Mathematical problems of reliability assurance the building constructions

Abstract

The paper deals with a mathematical model of console type based on the nonlinear differential equation having a mobile feature of the General solution (or a mobile singular point). The presence of mobile singular points indicates affiliation of this type of equations to the class of intractable in the general case in of quadratures. This fact, taking into account the interpretation of mobile singular point as the coordinate of structural failure, actualizes the development of an analytical approximate method for solving nonlinear differential equations. Taking into account these features for of structural analysis increases the authenticity of results and reliability of construction.

Research of a third-order nonlinear differential equation in the vicinity of a moving singular point for a complex plane

“…If the works [3][4][5] give a theoretical justification for taking into account the features of the applied class of nonlinear differential equations of the third order for the study of wave processes in elastic beams, then in the articles [6][7][8][9] the development of general theoretical provisions in the study of nonlinear differential equations with mobile singularities is given. Let us note a number of recent works with the application of this category of equations for building structures [10][11][12][13][14][15][16].…”

Exact boundaries for the analytical approximate solution of a class of first-order nonlinear differential equations in the real domain

“…In many areas of the problem: building optimal filters [1,2], mathematical physics, nonlinear optics [3,4], theory of evolutionary processes [5][6][7][8][9][10], the theory of elasticity [11], nonlinear diffusion [12], in the theory of sustainability of building structures' elements and in the analysis of buildings' vitality [13][14][15] (both of applied nature), are solved with the help of mathematical models, which are differential equations. The latter have a problem in finding a solution associated with the presence of movable singular points, which refer such equations to the class of equations in the general case not solvable in quadratures.…”