Search

© 2019, Kazan Federal University. All rights reserved. Based on the qualitative analysis of the geometric pattern of deformation of flat specimens from cross-ply fibrous composites with the [�45°]2s lay-up when they are under tension and compression and using the physical dependencies compiled earlier for this class of composites, the relationships have been derived that made it possible to determine the components of the strain and stresses in the material orthotropy axes through the axial strain of the specimen measured in the experiment. In the linear formulation of two-and three-dimensional problems, numerical experiments have been carried out to determine the parameters of the stress-strain state of specimens consisting of one and two laminas of unidirectional fibrous plastic with [+45°] and [�45°]2 structures, respectively. The cases of tension of long and compression of short specimens have been considered; the analysis of the forming stress components along the fibers located in the central part and in the vicinity of the corner points of the specimens has been carried out. Experiments on the tension of flat specimens from a fiber composite with a [�45°]2s lay-up to determine the deformed state using a non-contact strain measurement system have been performed. The obtained results allow to indicate areas in which the implementation and continuous change of internal non-classical buckling modes of structural elements of fibrous composites are possible during the loading process, which is probably one of the reasons for the physically nonlinear behavior of specimens with the [�45°]2s lay-up under tension and compression.

© 2019, Pleiades Publishing, Ltd. Using the previously constructed equations of the theory of the plane multi-layer beams with a thin-layer structure in thickness, based on a discrete-structural model, a linear problem on the formation of the initial (subcritical) stress-strain state in test specimens of a unidirectional laminated composites with the [90°]s structure was given in shear tensile-compression tests. A numerical method was developed for solving the formulated problem, based on the reduction of the original problem to a system of integro-algebraic equations and the construction of their solution by the method of finite sums. The properties of the constructed equations are investigated and numerical experiments are carried out on the basis of the developed method. It is shown that in the test specimens of the laminated composite of the considered structure at their tension (compression) in the direction across the fibers and in shear, predominantly normal tensile (compression) stresses are formed, which are constant along the length and width of the specimen, and the tangential stresses in these directions are variable.

© 2019, Pleiades Publishing, Ltd. For the laminated shells on the basis of the Timoshenko model, taking into account the transversal compression used for each layer, two versions of two-dimensional equations describing geometrically nonlinear deformation for arbitrary displacements and small strains are constructed. They are based on previously proposed consistent relationships of the non-linear elasticity theory, usage of which does not lead to the appearance of “false” bifurcation solutions. The first version corresponds to the contact problem statement, in accordance with which the contact stresses into the contact points of the layers as unknowns are introduced, and the second version corresponds to the preliminary satisfaction of the kinematic coupling relations for the layers along the displacements. An example is given of the application of the derived equations for solving the linear problem of a plane stress-strain state of a straight beam under the action of normal surface forces applied to the front boundary surfaces is given.

© 2019, Pleiades Publishing, Ltd. A numerical study of the geometrically nonlinear problem of deforming the cylindrical shape of a sandwich plate with a transversally soft core, supported in the end sections of absolutely rigid bodies, according to transforming calculation schemes as it is loaded, has been carried out. It is shown that such a transformation is necessary after the delamination of the adhesive layer connecting the end section of the core with the contour reinforcing beam, designed to ensure the transfer of external load on the carrier layers. The previously obtained equations were used, which are based on introducing into consideration, as unknown contact forces, the interaction of the outer layers with a core, as well as the external layers and the core with reinforcing bodies at all points of their interface surfaces. The problem under study required the sequential formulation and solving of two problems: on the stress-strain state of the structure until the beginning of the destruction of the adhesive layer between the core and the reinforcing beam and about determining the increments of the parameters of the stress-strain state after delamination. To simulate the delamination process, a method based on the parameter continuation method is proposed. This method provides for zeroing the tangential stresses formed in the adhesive layer at the first loading stage, by choosing the incremental tangent stresses specified above as the loading parameter. Numerical methods for solving the formulated problems were developed. They are based on a preliminary reduction of the initial problems to systems of integro-algebraic equations and the construction of their solutions by the finite sum method. To resolve the geometric nonlinearity, a two-layer iterative process is used.

© 2019 IOP Publishing Ltd. Experimental studies of test samples from a obliquely reinforced composite based on carbon tape on cyclic stretching were carried out. It is established that the loading and unloading branches do not coincide, forming a hysteresis loop, and the axial deformation at each subsequent cycle at the same stress level in the cycle gains an increment that decreases in the initial cycles and tends to a constant value with a further increase in the number of cycles. This process is called the process of adaptability of the composite material. On the basis of tests on multi-cycle stretching of a composite with an aging after unloading, a viscoelastic component was distinguished from accumulated strain at each loading cycle. It is shown that at the initial cycles, the total strain accumulated in the sample by the end of the unloading process can be represented as a sum consisting of residual strain formed due to structural changes in the composite and creep deformation that disappears in the sample after unloading and holding during a long time.

© 2019 IOP Publishing Ltd. The geometrically and physically nonlinear problem of the mechanics of deforming a sandwich plate with a transversally soft core under three-point bending is considered. It is shown that with this type of loading in test samples, it is possible to implement a mixed flexural buckling form, which is one of the reasons for their destruction with certain mechanical characteristics of the core. A method for determining the bifurcation point, a method for finding the supercritical branch of the solution are proposed, and the supercritical behaviour of the plate is studied. The method is based on the method of parameter continuation, in which quality is proposed to use the work of external forces due to its strongly increasing. Numerical experiments were carried out to study the process of geometrically and physically nonlinear deformation of the plate.

© 2019 IOP Publishing Ltd. The transformable calculation schemes for geometrically nonlinear problems of mechanics of sandwich plates with contour reinforcing beams are constructed. To solve the boundary value problem, it was used by the finite sum method. The solving the nonlinear problem arising in this case using a two-layer iterative process with the lowering of nonlinearity on the lower layer was carried out. A software package implemented in the Matlab environment has been developed. Numerical experiments were carried out and their results were analyzed.