Theory of axi-symmetric dimensional solids
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2017, Vol 1, Issue 67
Abstract
The actual software for the calculation of building constructions is based on universal numerical methods. The obtained numerical results should be additionally checked for their reliability and accuracy. The experimental verification is not always possible. The numerical verification should be carried out by methods which differ in nature from the calculation method. The proposed work is devoted to the development of an alternative approach to solving problems in the theory of elasticity. At first the initial problem is mathematically simplified, and then it is solved numerically. Simplification is done by expanding the functions and derivatives of the initial problem into a series of orthonormal Legendre polynomials by one or two coordinates. The application of this projection transformation is formalized in the form of an operational calculus procedure and is called the generalized method of finite integral transformations. The reduced problem is solved numerically. This algorithm is invariant to the degree of polynomial approximation. The numerical algorithm is implemented as a software complex «Integral». This software allows calculating the stress-strain state of three-dimensional axisymmetric bodies in a cylindrical and spherical coordinate system with a symmetrical or asymmetrical load. The convergence of numerical solutions is regulated by the degree of polynomial approximation and is controlled by the fulfillment of boundary conditions. The theory of axisymmetric three-dimensional bodies can be applied to the calculation of a wide class of engineering and construction objects. The effectiveness of the theory is demonstrated by solving the problem of strengthening a spherical glass meniscus.
Authors and Affiliations
А. М. , Smoliar, I. V. , Miroshkina
Keywords
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