Theory of composite cylindrical shells under quasistatic vibrations, based on an asymptotic analysis of the general viscoelasticity theory equations

• Published in: IOP conference series. Materials Science and Engineering Vol. 683; no. 1; pp. 12013 - 12018
• Main Authors: Dimitrienko, Yu I, Gubareva, E A, Pichugina, A E
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.11.2019
• Subjects: Algorithms; Angles (geometry); Asymptotic properties; Cylindrical shells; Exact solutions; Mathematical analysis; Multilayers; Pressure oscillations; Shells; Spherical coordinates; Stress concentration; Tensors; Viscoelasticity
• ISSN: 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/683/1/012013

A theory of thin multilayer anisotropic viscoelastic cylindrical shells with allowance for quasistatic oscillations, based on the application of asymptotic analysis of small geometric parameters to the general three-dimensional equations of the viscoelasticity theory for curvilinear coordinates, is proposed. Recurrent sequences of local problems of the viscoelasticity theory for shells under the quasistatic pressure oscillations are formulated and analytical solutions are obtained. It is shown that with this approach it is possible to obtain expressions for all 6 components of the stress tensor over the thickness of the shell. An example of the calculation of a cylindrical viscoelastic shell with axisymmetric bending with allowance for quasistatic oscillations is considered. The graphs of the dependences of the components of the stress tensor on the local coordinate are given for different angles of layers in the material. An algorithm is proposed for obtaining explicit analytical equations for calculating the distribution of the total stress tensor components over a cylindrical shell under the action of quasistatic oscillations.