Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1967–1986 | Cite as

Tension-Compression and Shear of Plane Test Specimens from Laminated Composites with the [90°]s Structure. Initial Stress-Strain State

  • V. N. PaimushinEmail author
  • S. A. KholmogorovEmail author
  • I. B. BadrievEmail author
  • M. V. MakarovEmail author


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.

Keywords and phrases

laminated composite structural element fiber resin test specimen unidirectional reinforcement tension compression shear equilibrium equations finite sum method integrating matrix 


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The research results were obtained in the framework of the fulfillment of the state task of theMinistry of Education and Science of Russia No. 9.5762.2017/VU (project no. 9.1395.2017/PCh, Introduction) and with the financial support of the Russian Science Foundation (project no. 19-19-00059, sections 2–5, appendix).


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Information TechnologiesKazan (Volga Region) Federal UniversityKazanRussia
  2. 2.Institute of Aviation, Land Vehicles and EnergeticsKazan Tupolev National Research Technical University-KAIKazanRussia

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