Vol 7, No 3-1 (2013)

The theory of thermo-mechanical processes, as an apparatus in the development of equations of state and thermodynamics of continuous media, includes all the main sections of the fundamental mechanics of deformable solids. The paper considers two aspects of the overall problem: 1) non-monotonic processes in visco-plastic flows; 2) panel flutter of viscoelastic plates. In the first case there is released a fundamentally new problem - the definition of the functional of contact friction and the construction of the theory of plasticity under complex loading of bodies with non-uniform initial stress-strain state. The solution is supposed to look by using the SN-EVM (CH-ЭВМ) method together with forming a data bank. In the second case there is risen the problem of definitive explaination of the well-known paradox of the definition of the critical parameters in the problem of flutter of viscoelastic plate. The article also addresses the issues of scientific ethics and morality; driving force behind this were the publications appeared in which subjective and biased historical facts relating to the development of the science of thermo-mechanical processes are interpreted subjective and interestedly.

The authors developed a mathematical model of the dynamics of highly nonlinear guided mechanical system on the example of an industrial robot of the “SKILAM” type taking into account dry friction in the kinematic pairs of the robot arms and the dynamic characteristics of the motors. The solution is based on the principles of d'Alembert and D'Alembert-Lagrange. At the same time an apparatus of homogeneous coordinate transformation matrices was used.

The article presents approaches to the formulation and methods of solving initial boundary value problems of solid mechanics. Classical formulations of problems are considered. Principal scheme of the generalized formulation of problems in the form of operator equations in function spaces is presented and illustrated on the example of boundary value problems in the theory of small elastic deformations. The mathematical structure of iterative methods (method of elastic solutions and its modifications) and incremental approaches are stated in the article. Theorems on the existence and uniqueness of solutions, the convergence of the methods are given. The author discusses specific issues of formulating initial boundary value problems for finite deformations. The difficulties of the Lagrangian and finiteness of Eulerian descriptions are noticed. The conditions of possibility of effective application of the Euler formulation of problems that lead to substantial restrictions on the mechanical properties of material are displayed. The examples of the lack of the solutions at finite strains are given and unreasonableness of a requirement of uniqueness of solutions of problems of statics is shown. For evolutionary problems the author proposes a hypothesis on uniqueness of solutions as continuous-time field processes.

Based on IR and PMR spectra there are identified cyclic derived ketosulfides 1,3-dioxolanes, which in addition to self-interest may be active reagents. Opening of a cycle 1,3-dioxole new system is implemented by organomagnesium compounds. Functional and unsaturated derivatives of cyclic ketals are characterized by physico-mechanical properties and spectroscopic methods.

The article shows that quantum phenomena can be explained by the algebraic structure of space of the fundamental physical value of action. The eigenvalue operator problem is obtained as a consequence of an algebraic action vector multiplication law, existence of which we conceded. Thus we come to the explanation of quantum phenomena by the algebraic structure of the space of action vectors. Also the authors planned the path for explanations of types of quantum operators in relation to classical differentiation operators: multipliers included into the structure constants can be transferred to the operators of differentiation. Such multipliers include imaginary unit. In addition, it was established understanding of wave function as a partial differential of an action vector.

The problems of modeling the stress-strain state of rheological materials by higher order Euler linear differential equations containing derivatives (second and higher order) in time of simultaneously presenting (by Curie condition) stresses and strains, obeying the conditions of stress-strain or deformative-temporal similarity with one or two functions determining the material constants and time functions which are defined by the "standard" system of experiments.

The problem of bifurcation of a thin-walled circular cylindrical cover is considered at complex subcritical deformation along a curvilinear trajectory of constant curvature in the Ilyushin deviatoric plane . There is taken into account the complex nature of loading in еру cover at the moment of stability loss.

Method of solid bodies is included in the group of adaptive numerical methods of continuum mechanics. It is applicable for the analysis of motion of solids, liquids and gases. Using construction techniques this method provides a priori division of the generalized coordinates for the finite object of the research volume into fast and slow variables. The total number of slow variables does not exceed 6 N, where N is a number of finite volumes. The paper mentions methods of forming mathematical model of the object state relatively to the slow variables without the participation of the fast variables.

This article is a logical continuation of the articles [1] and [2]. In the first article [1] there is shown the statement of the problem on flatter of strip at longitudinal flow in the linearized theory of supersonic potential flow. In the second article [2] there is shown an asymptotic similarity of accurate and piston theory at high supersonic speeds. Particularly in this paper the problem of flatter strip at longitudinal flow is solved based on the accurate theory for moderate and low supersonic speeds. It is solved at the flow modes, when the validity of using a piston theory is not proven.

The article provides the formulation and numerical solution of the stationary flow of compressible fluid through solid deformable porous cylindrical layer of incompressible material with regard to the Darcy type interactive forces and frontal pressure.