Modeling of building frames as spatial rod structures with geometric and physical nonlinearities

Abstract

Проведено комплексное численное моделирование внутрикамерных процессов, протекающих при выходе на расчётный режим работы ракетного двигателя твёрдого топлива. Рассматривается сопряжённая задача, включающая в себя: -нестационарное срабатывание воспламенительного устройства; -прогрев, воспламенение и последующее нестационарное горение заряда твёрдого топлива; -нестационарное трёхфазное гомогенно-гетерогенное течение продуктов сгорания в камере сгорания, сопле и за сопловым блоком ракетного двигателя; -разгерметизацию двигателя и вылет заглушки соплового блока. Приводятся результаты расчётов. Complex numerical modeling of the intrachamber processes, proceeding at the output settlement mode of operation of a solid propellant rocket engine, is carried out. We consider the coupled problem, which involves nonstationary operation of an ignition device; warming up, ignition and subsequent non-stationary burning of a propellant grain; non-stationary three-phase homogeneous-heterogeneous flow of the products of combustion in the combustion chamber, in the nozzle and behind the nozzle of the rocket engine; depressurization and moving of the nozzle block membrane. The results of modeling are given.

A novel director-based Bernoulli–Euler beam finite element in absolute nodal coordinate formulation free of geometric singularities

“…The proposed element underlies the absolute nodal coordinate formulation, which is designed for large displacements, large 450 rotations and large deformations and multibody dynamics problems. The element kinematics and deformation energy are chosen according to Vetyukov and Eliseev (2010), including an additional rotation director, which is updated during computation process. The investigation of numerical exam-455 ples, both in the static and dynamic case, shows the expected accuracy and a fast performance of the proposed element.…”

“…The kinematic description and the virtual work for the proposed element is chosen in a way similar to Vetyukov and Eliseev (2010) or rather Vetyukov (2008). In the latter paper, only static problems are regarded, while in the present paper, also dynamic behavior is analyzed.…”

Nonlinear Mechanics of Thin-Walled Structures

“…Variational approaches with approximations of mechanical fields in the cross section are efficient in the case of physically nonlinear behavior, when non-quadratic terms in U need to be kept, see, e.g., Vetyukov and Eliseev [164]. Variational approaches with approximations of mechanical fields in the cross section are efficient in the case of physically nonlinear behavior, when non-quadratic terms in U need to be kept, see, e.g., Vetyukov and Eliseev [164].…”

“…Better results can be expected when the reference directionê is just fixed in space, see [91,107,164]. With a directorê, chosen for all particles of the rod we construct an intermediate basis, which determines the first rotation:…”

“…Derivatives of U with respect to κ k and ε are especially simple with the quadratic strain energy (3.26); for an example of the analysis of a physically nonlinear rod structure with non-quadratic U see [164]. Further we compute…”