The collective monograph edited by the corresponding member of the NAS of Ukraine V.S. Hudramovich is devoted to the problems of mathematical and computer modeling of engineering systems. The monograph includes chapters on the genetic algorithm using, machine learning, the finite element analysis, buckling analysis, the local variations method, software design patterns, the contact mechanics of composites, nonlinear oscillations. Chapters describe novel approaches of computer and mathematical modeling in problem domains.
Projection-iterative modification of the local variations method for solving variational problem with a quadratic functional is proposed. The convergence theorem is formulated. Application of the proposed modification of the problem of local stability of spherical shells under a substantially inhomogeneous stress state, which is caused by local edge loading, is considered. These tasks are important for the construction of space rocket, antenna technology, etc.
The developed projection-iterative modification of the local variations method are effective and can significantly (more than 4 times) reduce the time of computer calculations. Numerical results are confirmed by experimental data.
