compromise optimization of a rectangular composite plate subjected to biaxial thermal loading and buckling under the action of shear

The compromise optimization of the structure and geometry of a laminated anisotropic composite plate subjected to biaxial thermal shear loading is considered. From the known properties of the monolayer and given values of a variable structural parameter, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal and transverse thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 471–478, July–August, 2008.     

Multicriteria optimization of a composite cylindrical shell under an external pressure and longitudinal thermal stresses

The multicriteria optimization of the structure and geometry of a laminated cylindrical shell under the action of external pressure and longitudinal thermal stresses is considered. From the known monolayer properties of the composite and the given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external pressure and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 495–502, July–August, 2006.     

Multicriteria optimization of a composite cylindrical shell subjected to longitudinal thermal stresses and buckling under the action of torque

The multicriteria optimization of the structure and geometry of a multilayer cylindrical shell under the action of external torque and longitudinal thermal stresses is considered. From known monolayer properties of the composite and given values of variable structural and geometric parameters, the thermoelastic properties of the anisotropic layered composite are determined. The criteria to be optimized — the critical external torque and thermal stresses — depend on two variable parameters and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 223–230, March–April, 2009.     

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.     

Characteristics of four-dimensional normal distribution of properties of composite in stochastic compromise optimization

In a numerical example of compromise optimization by computerized mathematical modeling (2000 realizations) for a known deterministic solution, in the case of an isotropic spatially reinforced porous composite, certain scatter characteristics of the optimal solution have been established, namely four standard deviations and six coefficients of linear correlation for four properties—density, modulus of elasticity, thermal conductivity, and linear thermal expansion coefficient. Of the 17 input data (parameters of the composite components), 10 are stochastic, the others deterministic. An equation is presented for the four-dimensional hyperellipsoid of normal distribution with numerical values of the coefficients, as well as all invariants and roots of the characteristic equation, the matrix of direction cosines of the principal axes of the hyperellipsoid, and the lengths of the principal semiaxes, depending on the dimensionality of the scattering region and the assigned probability P. The four-dimensional hyperellipsoid has been projected onto three-dimensional space and then onto a plane. A section of the scattering region has been constructed. Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 625–635, September–October, 1996.     

Yield condition for circular cylindrical shells made of a fiber-reinforced composite

A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results of numerical calculations are represented in the form of graphs. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006.     

Multiobjective Optimization of a Composite Cylindrical Shell with an Elastic Core with Account of Reliability

Multiobjective optimization of the structure and geometry of a laminated anisotropic composite shell with an elastic core under thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known properties of the monolayer and the given values of the variable structural and geometric parameters. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite, and the temperature. In the space of the properties being optimized, the domain of allowable solutions and the property scatter ellipses for the optimum compromise project are found. The reliability of the project is determined with regard for the correlation between the critical and thermal stresses.     

A composite material based on recycled tires

The present study is devoted to the elaboration and investigation of a composite material based on mechanically grinded recycled tires and a polymer binder. The correlation between the content of the binder, some technological parameters, and material properties of the composite was clarified. The apparent density, the compressive stress at a 10% strain, the compressive elastic modulus in static and cyclic loadings, and the insulating properties (acoustic and thermal) were the parameters of special interest of the present investigation. It is found that a purposeful variation of material composition and some technological parameters leads to multifunctional composite materials with different and predictable mechanical and insulation properties. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 145–150, January–February, 2009.     

Axiomatizations of the Euclidean compromise solution

A multicriteria optimization problem is one of choosing an alternative that optimizes several—possibly conflicting—objective functions simultaneously. The utopia point of a multicriteria optimization problem is the vector that specifies for each objective function the most favorable feasible value. The Euclidean compromise solution in multicriteria optimization is a solution that selects from a feasible set the alternative such that its vector of criteria values has minimal Euclidean distance to the utopia point. This paper provides several axiomatic characterizations of the Euclidean compromise solution that are based on consistency properties.     

Effect of viscosity of a thermoplastic prepreg and matrix upon winding of rings

The problem of compression of a unidirectional layer and shear of a polymer interlayer during winding of rings is considered. The equations determining the dependence of the layer thickness and stresses on the parameters entering into the power flow law for a prepreg and polymer matrix and on the basic parameters of the winding process—the initial tension of the prepreg, its placement rate, and the radius of a mandrel—are derived. The ring thickness measurements obtained at various temperatures and initial tension forces of plies confirm the adequacy of the model offered. It is found that the viscous properties of the prepreg and matrix upon winding affect the relative change in the layer thickness to a greater extent than the stresses in these layers. With increase in temperature and tension force upon winding, the effect of viscous deformations of the prepreg and matrix increases. A decrease in viscosity and an increase in the tension force of the tape lead to a higher strength of the ring in tension and interlaminar shear; however, the growing percolation of the polymer melt leads to a greater inhomogeneity of the structure of the composite in the ring and to a lower reinforcing effect of the factors mentioned. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 419–428, 2000.     

