Theoretical Foundations of the Method of Superimposed Meshes




finite-element method, viscoelasticity, composite material, Lagrangian functional


The problem of correct modeling of anisotropic properties of composite materials is not fully covered at the moment. This forces engineers and scientists to significantly simplify a description of physical and mechanical parameters when determining a mechanical behavior of solid deformable bodies, especially in case of the viscoelasticity phenomenon. As a result, commercial finite-element codes model these properties using hereditary functions that are proportional to the initial elasticity tensor, which in some cases is not a valid assumption. The proposed method of superimposed meshes eliminates such disadvantages. It allows to model physical and mechanical properties, in particular viscoelastic ones, taking into account any degree of their anisotropy. This method made it possible to solve a number of problems of the anisotropic viscoelasticity theory, which gave correct results. A theoretical substantiation of this method considers the total energy functional of a deformed body for linear static and dynamic problems of elasticity and viscoelasticity theories. Such an approach to a problem consideration established the rules for obtaining the parameters of the stress-strain state of deformable bodies in accordance with the features of the method of superimposed meshes and identified possible scenarios for its application


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How to Cite

V. Martynenko, “Theoretical Foundations of the Method of Superimposed Meshes”, Mech. Adv. Technol., no. 1(85), pp. 93–100, Apr. 2019.



Original study