Theoretical and experimental investigations of the formation mechanisms of residual deformations of fibrous layered structure composites

© The Authors, published by EDP Sciences, 2017. On the example of a unidirectional fibrous composite made of unidirectional carbon fibre composite and cold-hardening epoxy XT-118, tests of specimens with a stacking scheme [+45 0 /-45 0 ]2s, where s is the number of monolayers, were carried out for cyclic loading by tension and compression. When the samples are stretched, both the fibers and the epoxy of composite are under shear stresses and stretching in the transverse direction by normal stresses, and under compression, under shear stresses and compression by normal stresses across the fibers. It is shown that in each loading cycle there is a consolidation of the material associated with the rearrangement of its microstructure, an increase in the secant modulus of elasticity and a decrease in the magnitude of the deformation increment at each cycle. The mechanism of accumulation of residual deformations under multiple loading of test samples was qualitatively studied and their level formed in the composite after each loading cycle was quantitatively found

Consistent Equations of Nonlinear Multilayer Shells Theory in the Quadratic Approximation

© 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

Consistent Equations of Nonlinear Multilayer Shells Theory in the Quadratic Approximation

© 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

Theoretical and experimental investigations of the formation mechanisms of residual deformations of fibrous layered structure composites

© The Authors, published by EDP Sciences, 2017. On the example of a unidirectional fibrous composite made of unidirectional carbon fibre composite and cold-hardening epoxy XT-118, tests of specimens with a stacking scheme [+45 0 /-45 0 ]2s, where s is the number of monolayers, were carried out for cyclic loading by tension and compression. When the samples are stretched, both the fibers and the epoxy of composite are under shear stresses and stretching in the transverse direction by normal stresses, and under compression, under shear stresses and compression by normal stresses across the fibers. It is shown that in each loading cycle there is a consolidation of the material associated with the rearrangement of its microstructure, an increase in the secant modulus of elasticity and a decrease in the magnitude of the deformation increment at each cycle. The mechanism of accumulation of residual deformations under multiple loading of test samples was qualitatively studied and their level formed in the composite after each loading cycle was quantitatively found

Investigation of a geometrically and physically nonlinear three-point bending problem for a sandwich plate with transversally soft core

© 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

Investigation of a geometrically and physically nonlinear three-point bending problem for a sandwich plate with transversally soft core

© 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

Transforming Calculated Schemes in Geometrically Non-linear Mechanics Problems of the Sandwich Plates with Contour Reinforcing Beams

© 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

Transformable calculation schemes in geometrically nonlinear problems of mechanics of sandwich plates with the contour reinforcing beams

© 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

Transforming Calculated Schemes in Geometrically Non-linear Mechanics Problems of the Sandwich Plates with Contour Reinforcing Beams

© 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