Mathematical modeling of the stressed-deformed state of circular arches of specialized

Abstract

We present the possibilities to calculate the stressed-deformed state of circular arches under various conditions of bearing based on the algorithm of a numerical-analytical variant of the method of boundary elements and application of the MATLAB programming and calculation environment. The exact solution to the problem of flat deformation of a circular rod is shown, considering the deformations of bending and stretching-compression, which has not so far been implemented in professional packages of the finite element method. We have constructed solving equations for the boundary value problems on flat deformation of circular arches under various bearing conditions. An example is given for calculating the circular arch SDS employing BEM; by using the MATLAB environment, we represented the results numerically and visually in the form of diagrams. It was established that the boundary element method in the calculation of circular arches has the simplest algorithm logic among other methods and it allows obtaining accurate and reliable results of the stressed-deformed state of crane structures with specialized designation. BEM presented in the given work could be successfully applied to solving boundary value problems for differential equations with variable coefficients. The structure in this case should be discretized while the BEM algorithm does not change. Additional advantage is the minimal requirements to variable coefficients of the differential equation. They may possess first-order discontinuities, breakpoints, and an arbitrary set of continuous functions, which significantly expands the range of problems to be solved. It is obvious that the boundary element method enables fulfillment of the increased requirements to calculation results, which therefore renders relevance to the present study, as well as scientific and practical value for professionals involved in the design of crane structures

Представлена методика розрахунку напружено-деформованого стану (НДС) кругових арок із урахуванням деформацій вигину і розтягування-стиснення, зосереджених та розподілених зовнішніх навантажень. Врахування умов обпирання опорних перетинів виконаний в рамках алгоритму чисельно-аналітичного варіанту методу граничних елементів (МГЕ). Розглянуто приклад розрахунку НДС арки, де представлено повне рішення для кінематичних і статичних параметрів стану арки

Представлена методика расчета напряженно-деформированного состояния (НДС) круговых арок с учетом деформаций изгиба и растяжения-сжатия, сосредоточенных и распределенных внешних нагрузок. Учитывание условий опирания опорных сечений выполнено в рамках алгорит- ма численно-аналитического варианта метода граничных элементов (МГЭ). Рассмотрен пример расчета НДС арки, где представлено полное решение для кинематических и статических параметров состояния арки