Yu. V. Kokhanenko

Numerical Study of Three-Dimensional Stability Problems for Laminated and Ribbon-Reinforced Composites

Classes of basic problems (classical problems and new problems derived by partial separation of variables) of the theory of elasticity and three-dimensional linearized stability are formulated in Cartesian coordinates. For each class of problems, the base scheme and the base system of equations are constructed and substantiated. They allow us to write explicitly the global mesh equations corresponding to an arbitrary problem from the class under consideration

NUMERICAL SOLUTION OF THREE-DIMENSIONAL STABILITY PROBLEMS FOR ELASTIC BODIES

A solution in Cartesian coordinates to plane and spatial stability problems for composites is obtained within the framework of the second variant of the three-dimensional linearized theory of stability of deformable bodies. Two mechanical models are used: a homogeneous anisotropic medium with averaged mechanical characteristics and a piecewise-homogeneous medium with orthotropic linearly elastic components. To solve the problems, a mesh approach is applied. Discrete models are constructed using the concept of a base scheme. The calculated results are analyzed

Discrete Models of Problems in the Elastic Theory of Composites in Circular Cylindrical Coordinates. 1. Three-Dimensional Problems

The concept of basic schemes is employed to construct discrete problems that approximate the basic three-dimensional problems of the elastic theory of composites in circular cylindrical coordinates for domains of arbitrary connectivity and complex geometry

Solution of plane problems of the three-dimensional stability of a ribbon-reinforced composite

The plane problem of three-dimensional elastic stability is solved for a ribbon-reinforced composite under lateral compression if its initial state is nonuniform. The net approach is used to numerically solve the problem. The influence of the ratio of the elastic moduli of the matrix and the filler and the ribbon shape factor on the critical load of the material is studied

Discrete models of problems in the elastic theory of composites in cylindrical coordinates. 2. Two-dimensional problems

The base factors and global mesh equations corresponding to classes of basic two-dimensional problems of the elastic theory of composites are constructed in circular cylindrical coordinates (axisymmetric problems in polar coordinates). The domain occupied by the composite may be of arbitrary connectivity and configuration. The difference scheme or the global system of linear algebraic equations that corresponds to any differential problem from the given class of problems may be written explicitly

Stability of laminated composite material in compression along a microcrack

The stability problem for an arbitrary laminated structure in compression along interlayer cracks was formulated. This formulation used the model of a piecewise-homogeneous medium and the basic relations of the three-dimensional linearized theory of deformable body stability (TLTDBS). Also introduced were the terms - microcrack, macrocrack, and structural crack, depending on the relationship between the crack length and the thicknesses of the layers. The present article is devoted to numerical solution of the stability problem for one of the laminated structures examined in the case of compression along a microcrack.

Influence of the Coefficients of Thermal Expansion on the Nature of Stresses and Local Effects in a Uniformly Heated Sandwich Plate

Thermal stresses are determined in a sandwich plate uniformly heated under plane-strain conditions. Linearly elastic isotropic bodies model the plate components. An approximate solution is found by the finite-difference approach. The influence of the coefficients of thermal expansion on the nature of stress concentration regions is studied.

Numerical study of edge effects in laminated cylinders

A formulation is presented to determine transient, regional stresses in composite materials or structural elements made of composites. The method of characteristic solutions is used, with the addition of approximate theoretical models. Differential equations are used, rather than three-dimensional equations, and uniform media are modeled by uniform bodies with corrected characteristics (continuum approach). This general approach is used to examine edge effects in a multilayers cylinder subjected to axial loading. Linear elasticity equations for piecewise-uniform anisotropic media are used as the mathematical model. The calculated data shows edge effects in laminated cylinders of composite materials under an axial load developing at regions of abrupt load and geometry changes (near the ends), as well as in regions of contact of the layers of filler and binder. The effects do not extend more than two thicknesses of the shell. 10 refs., 5 figs.

Procedure for the construction of discrete models of static problems in the theory of elasticity

UDC 539.3 The finite-difference approach is widely used in the solution of elasticity problems. It is implemented on a computer in two stages: the formulation of discrete problems and the solution of those problems. Here we discuss aspects of the construction of discrete models (differencing problems and systems of linear algebraic equations) in application to a set of problems of the linear theory of elasticity of piecewise-homogeneous, anisotropic media in an arbitrary coordinate system subject to various boundary conditions. We propose a procedure by which to obtain an explicit expression for the dynamic problems in the case of an arbitrary continuous problem from the given set. The procedure entails the construction of a differencing scheme (system of equations), called the basic scheme (basic system of equations), on a mesh stencil. For a specific elasticity problem (i.e., for a given region, coordinate system, boundary conditions, and elastic constants of the components of the medium) the expression for the differencing scheme at an arbitrary grid node is written as the sum of the expressions for the basic scheme at certain nodes of the mesh. The corresponding system of linear algebraic equations represents the sum of the basic system of equations over all meshes of the grid with the subsequent correction of certain rows of the system of equations. Basic schemes are constructed for an arbitrary coordinate system. Discrete models are constructed for a specific problem. We investigate three-dimensional = 3) and two-dimensional (p = 2) problems. Unless otherwise stated, summation from 1 to p is implied by repeated subscripts on one side of an equation.

Investigation of the Stressed State and Edge Effects in a Three-Layer Cylinder

We study an axisymmetric problem of determination of the zones of stress concentration in a three-layer circular cylinder with isotropic layers. The cylinder is subjected to uniform axial loading. An approximate solution of the problem of the linear theory of elasticity is obtained by the net method. We present a solution of this sort as an example and analyze the results.