On the Equilibrium Problem of a Soft Network Shell in the Presence of Several Point Loads

Abstract

We consider a spatial equilibrium problem of a soft network shell in the presence of several external point loads concentrated at some pairwise distinct points. A generalized statement of the problem is formulated in the form of integral identity. Then we introduce an auxiliary problem with the right-hand side given by the delta function. For the auxiliary problem we are able to find the solution in an explicit form. Due to this, the generalized statement of the problem under consideration is reduced to finding the solution of the operator equation. We establish the properties of the operator of this equation (boundedness, continuity, monotonicity, and coercitivity), which makes it possible to apply known general results from the theory of monotone operatorsfor the proof of the existence theorem. It is proved that the set of solutions of the generalized problem is non-empty, convex, and closed.

Mathematical Simulation of the Problem of the Pre-Critical Sandwich Plate Bending in Geometrically Nonlinear One Dimensional Formulation

“…Note that the generalized statement of physically non-linear and geometrically linear problem in the form of saddle problems, as well as a method for its solution were considered in [7][8][9][10]. The study of nonlinear problems of the shells theory, including the approximate methods for their solution in [11][12][13][14][15][16][17][18] is carried out.…”

Numerical Investigation of a Physically Nonlinear Problem of the Longitudinal Bending of the Sandwich Plate With a Transversal-Soft Core

“…Отметим, что физически нелинейные задачи теории обо-лочек изучены в [37-43], в том числе задачи теории мягких сетчатых оболочек -в [44,45]. Численное решение геометрически нелинейных задач и физически линейных задач об из-гибе трехслойных пластин с трансверсально-мягким заполнителем проводилось в [46-48].…”

Тенденции Развития Науки И Образования

“…В работах [9][10][11][12][13][14][15][16] изучены задачи об изгибе трехслойной пластины с трансверсально-мягким заполнителем в геометрически линейной и физически нелинейной постановке. Отметим, что физически нелинейные задачи теории мягких сетчатых оболочек исследованы в [17][18][19][20][21][22][23][24][25].…”