A model of a transversely isotropic compressible elastic medium with finite strains is proposed. The model belongs to the class of the so-called universal models, which are formulated in terms of energy (conjugated) pairs of stress and strain tensors - simultaneously for several types of pairs. An algorithm is proposed for calculating the constants included in the constitutive relations of this model, based on a comparative analysis of the results of calculating deformation diagrams under uniaxial loading according to this model and using the asymptotic averaging method. An example of numerical modeling for a layered composite is given.
The article is devoted to the strategy for the development of digital education at the Bauman Moscow State Technical University. The theoretical and practical aspects of the development of online courses are considered, in accordance with the requirements of the National Open Education Platform (NOEP) using the Open BMSTU platform. The paper includes the program of the advanced training course for teachers in in online courses development and implementation areas, tested at the Bauman Moscow State Technical University.
The article considers the modeling results of layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered composites with finite deformations and periodic structure. The method allows calculating the effective deformation diagrams connecting the averaged Piola-Kirchhoff stress tensors components and the strain gradient.
Abstracts
The article is devoted to solving the problem of cylindrical bending of a flat panel made of a transversely isotropic incompressible composite material with finite deformations. The focus of the article is that in this problem the so-called universal model of constitutive relations is considered, which allows one to obtain solutions to problems simultaneously for several classes of models related to different conjugate pairs of stress-strain tensors. This method was proposed earlier in the works of Yu.I. Dimitrienko. Using this method, the difference in the calculation results, which are obtained using various models of composites with finite strains, is shown.
A method for multiscale supercomputer calculations of the composite structures strength has been developed. A feature of the proposed methodology is of division of the solution algorithm into 2 parts: solving problems at the micro level (in turn, these problems can consist of several sub-levels of calculation) and solving the problem at the macro level. Such a division, in which the solution of some problems is the input to problems at a higher level, helps to significantly reduce the consumption of computing resources. When solving problems, curvilinear anisotropy is taken into account at the macro level (structures), as well as at the micro level (composite material). The 3D finite element method was used for the numerical solution. To take into account curvilinear anisotropy, a special assembly algorithm is used, which requires the construction of anisotropy blocks (cells). A method is proposed for taking into account integral boundary conditions when solving problems of the linear theory of elasticity. A finite element modeling of the stress-strain state and damageability of a cylindrical structure with power ring elements has been carried out. As an example, textile composite materials (CM) with carbon and glass fibers are considered.
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