Geometrically nonlinear plate bending under the action of moving load

Considerable scientific interest is the development of mathematical models that describe the behavior of materials that are sensitive to deformation rate and can improve the accuracy of analytical calculations of their deformation in the region of noticeable changes of loading rates. Nonetheless, in most works, the problems were solved under the assumption of small displacements (geometrically linear statement of the problem). Meanwhile, in practice, this is not always true and bending of cover can be commensurable with its thickness, this article approximately solves the problem of geometrically nonlinear deformation of a thin elastic plate in aquasistatic setting under the action of an infinite normal uniformly distributed load moving along its surface at a constant speed. In the article, the methods of mathematical modeling, the analytical method, as well as the methods of spatial characteristics and bicharacteristics are used. The problem is solved in the quasistatic formulation and is reduced to a system of two nonlinear differential equations for deflections of the plate and the stress function, which include the speed of the load as a parameter. The results of methodological calculations are presented; based on these solutions of linear and nonlinear problems, they were compared, and the influence of finiteness of displacements on the critical speeds of the forces was determined. Materials of the article can be useful in the study of wave dynamics, aircraft, mechanics, and engineering.

Principle of the overlay deformations in the theory of creep

The aim of the research is to justify in the non-linear statement the overlay principle of fraction creep deformation, known in the linear creep theory as Bolzmann’s principle of superposition. Methods. In contrast to the traditional approach the material of constructive elements is considered as an union of its links with statistical disturbed strength. The model of structural strength allows the deduction of rheological equations. In loading process so called structural stresses of capable to resist links are considered. Results. The modification Bolzmann’s principle of superposition for fraction creep deformations is proposed. This permits its applicability also under non-linearly dependence of deformations on stresses. In according to concept of the statistical distribution of the strengths of links and linear dependence of determinations on structural stresses the rheological of mechanical statement is reduced. This equation implies the suitable on relation problems the linear integral equation. The relation of structural strength of material with its energy of entirety and with the experimentally known independency of specific to strength deformation on age of concrete is showed. The correct interpretations of certain known mechanical state equations for concrete are represented.

Stress state of a polygonal plate having a central circular hole with two linear cracks in the small physical non-linear condition

In this study, the stress state of a polygonal plate having a central circular hole with two linear cracks was considered. External forces were applied to the contours of polygonal plate and internal forces were applied to the contours of the circular hole. Conformal mapping function, initially developed by Kuliyev, was used to the make stress analysis of the polygonal plate in physical non-linear statement. As a result, stress concentrations were determined by using conformal mapping function at the end points of cracks. Critical loads where fracture began were defined for different loads. Analytical results of solutions were compared and found to be in agreement with the numerical results in the literature.

Stress distribution caused by co-phase locally spatially curved layers in an infinite elastic body under bi-axial compression

In the present paper, the stress distribution is studied in an infinite elastic body, reinforced by an arbitrary number of non-intersecting co-phase locally spatially curved filler layers under bi-axial compression is studied. It is assumed that this system is loaded at infinity with uniformly distributed normal forces with intensity p1(p3) acting in the direction which is parallel to the layers? location planes. It is required to determine the self-equilibrated stresses within, caused by the spa?tially local curving of the layers. The corresponding boundary and contact value problem is formulated within the scope of geometrically non-linear exact 3-D equations of the theory of elasticity by utilizing of the piece-wise homogeneous body model. The solution the formulated problem is represented with the series form of the small parameter which characterizes the degree of the aforementioned local curving. The boundary-value problems for the zeroth and the first approximations of these series are determined with the use of the exponential double Fourier transform. The original of the sought values is determined numerically. Consequently, in the present investigation, the effect of the local curving on the considered interface stress distribution is taken into account within the framework of the geometrical non-linear statement. The numerical results related to the considered interface stress distribution and to the influence of the problem parameters on this distribution are given and discussed.

CAD in interdisciplinary integration as a tool to increase specialist training quality in “Construction” education

Subject: subject of research is characterized by the requirement to master and efficiently apply CAD tools in the teaching process for analyzing reinforced concrete structures and engineering of facilities to be built under current construction standards and regulations. Objectives: consideration and analysis of updated software applications for simulation enabling to reduce academic load and improve process of education for less period of time. Methods of teaching such subjects as “Reinforced concrete and masonry structures” and “Construction engineering” are improving together with updating of simulation software, meaning consideration of the process for problem solving in calculations, engineering and mounting of reinforced frame elements to one-storey industrial facilities. Materials and methods: scientific papers by authors of this work were used as reference literature, the article methodology is based on standards of objectivity and development, statistical level of methodological analysis was applied. Results: comprehensive description for getting modern IT learning skills in using software simulation facilities was prepared under analysis of the below mentioned materials. Problems in making 3D simulation model of a frame of a building considering facilitation for the students in their appreciation and maximum approach to actual behavior of structures were reviewed either. In the course of analysis a number of assumptions was proposed for engineering of connection between bearing elements of the frame and statistical estimation in linear statement. Conclusions: bases for calculation, engineering and mounting of reinforced concrete structures were considered therewith in accordance with present norms and regulations. Currently a problem in making simulation algorithm for 3D calculation scheme of standard frame to one-storey industrial facilities is still very important.