Numerical modeling of nonlinear deformation processes for shells of medium thickness

When modeling a nonlinear isotropic eight-node finite element, the main kinematic and physical relationships are determined. In particular, isoparametric approximations of the geometry and an unknown displacement increment vector, covariant and contravariant components of basis vectors, metric tensors, strain tensors (Cauchy - Green and Almansi) and true Cauchy stresses in the initial and current configuration are introduced. Next, a variational equation is introduced in the stress rates in the actual configuration without taking into account body forces and the Seth material is considered, where the Almansi strain tensor is used as the finite strain tensor. Linearization of this variational equation, discretization of the obtained relations (stiffness matrix, matrix of geometric stiffness) is carried out. The resulting expressions are written as a system of linear algebraic equations. Several test cases are considered. The problem of bending a strip into a ring is presented. This problem is solved analytically, based on kinematic and physical relationships. Examples of nonlinear deformation of cylindrical and spherical shells are also shown. The method proposed in this paper for constructing a three-dimensional finite element of the nonlinear theory of elasticity, using the Seth material, makes it possible to obtain a special finite element, with which it is quite realistic to calculate the stress state of shells of medium thickness using a single-layer approximation in thickness. The obtained results of test cases demonstrate the operability of the proposed technique

Nonlinear problem on hyperelastic deformation of the shell of average thickness FEM

© 2014 M. K. Sagdatullin and D. V. Berezhnoi. In work the numerical research of finite deformations of isotropic hyperelastic bodies is resulted. In the first section it is resulted resolving linearise the equation in a current configuration and the parities defining speed of change stress tensor Cauchy-Euler as linear function from tensor of a spatial gradient of speed are deduced. In the second section within the limits of finite-element technique numerical realization of research algorithm of finite deformations isotropic hyperelastic bodies is considered. In the third section numerical decisions of some deformation problems of hyperelastic bodies are resulted

Statement of the problem of numerical modelling of finite deformations

© 2014 Marat Sagdatullin and Dmitri Berezhnoi. In operation the fundamentals of a technique of numerical research of finite strains of the isotropic hyperelastic bodies, oriented on application FEM are stated. The first section is devoted kinematics of finite strains in the Lagrangian frame, tensors and measures of the strain, defining are entered speeds, various tensors of stress are reduced. In the second section physical parities of the hyperelastic isotropic environment are formulated, using the thermodynamics equations. In the third section it is reduced resolving the equation in a current configuration and the parities defining speed of change of a stress tensor of Cauchy-Euler as linear function from a tensor of a spatial gradient of speed are output

Research of interaction of the deformable designs located in the soil

© 2014 D. V. Berezhnoi et al. In work construction of algorithm of the contact interaction based on introduction between parts of designs of a special contact layer is considered. Different variants of the deformation of the contact layer, for clarity presented by two overlays, depending on the impact of the efforts of substructures at each other. A general governing equation, which is solved on the basis of physically nonlinear problem formulated. To solve the problem, a method of solving problems in increments when iteration step the unknowns are not full of the displacement field, and their increments. It is solved model problems about modeling of stage-by-stage dredging from a foundation ditch with retaining walls

Calculation of interaction of deformable designs taking into account friction in the contact zone by finite element method

© 2015 D. V. Berezhnoi and M. K. Sagdatullin. Finite element "master-slave" a technique of contact interaction of elastic deformable bodies taking into account friction in a contact zone is realized. The proved from the point of view of the solution of extreme tasks with restrictions like inequalities, projective algorithm which received the name "algorithm of a projection of the next point" was used. The model problem of contact interaction of two deformable subdesigns is solved, comparison of results with the data obtained by other authors is carried out

Geometrically nonlinear deformation elastoplastic soil

© 2014 D. V. Berezhnoi, A. A. Sachenkov and M. K. Sagdatullin. In work statement of a problem of numerical modeling of finite deformations elastoplastic soil environments, focused on application FEM is given. Implemented and tested method of solving the problem of elastic-plastic deformation of soil masses on the basis of defining relations between the increments of the true stress and strain, resolved a number of model problems of determining the stress-strain and limiting condition of soils

Improving the energy efficiency of oil production using identification and prediction of operating modes of production wells based on data analysis methods, machine learning and neural networks

Currently, there is a need to improve the systems and control of pumping equipment in the oil and gas production and oil and gas transport industries. Therefore, an adaptive neural network control system for an electric drive of a production well was developed. The task of expanding the functional capabilities of asynchronous electric motors control of the oil and gas production system using the methods of neural networks is solved. We have developed software modules of the well drive control system based on the neural network, an identification system, and a scheme to adapt the control processes to changing load parameters, that is, to dynamic load, to implement the entire system for real-time control of the highspeed process. In this paper, based on a model of an identification block that includes a multilayered neural network of direct propagation, the control of the well system was implemented. The neural network of the proposed system was trained on the basis of the error back-propagation algorithm, and the identification unit works as a forecaster of system operation modes based on the error prediction. In the initial stage of the model adaptation, some fluctuations of the torque are observed at the output of the neural network, which is associated with new operating conditions and underestimated level of learning. However, the identification object and control system is able to maintain an error at minimum values and adapt the control system to a new conditions, which confirms the reliability of the proposed scheme

Calculation of interaction of deformable designs taking into account friction in the contact zone by finite element method

© 2015 D. V. Berezhnoi and M. K. Sagdatullin. Finite element "master-slave" a technique of contact interaction of elastic deformable bodies taking into account friction in a contact zone is realized. The proved from the point of view of the solution of extreme tasks with restrictions like inequalities, projective algorithm which received the name "algorithm of a projection of the next point" was used. The model problem of contact interaction of two deformable subdesigns is solved, comparison of results with the data obtained by other authors is carried out

Calculation of interaction of deformable designs taking into account friction in the contact zone by finite element method

© 2015 D. V. Berezhnoi and M. K. Sagdatullin. Finite element "master-slave" a technique of contact interaction of elastic deformable bodies taking into account friction in a contact zone is realized. The proved from the point of view of the solution of extreme tasks with restrictions like inequalities, projective algorithm which received the name "algorithm of a projection of the next point" was used. The model problem of contact interaction of two deformable subdesigns is solved, comparison of results with the data obtained by other authors is carried out