###
Transient stress-strain state of a composite cylindrical shell

Fedotenkov G.V., Lokteva N.A., Serdyuk D.O., Skopintsev P.D.

#### Abstract:

This work is devoted to the description of an approach to studying the propagation of non-stationary disturbances, stresses and strains in a thin elastic composite cylindrical shell. The shell is accepted unlimited, with a constant thickness. An aggregate of non-stationary moving pressures affects along the normal to the outside surface of the shell. The shell is assumed to be unbounded, with a constant thickness. The outer face of the shell is subjected to a set of non-steady moving loads. It is assumed also that the composite material of the shell is linearly elastic, with a lamination scheme symmetric with respect to the midsurface. The shell model is based on the Kirchhoff-Lowe hypotheses, while the load instantly applied to the shell are modeled by Dirac functions. The study of non-steady deformation of the shell is carried out using the transient function, which is a normal displacement that occurs as a response to a single load concentrated in time and coordinates. The transient function is constructed using exponential Fourier series expansion, Laplace integral transformations in time domain and Fourier transforms with respect to the longitudinal coordinate. The inverse Laplace transform is performed analytically, whereas the original of the Fourier transform is found by using the numerical method of integrating rapidly oscillating functions. The non-steady normal deflection of the cylindrical shell is represented as a triple convolution of the transient function with the functions defining the moving concentrated loads with time-varying amplitudes and coordinates of the impact. The convolution integrals are evaluated using rectangle quadrature formulae. The study of the space-time stress-strain state of an unbounded thin elastic composite cylindrical shell becomes possible after constructing a non-steady deflection function with further use of constitutive and kinematic relations to obtain the stress state of the shell. In the study of the non-steady stress-strain state of the composite shell, the given technical constants determined through the generalized stiffness of the material are used. As an example, the space-time dependences of the non-steady deflection, the distribution of stresses and deformations on the outer surface of the polymer composite shell are constructed. Non-steady impact was considered as a set of moving concentrated loads.

0