Differential equations of the spatial bending of reinforced concrete beams and frames, taking into account physical and geometrical nonlinearities and plasticity of concrete
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2016, Vol 1, Issue 65
Abstract
In solving static and dynamic problems for reinforced concrete frames based on nonlinear and plastic properties of materials in order to achieve sufficient accuracy, it is necessary to make reinforced concrete frames elements partitioning on large number of small finite elements because of dependence of concrete deformation properties from its stress-strain state, what leads to the system of resolving equations of finite element method of high order. Therefore there is a need to use alternative methods, such as the boundary element method, application of which requires presence of bending differential equations. Based on associated plastic concrete flow law the representations of the total vector increments and the total moment of internal forces in a beam cross section caused by the external forces increments, in the form of Krylov’s angles increments functions, determining section position change, and their derivatives on arc coordinate have been derived. As a result of substitution of those representations into differential dependencies between increments of the total moment and the total vector of internal forces the constructions of the differential equation system on Krylov’s angle derivatives taking into account physical and geometric nonlinearities and plasticity of concrete has been made. The presence of these equations is necessary for the matrix constrcution of fundamental solutions of the Cauchy problem and the vector of particular solutions associated with the current load, used in the algorithm of the boundary elements method.
Authors and Affiliations
V. M. , Fomin
Keywords
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