Modeling of the Behavior of Plane-Deformable Elastic Media with Elongated Elliptic and Rectangular Inclusions
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MODELING OF THE BEHAVIOR OF PLANE-DEFORMABLE ELASTIC MEDIA WITH ELONGATED ELLIPTIC AND RECTANGULAR INCLUSIONS V. S. Gudramovich,1, 2 É. L. Gart,3 and K. А. Strunin4
UDC 539.3
We propose a numerical model of the stress-strain state of a plane element of an elastic inhomogeneous medium with long elliptic and rectangular inclusions based on the use of the standard ANSYS finiteelement package. The mutual influence of inclusions is investigated depending on their orientation, shapes, sizes, and stiffnesses. We determine the safest possible versions of their mutual location. Keywords: plane elements of elastic media, elongated elliptic and rectangular inclusions, finite-element method, computer modeling, stress-strain state.
The investigation of the stress-strain state (SSS) of bodies with inclusions is important for the optimization of the processes of manufacturing of materials (powder metallurgy, ceramic production, casting, etc.) [1–4]. Inclusions can be used to model striated formations formed in the course of plastic prestraining in the microstructure of metals [5]. As one of directions in the investigation of the SSS of structural elements with inclusions of special types, we can mention the discrete hardening of materials [6]. Inclusions strongly affect the processes of deformation, lead to the concentration of stresses and the appearance of defects of the shape, and cause local fractures [7–9]. The processes of deformation may lead to phase transformations in materials, e.g., to the formation of martensitic structures [10]. It is especially important to study crack initiation in the course of phase transformations, which determines the onset of fracture of the material [11, 12]. Note that elongated inclusions can model the stiffening elements of thin-walled structures.
Inclusions and discontinuities in the form of cracks and pores play the role of local stress concentrators. In the study of the SSS of media containing these inclusions, it is reasonable to use numerical methods. They are fairly universal and applicable for the analyses of objects of various shapes and sizes and various types of loading, unlike the analytic methods, which are often cumbersome and, in some cases (noncanonical shapes of inclusions, complicated modes of deformation, etc.), inapplicable. Among the numerical methods, the finite-difference method, boundaryelement method, and finite-element method (FEM) are used especially extensively [13–15]. We especially mention the urgency of development of projective-iterative schemes for the realization of grid methods capable of significant reduction of the computer time in numerous problems of the mechanics of deformable solid [16–18]. These schemes based on the FEM were also used for the media with inclusions [19–22]. We also indicate the possibility of construction of these schemes for the method of local variations, i.e., for the numerical method used for the solution of variational problems [23]. 1 2 3 4
Institute of Technical Mechanics, Ukrainian National Academy of Sciences, State Space
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