ON AUTOMATIC SEGMENTATION METHOD USING IN SOLVING NONLINEAR INITIAL BOUNDARY VALUE PROBLEMS OF MECHANICS OF SOFT-SHELL STRUCTURES

An approach to improving nonlinear initial boundary value problems of thin-walled structures solution algorithm is represented in the work. The algorithm is based on using line method and parameter differentiation method and is oriented to analysis of composite structures behavior at arbitrary physical and geometrical nonlinearity. Obviously, the less restrictions the calculation algorithm imposes on problem statement, the more features of its realization must be taken into account when developing corresponding software module. The drawback of universality of the algorithm represented is that its direct implementation in some cases can lead either to wrong results, or to loss of calculation stability. To avoid these problems we suggest automatic segmentation method using as a step of the algorithm developed. The essence of the method lies in testing fulfillment of the condition of normalized integral matrices of initial and conjugate differential equation systems orthogonality at the step of problem preprocessing. In the points of integration interval where orthogonality condition is not fulfilled segmentation of the interval is carried out. For testing this approach we select nonlinear problems of dynamic inflation of an infinite cylinder of Mooney-Rivlin material and a sphere of Neo-Hookean material by suddenly applied pressure. It is shown that automatic segmentation method allows improving period and amplitude calculation accuracy, as well as increasing iteration process convergence rate. A problem of dynamic inflation of a hinged hemisphere of Neo-Hookean material by suddenly applied pressure is considered. On the basis of its solution results we suggest the approach to determining parameters of calculation algorithm which allow obtaining correct solution.