Construction of ground control points for spacecraft using optimization-simulation model

The article deals with the application of simulation modeling and optimization-simulation approach to solving problems of synthesis of structures of automated spacecraft control systems, namely, the choice of spacecraft control points, which are multifunctional aggregates of stationary and mobile elements dispersed in space with developed technical means of receiving, transmitting and processing information. Various approaches to the joint use of optimization and simulation models in the synthesis of the structure of complex systems are analyzed. The main attention is paid to the possibility of joint use in the synthesis of optimization and simulation models, their rational interaction in optimization and simulation procedures that describe both the composition and interrelationships of the structural elements of the system, as well as dynamic and stochastic aspects of their functioning. An optimization-simulation approach based on the joint use of optimization and simulation models in the process of searching for optimal structure options is proposed. Rational mapping of a set of interrelated functions performed by a control system into a set of interconnected nodes with appropriate technical means, taking into account the costs of creating or reconstructing the system, the costs of operation and operation, the requirements of operational efficiency of management, the reliability of technical means, the survivability and globality of the control system and other characteristics. Consideration of the problem of optimizing the distribution of tasks included in the control loop by levels and control nodes of the system and determining a set of technical means that minimize the costs of equipping nodes with technical means and their operation when performing restrictions on efficiency, hardware reliability of performing control tasks, weight and energy consumption of on-board equipment, loading of nodes, etc.

Construction of ground control points for spacecraft using optimization-simulation model

The article deals with the application of simulation modeling and optimization-simulation approach to solving problems of synthesis of structures of automated spacecraft control systems, namely, the choice of spacecraft control points, which are multifunctional aggregates of stationary and mobile elements dispersed in space with developed technical means of receiving, transmitting and processing information. Various approaches to the joint use of optimization and simulation models in the synthesis of the structure of complex systems are analyzed. The main attention is paid to the possibility of joint use in the synthesis of optimization and simulation models, their rational interaction in optimization and simulation procedures that describe both the composition and interrelationships of the structural elements of the system, as well as dynamic and stochastic aspects of their functioning. An optimization-simulation approach based on the joint use of optimization and simulation models in the process of searching for optimal structure options is proposed. Rational mapping of a set of interrelated functions performed by a control system into a set of interconnected nodes with appropriate technical means, taking into account the costs of creating or reconstructing the system, the costs of operation and operation, the requirements of operational efficiency of management, the reliability of technical means, the survivability and globality of the control system and other characteristics. Consideration of the problem of optimizing the distribution of tasks included in the control loop by levels and control nodes of the system and determining a set of technical means that minimize the costs of equipping nodes with technical means and their operation when performing restrictions on efficiency, hardware reliability of performing control tasks, weight and energy consumption of on-board equipment, loading of nodes, etc.

Measures of irrationality for hypersurfaces of large degree

We study various measures of irrationality for hypersurfaces of large degree in projective space and other varieties. These include the least degree of a rational covering of projective space, and the minimal gonality of a covering family of curves. The theme is that positivity properties of canonical bundles lead to lower bounds on these invariants. In particular, we prove that if $X\subseteq \mathbf{P}^{n+1}$ is a very general smooth hypersurface of dimension $n$ and degree $d\geqslant 2n+1$, then any dominant rational mapping $f:X{\dashrightarrow}\mathbf{P}^{n}$ must have degree at least $d-1$. We also propose a number of open problems, and we show how our methods lead to simple new proofs of results of Ran and Beheshti–Eisenbud concerning varieties of multi-secant lines.

An infinite plate with a curvilinear hole having three poles with complex parameters

This paper covered the study of the boundary value problem for isotropic homogeneous perforated infinite elastic media. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origin lie outside the hole is conformally mapped outside a unit circle by means of a specific rational mapping . The complex variable method has been applied and it transforms the problem to the integrodifferential equation with Cauchy kernel that can be solved to find two complex potential functions which called Gaursat functions. Many special cases are discussed and established of these functions .Also, many applications and examples are considered. Moreover the components of stress , in each application , are computed.

Research on the Mapping Model between Users’ Cognitive Concept and Product Shape Information

To make products understood by users more easily, it has become a hot topic in industrial design that how to fill the gap of semantic cognition differences between designers and users. In this paper, users’ cognition process is built and analyzed, a concept of abstracted symbol is proposed. Then different kinds of shape information are abstracted into simple shape symbol. At last, a rational mapping between users’ cognitive concept and product shape information is built up. This mapping model provides designers a way to know better about the users’ cognition, thereby guides designers to design product shape more rationally.

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

Stress Intensity of Debonding for A Rigid Inclusion Near An Angle Dislocation

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner. We also obtain the stress intensity of a debonding in terms of the stress functions. It can be found that when a debonding starts from a corner of the inclusion and extends to another corner progressively, the stress intensity of the debonding increases monotonously; once the debonding extends over the corner points, the value of the stress intensity of the debonding gradually decreases. The relationships between the stress intensity of the debonding and the direction and position of the dislocation are also presented in this paper.