Abstract
Composite materials consisting of several phases are widely used in modern construction. Numerous experiments have shown that the properties of structurally heterogeneous materials can differ significantly from those of the individual components making up the composition. Besides, rapidly changing coefficients of differential equations describing such composite materials greatly complicate the solution of boundary value problems even with the help of computer calculation methods. Therefore, the homogenization method is used. In this paper the approach propose to obtain in explicit analytical form the effective model of the problem of loading a heterogeneous pipe made of layered material, provided that the elastic properties of the material only depend on the distance from the center of pipe cross section. We point to a method that obviously leads to an analytical result. It follows from the article that it is possible to choose the function that determines the structure of the “winding” in such a way as to obtain the stiffness characteristics of the pipe as close as possible to the desired with fixed mass fractions of the materials used.
Highlights
Problems for products from heterogeneous materials, in particular pipes, arise in many areas of construction
The approach proposed in this paper proposes to obtain in explicit analytical form the solution of the problem of loading a non-uniform pipe made of laminated material, provided that the elastic- creeping properties of the material depend only on the distance from the center of pipe cross section
The approach proposed in this paper permits one to obtain in an explicit analytical form the effective, slowly varying and radius-dependent elastic and elastic-creeping characteristics of a non-uniform pipe made of laminated material, provided that the elasticity of the material depends only on the distance from the center of the section of the pipe
Summary
Problems for products from heterogeneous materials, in particular pipes, arise in many areas of construction. These boundary value problems have periodic boundary conditions along the elastic rod and the corresponding Neumann conditions on the lateral surface In this case, by introducing cylindrical coordinates, we can reduce these auxiliary three-dimensional problems of the theory of elasticity to one-dimensional systems, where only the radial variable is an independent variable (the angular and axial variables are not included in this system of equations). It is the choice of these constant matrices that will ensure that the solvability conditions are satisfied The elements of these matrices will be the numbers that determine the effective characteristics of the heterogeneous pipe, namely, the effective indicators of flexural rigidity, tensile stiffness and torsion. Authors receive these effective indicators and auxiliary functions in an explicit analytical form. The available analytical solutions allow to evaluate qualitative and quantitative characteristics of obtained stress-strain states
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