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.     

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 145–164, March–April, 2008.     

An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams

This paper deals with the shear strengthening of Reinforced Concrete (RC) flexural members with externally bonded Fiber-Reinforced Polymers (FRPs). The interaction between an external FRP and an internal transverse steel reinforcement is not considered in actual code recommendations, but it strongly influences the efficiency of the shear strengthening rehabilitation technique and, as a consequence, the computation of interacting contributions to the nominal shear strength of beams. This circumstance is also discussed on the basis of the results of an experimental investigation of rectangular RC beams strengthened in shear with “U-jacketed” carbon FRP sheets. Based on experimental results of the present and other investigations, a new analytical model for describing the shear capacity of RC beams strengthened according to the most common schemes (side-bonded and “U-jacketed”), taking into account the interaction between steel and FRP shear strength contributions, is proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 339–356, May–June, 2008.     

Constructing the governing equations for a layered composite of regular structure within the limits of the theory of asymmetric elasticity on the basis of energy criteria of equivalence

Within the limits of the theory of asymmetric elasticity, two (kinematic and static) approaches are offered to constructing the governing equations for a layered hybrid composite of regular structure with isotropic constituents. As a criteria of equivalence between the layered composition and a homogeneous transversely isotropic material, the equality of the specific free energy and the specific thermodynamic Gibbs energy in them is used, which allows one to determine the upper and lower bounds for the effective rigidities of the layered material. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 3–16, January–February, 2009.     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

FRP-strengthened reinforced concrete beams: a review and the assessment of cracking and deflection models

A review of some cracking and deflection models used for a structural analysis of FRP-strengthened reinforced concrete beams is presented, and, with reference to short-term deflections, a comparison between model predictions and experimental results is made. By using predictions provided by a nonlinear model derived from a cracking analysis, founded on slip and bond stresses, and experimental results for 63 FRP-strengthened beams, a modification of the well-known semi-empirical Branson’s formula to compute beam deflections is proposed. Finally, the efficiency of the modification is evaluated by comparison with experimental results.     

Investigation of free vibrations of composite beams by using the finite-difference method

The free-vibration behavior of symmetrically laminated fiber-reinforced composite beams with different boundary conditions is examined. The effects of shear deformation and rotary inertia, separately and/or in combination, on the free-vibration properties of the beams are investigated. The finite-difference method is used to solve the partial differential equations describing the free-vibration motion in each case. The effect of shear deformation on the natural frequencies is considerable, especially for higher frequencies, whereas the influence of rotary inertia is less significant. The study includes comparisons with results available in the literature. In addition, the impact of such factors as the span/depth ratio, fiber orientation, stacking sequence, and material type on free vibrations of the composite beams is investigated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 331–346, May–June, 2006.     

Transient response of sandwich viscoelastic beams, plates, and shells under impulse loading

The transient response of sandwich beams, plates, and shells with viscoelastic layers under impulse loading is studied using the finite element method. The viscoelastic material behavior is represented by a complex modulus model. An efficient method using the fast Fourier transform is proposed. This method is based on the trigonometric representation of the input signals and the matrix of the transfer functions. The present approach makes it possible to preserve exactly the frequency dependence of the storage and loss moduli of viscoelastic materials. The logarithmic decrements are determined using the steady state vibrations of sandwich structures to characterize their damping properties. Test problems and numerical examples are given to demonstrate the validity and application of the approach suggested in this paper. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 367–378, March–April, 2000.     

Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates

The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer (CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 667–686, September–October, 2007.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

Dynamic assessment of reinforced concrete beams repaired with externally bonded FRP sheets

This research deals with RC beams strengthened with FRP. An experimental research is presented which is aimed at evaluating the capability of an experimental modal analysis to assess the stiffness decrease due to damage, as well as the stiffness recovery due to strengthening. Ten beams were tested. All of them were subjected to loading cycles with increasing load levels in order to induce cracking of different severity in them. The beams were then retrofitted by externally bonded FRP sheets. Three types of composites were used. The number of layers was varied, too. Modal tests were carried out after each loading-unloading cycle. The modal frequencies and damping ratios were determined for the first four vibration modes. The results obtained indicate that an experimental modal analysis can give useful information on the severity of damage and the effectiveness of strengthening. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 3–20, January–February, 2006.     

An analysis of the joint operation of a CFRP concrete in flexural elements

The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 687–700, September–October, 2007.     

Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations

The purpose of this paper is to establish strong lower energy estimates for strong solutions of nonlinearly damped Timoshenko beams, Petrowsky equations in two and three dimensions and wave-like equations for bounded one-dimensional domains or annulus domains in two or three dimensions. We also establish weak lower velocity estimates for strong solutions of the nonlinearly damped Petrowsky equation in two and three dimensions. The feedbacks in consideration have arbitrary growth close to the origin. These results improve the strong lower energy decay rates obtained in our previous papers (Alabau-Boussouira in J Differ Equ 249:1145–1178, 2010; J Differ Equ 248:1473–1517, 2010) for strong solutions of the nonlinearly locally damped wave equation and extend to systems and to Petrowsky equation the method of Alabau-Boussouira (J Differ Equ 249:1145–1178, 2010; J Differ Equ 248:1473–1517, 2010). These results are the first ones for Timoshenko beams and Petrowsky equations.     

Designing of layered rod structures from viscoelastic materials at a given service life

The problem on the rational design of a layered rod structure subjected to force and temperature actions under the conditions of creep is considered. The linear hereditary theory is used for the viscoelastic materials of layers. The rods are packages of several homogeneous layers with a rectangular cross section. The variable geometrical parameters of the rods are determined from the energy equal-strength condition at a given in stant of time. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 581–594, September–October, 2007.     

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.     

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 Optimal Design of a Rectangular Composite Plate Subjected to Biaxial and Thermal Loading

Multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to the thermal and biaxial action is considered. From known properties of the monolayer and the given values of variable structural parameters, the thermoelastic properties of the layered composite are determined. The criteria to be optimized—the transverse critical load and the longitudinal thermal stresses—depend on two variable design parameters of composite properties and temperature. In the space of the optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 683–690, September–October, 2005.     

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.     

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.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.