Abstract
The problem on low-velocity impact of an elastic body upon a pre-stressed circular orthotropic plate possessing cylindrical anisotropy is considered. The dynamic behavior of the plate is described by equations taking the rotary inertia and transverse shear deformations into account. Longitudinal compressing forces are uniformly distributed along the plate’s median plane. Contact interaction is modeled by a linear spring, and a force arising in it is the linear approximation of Herts’z contact force. During the shock interaction of the impactor with the plate, the waves which are the surfaces of strong discontinuity are generated in the plate and begin to propagate. Behind the fronts of these waves, the solution is constructed in terms of ray series, which coefficients are the different order discontinuities in partial time-derivatives of the desired functions, and a variable is the time elapsed after the wave arrival at the plate’s point under consideration. The ray series coefficients are determined from recurrent equations within accuracy of arbitrary constants, which are then determined from the conditions of dynamic contact interaction of the impactor with the target. The found arbitrary constants allow one to construct the solution both within and out of the contact region. The analysis of the solution obtained enables one to find out the new effect and to make the inference that under a certain critical magnitude of the compression force the orthotropic plate goes over into the critical state, what is characterized by ‘locking’ the shear wave within the contact region, resulting in plate damage within this zone as soon as the compression force exceeds its critical value.
Highlights
During the past two decades foreign object impact damage to composite structures has received a great deal of attention, since laminated fiber-reinforced composite plates are known to be susceptible to damage resulting from accidental impact by foreign objects [5,6,7,8,11,12,13,20,21,22,23,26]
As a result of impact of a body upon the elastic orthotropic plate, only one wave is generated in the plate which further propagates with the velocity G(1), but the second wave turns out to be ‘locked’ within the contact region
Even without detail analysis of the case a < 0, the following considerations could be made about the post-critical behavior of the plate: since all energy of shock interaction is concentrated in the contact region, this may result in damage of the structure within the contact zone
Summary
During the past two decades foreign object impact damage to composite structures has received a great deal of attention, since laminated fiber-reinforced composite plates are known to be susceptible to damage resulting from accidental impact by foreign objects [5,6,7,8,11,12,13,20,21,22,23,26]. When investigating dynamic large deflection response of prestressed composite laminates subjected to impact [6] using the finite element method, it is found that initial tensile stress tends to intensify the contact force while reducing the contact time, and an opposite conclusion is obtained for initial compressive stress. Coefficients of the ray series, within an accuracy of arbitrary functions dependent on two coordinates on the plate mid-plane, were determined from recurrent differential equations of the ray method, which had been derived from the system of equations describing the dynamic behavior of the anisotropic half-space using the theory of discontinuities [24] Arbitrary functions, in their turn, were found from the condition of absence of tangential stresses and the condition of continuity for normal displacements and normal stresses on the contact boundary of the plate and the half-space, as well as from the initial conditions. Stability or instability of the plate is established by analyzing the behavior of transient waves generating in the plate at the moment of impact, which further propagate along its median surface as ‘diverging circles’
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