Measuring and modeling the thermal conductivities of three-dimensionally woven fabric composites

The effect of a three-dimensional fiber reinforcement on the out-of-plane thermal conductivity of composite materials is investigated. Composite preforms with different fibers in the thickness direction were fabricated. After in fusion by using a vacuum-assisted resin transfer molding process, their through-thickness thermal conductivities were evaluated. The measured thermal conductivities showed a significant increase compared with those of a typical laminated composite. Although the through-thickness thermal conductivity of the samples increased with through-thickness fiber volume fraction, its values did not match those predicted by the simple rule of mixtures. By using finite-element models to better under stand the behavior of the composite material, improvements in an existing analytical model were performed to predict the effective thermal conductivity as a function of material properties and in-contact thermal properties of the composite. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 241–254, March–April, 2009.     

Experimental and theoretical investigation of a composite beam for bridge structures

Results of an experimental and theoretical investigation of composite beams as elements of bridge superstructure are presented. Experiments on beams of two types — made of wood and the same beams with a composite sheath — were carried out. The rigidity of the beams of the second type was about twice as high as that of the first ones. The classical bending model of composite beams gave deflections smaller than experimental ones. To reconcile these results, the model is refined by including the effect of shear. The deflections are represented as classical ones multiplied by a shear factor which depends on the bending and shear stiffnesses and the span length of the beams. As a result, a good agreement between calculations and experiments is achieved. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 449–462, July–August, 2006.     

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 Composite Plate Buckling under Thermal Action with Account of Reliability

Optimization of the structure of a laminated anisotropic composite plate subjected to thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known stochastic properties of the components and the given values of the variable structural parameters, using the method of orientational averaging. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite and the temperature. In the space of the properties being optimized, the domain of admissible solutions and the parameters of the property scatter ellipses at the characteristic points of the project are found. For the compromise optimum project obtained, the reliability is determined with account of the correlation between the critical and thermal stresses. Reduced requirements to the critical loads and thermal stresses lead to an increase in the reliability of the project.     

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic—based on the CGRASP and GENCAN methods—for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP–GENCAN on a set of benchmark multimodal test functions.     

Spatial braiding of cylindrical articles

The effective deformative characteristics of spatially reinforced composites made by spatial braiding along the generatrices of a one-sheet hyperboloid are analyzed. The geometrical relationships determining the structure of a unit cell of a braided composite are derived. The effective thermoelastic characteristics are calculated by the method of orientational averaging. The dependences of the bending and torsional stiffnesses of thick-walled cylindrical rods — made by the method suggested and by winding — on the braiding/winding angle are compared. The numerical estimations are given for rods made of carbon (CFRP) and aramid (AFRP) epoxy plastics. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompzitnykh Materialov, Vol. 36, No. 3, pp. 341–354, May–June, 2000.     

Effect of surface modification of fibers with a polymer coating on the interlaminar shear strength of a composite and the translation of fiber strength in an F-12 aramid/epoxy composite vessel

The surface of aramid fibers was modified with a polymer coating — a surface treatment reagent containing epoxy resin. The resulting fibers were examined by using NOL tests, hydroburst tests, and the scanning electron microscopy. The modified fibers had a rougher surface than the untreated ones. The interlaminar shear strength of an aramid-fiber-reinforced epoxy composite was highest when the concentration of polymer coating system was 5%. The translation of fiber strength in an aramid/epoxy composite vessel was improved by 8%. The mechanism of the surface treatment of fibers in improving the mechanical properties of aramid/epoxy composites is discussed. Russian translation publeshed in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 729–738, November–December, 2006.     

Calculation of statically indeterminate composite beam elements by using refined boundary conditions and with account of their state diagrams

The effect of compliance of support units on the calculation of strength of composite beams with account of the nonlinear deformation diagram of the composite is examined. The basic equilibrium equations of the mechanics of deformable solid bodies are used to solve the problems of strength, rigidity, and displacements, with introduction into them extreme criteria for the parameters to be calculated. The procedure developed al lows one to find the final solutions by using iterative processes. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 75–84, January–February, 2009.     

Comparison and robustification of Bayes and Black-Litterman models

For determining an optimal portfolio allocation, parameters representing the underlying market—characterized by expected asset returns and the covariance matrix—are needed. Traditionally, these point estimates for the parameters are obtained from historical data samples, but as experts often have strong opinions about (some of) these values, approaches to combine sample information and experts’ views are sought for. The focus of this paper is on the two most popular of these frameworks—the Black-Litterman model and the Bayes approach. We will prove that—from the point of traditional portfolio optimization—the Black-Litterman is just a special case of the Bayes approach. In contrast to this, we will show that the extensions of both models to the robust portfolio framework yield two rather different robustified optimization problems.