ИНКРЕМЕНТАЛЬНЫЕ МЕТОДЫ РЕШЕНИЯ ГЕОМЕТРИЧЕСКИ НЕЛИНЕЙНЫХ ЗАДАЧ

Abstract

In the sequence of displacement – deformation – stress, two types of nonlinear dependence are possible: geometric and physical. Physically related, mainly with the plastic properties of the material. Geometric nonlinearity is due to a wider range of reasons. Both nonlinearities create a nonlinear displacement-load relationship, which, in most cases, can be expressed by some integral function. In this case, the solution can be obtained by incremental (step) methods. Two incremental methods are considered: the tangential stiffness method and the calculation method using a deformed scheme. The methods are applied to three problems of geometric nonlinearity: 1) small deformations with large displacements, 2) displacements and deformations occur in different directions, 3) large deformations with small displacements. The studies considered both uniaxial stress-strain bars and bars modeled by volumetric elements. Conclusions are drawn about the universality and accuracy of the methods considered.