A numerical solution for geometrically nonlinear bending plates problems subjected to local-loads

Abstract

Abstract. the following scientific content is demonstrating a new proposed numerical procedure for calculating deformations & stresses generated on geometrically nonlinear flexible (thin) plates under local loads. solving the predominating system of differential equations is based on generalized equations of the finite difference method. the proposed algorithm is verified by an example of solving a hinged-edges plate loaded with a point load centrally. Through manuscriptNowadays, Flexible (thin) plates and shells are widely used in modern technology and by many various aspects such as aircraft construction, ship-building, engineering, energy, construction and much many others. The most common and universal numerical method for calculating such structures (including nonlinear calculations) is the extra-famous finite element method (FEM) [1][2][3][4][5][6][7][8][9][10][11][12][13]. At the same time, engineers are always in need to compare the results obtained by (FEM) (especially for performed nonlinear calculations), with the results of solutions obtained by other methods [10,13]. Down-below, authors are suggesting a numerical technique for doing rectangular plates calculations with the aid of generalized equations of finite differences method [15]. As well-known [14], for geometrically nonlinear rectangular thin-plates, the next 4 th order differential equations system is considered to be the predominating one, which formulation can reduce to the solution to as follows:

The analysis of a free two-layer composite beamon the elastic foundation

“…Задачи по определению напряженно-деформированного состояния (НДС) составных балок конечных размеров, загруженных произвольной нагрузкой, с учетом различных краевых условий и отпора упругого основания, могут быть решены с привлечением численных методов. В числе методов, успешно применяемых в расчете конструкций на действие статических и динамических нагрузок на устойчивость, упомянем конечно-разностные методы: метод конечных разностей (МКР) в его классической форме [17][18][19], обобщенные уравнения МКР [20][21][22][23][24], метод последовательных аппроксимаций (МПА) [25][26][27][28][29]. В трудах [17-20, 25, 26, 29] учтена совместная работа конструкции и упругого основания, а в [26] мы уже обращались к вопросам расчета двухслойных составных балок на винклеровском основании, где решение построено с использованием разностной формы МПА [25].…”