International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Golushko S.  

Composite Structures: Mathematical Modeling, Calculation and Optimization

    The first part of the report is dedicated to modeling the properties of composite materials. Two major approaches are discussed: phenomenological and structural [1]. Within the framework of the first approach reinforced materials are modeled as homogeneous anisotropic medium with efficient physical and mechanical properties. In this case mechanical parameters of the material are determined basing on experimental data. In a structural approach, physical and mechanical parameters of the composite are expressed in terms of the parameters of its components and design of reinforcement that open up opportunities for improvement of the properties of composite structures.
    The second part of the report is devoted to methods of solving boundary value problems for the mechanics of elastic composite plates and shells [2-4]. The systems of differential equations have a high order, variable coefficients and small parameters that result into edge effects. Various aspects of the application of discrete orthogonalization, spline collocation, collocation and least residuals methods for problems of classical and non-classical theories for plates and shells have been studied.
     The third part of the report discusses the problem of rational and optimal design of composite plates and shells. The conditions of solvability, analytical and numerical solutions of rational design problems for cylindrical, conical, spherical, ellipsoidal shells, pressure vessels have been obtained.

[1] Golushko S.K., Nemirovskiy Yu.V. Direct and inverse problems of mechanics of composite plates and shells, (Moscow: Fizmatlit, 2008). (in Russ.)
[2] Golushko S.K., Idimeshev S.V., Shapeev V.P. “Application of collocations and least residuals method to problems of the isotropic plates theory”, Computational technologies Vol. 18, Is. 6., P. 31–43 (2013). (in Russ.)
[3] Golushko S.K., Idimeshev S.V., Shapeev V.P. “Development and application of collocations and least residuals method to the solution of problems in mechanics of anisotropic laminated plates”, Computational technologies Vol. 19, Is. 5., P. 24–36 (2014). (in Russ.)
[4] Golushko. S.K., Idimeshev S.V., Semisalov B.V. “Methods for solving boundary-value problems of mechanics of composite plates and shells" : school-book of the curse «Direct and inverse problems of composite mechanics» DTI DT SB RAS Novosibirsk, 2014. 131 p. [electronic resource] ISBN 978-5-9905791-0-1 (in Russ.)

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