Edge effects in a rectangular sandwich plate with isotropic components are studied. The mathematical model is represented by the homogeneous equations of linear elasticity, which is indicative of an approximate approach in edge-effect theory. The initial equations are reduced to inhomogeneous ones and an exact problem is formulated. Approximate solutions are found by the mesh method. Discrete problems are based on the concept of base scheme. The mesh equations are written in an explicit form and then solved using a computation optimization procedure. As an example, edge-effect zones in a real composite are analyzed.Keywords: edge effect, exact approach, free strains, sandwich plate, base scheme Introduction. Edge effects in deformable media can be studied using either exact or approximate approach. The exact approach employs exact mathematical and mechanical models and an exact (quantitative) criterion of edge-effect zones [3]. Other approaches are approximate.For the problem under consideration, the exact approach is characterized by the inhomogeneous equations of linear elasticity (exact mathematical model), a piecewise-homogeneous medium model (exact mechanical model), and a quantitative (exact) criterion of edge-effect zones. The exact approach allows determining, with prescribed accuracy, the boundaries of stress-concentration zones and analyzing the geometry and stress state within these zones.Almost all approximate approaches in edge-effect theory employ homogeneous (eigen)solutions, which are used in the case of self-balanced loading [1,2,4,8]. These solutions do not allow analyzing the stress state within the edge-effect zones.The criterion of edge effect is decrease in the surface load at a point of interest by a given factor. Since quantitative and qualitative characteristics of loading are disregarded, this criterion is called approximate (qualitative). Eigensolutions allow us to estimate quantitatively (to admit or reject) Saint Venant's principle.The present paper analyzes edge effects in a sandwich plate under the conditions of uniaxial loading and plane strain. The governing equations describe a plane homogeneous problem of elasticity for piecewise-homogeneous media and imply, as mentioned above, an approximate approach in edge-effect theory.We will set up inhomogeneous equations of elasticity. To derive inhomogeneous equations and to formulate an exact problem for edge effects, we will use the concept of free strains. The inhomogeneous boundary-value problem will be solved approximately by the mesh method based on the concept of base scheme [5,[9][10][11]. Discrete problems will be formulated and methods for their solution selected. Since the stresses σ ij may exhibit singularity near the free edge [2], we will use a computation optimization procedure to improve the accuracy of solving the mesh equations. An example will be given.1. Problem Formulation. Consider a three-layer rectangular plate with isotropic layers. The face layers are identical, which results in the geometrical symmetry of the s...

The plane stability problem for a rectangular plate with two symmetric end cracks is solved in three-dimensional formulation. The three-dimensional linearized theory of stability and the finite-difference method are used. The effect of the crack parameter on the critical load is examined

The paper is concerned with the determination of edge effect zone in a laminated composite with laminas subject to longitudinal compression. The dependence of the maximum decay length on the ratio between the period of external loading and the structure parameter is studied. The load period depends on the number of unloaded laminas. The decay of the edge effect is analyzed by numerically solving a boundary-value problem of elasticity for piecewise-homogeneous materials and using a quantitative decay criterion for the near-edge normal stresses Keywords: Saint-Venant's edge effect, laminated composite, representative element, piecewise-homogeneous material, end effect decay criterion Introduction.In studying the edge effect in composite materials, it is of interest to examine the joint influence of external load and material structure on how it decays [1-3, 6, 12]. The dependence of the decay length in coated materials on the ratio between the period of piecewise-constant surface load and the thickness of the coating (which is generally multilayer) as a structure parameter was examined in [1, 3, 6]. It was established there that the ratio of the decay length to the load period monotonically increases with the load period, tending to some constant value. The decay of the edge effect in a laminate with laminas longitudinally compressed by a uniform surface load of constant intensity was studied in [4]. It was shown there that the maximum length of the edge effect, evaluated to within 1%, is equal to one or two structure parameters, the structure parameter being the total thickness of one lamina and one matrix layer. The decay of the edge effect was analyzed in [2] comparing two cases: uniform compression of laminas and the presence of an unloaded lamina. It was shown there that in the presence of an unloaded lamina, the near-edge stresses redistribute resulting in a smaller decay length of the edge effect in the matrix and a greater decay length in the reinforcement, compared with the case of uniformly compressed laminas.The present paper sets out to determine the decay length of the edge effect in a longitudinally compressed laminate and to study the dependence of the decay length on the ratio between the load period and the structure parameter. The load period depends on the number of unloaded laminas. The design model includes a mixed boundary-value problem of elasticity for piecewise-homogeneous materials and a quantitative decay criterion for near-edge normal stresses. The boundary-value problem is solved using the finite-difference method and the concept of base scheme [5,[9][10][11]. To analyze the decay of the edge effect, we will use a stress decay function~( ) ρ x that describes the relative change of the near-edge normal stresses compared with the self-balanced load on the boundary of the domain of interest. The decay length of the edge effect is defined as the distance from the line of application of the self-balanced load to the points where the normal stresses are equal to ρ % of their magnitude on the ...