Papers by Keyword: Solutions

Abstract: A variant of the mathematical theory of deformation of multilayer nonlinearly elastic (according to Kauderer) plates of arbitrary constant thickness with non-symmetric structure in thickness has been constructed. The transverse load on the horizontal faces can be arbitrary static. The components of the stress-strain state (SSS) and the boundary conditions on the lateral surface are functions of three spatial coordinates. Spatial boundary value problems for multilayer plates are reduced to two-dimensional using three-dimensional equations of the theory of elasticity, the Reissner variational principle, and the expansion of the components of the SSS into infinite mathematical series by combinations of Legendre polynomials within each layer. This approach differs significantly from the approaches of other authors. The main dependencies, boundary conditions and systems of equilibrium differential equations with high-order partial derivatives with respect to the displacement components are derived. All dependencies and equations contain nonlinear terms. The new methodology for constructing a variant of the nonlinear theory makes it possible to accurately satisfy the boundary conditions on the horizontal faces of the plate and on the lateral surface, and to accurately satisfy the conditions of rigid conjugation of adjacent layers. The system of equilibrium equations has a high order. An analytical method for solving these systems is proposed and developed. The method is based on algebraic, differential and operator transformations of the initial systems. They are reduced to two convenient defining systems: one describes the vortex edge effect with a refinement of the SSS, and the other describes a refined internal SSS with a potential edge effect. The order of the systems of differential equations does not depend on the number of layers, but depends only on the number of retained terms in the mathematical seriess. The internal SSS is separated from the potential edge effect. By the method of order reduction, the determining systems are reduced to second-order differential equations. This significantly simplifies the solution of boundary value problems. General solutions for all components of the SSS were found through general solutions of second-order differential equations. For plates with non-symmetric structure, the equations of skew-symmetric and symmetric deformation are interconnected, unlike plates with a symmetric structure. Numerical results are presented for a two-layer linearly elastic plate under cylindrical bending.

Abstract: A new version of the mathematical theory of non-thin multilayer nonlinearly elastic Kauderer plates of symmetric structures has been constructed. The components of the stress-strain state (SSS) and boundary conditions on the side surface of the plate are considered functions of three spatial coordinates. The variant is based on the development of components of the SSS of the plate along the transverse coordinate with the help of combinations of Legendre polynomials within each layer. The three-dimensional physically nonlinear boundary value problem for a multilayer non-thin plate is reduced to a two-dimensional one using the three-dimensional equations of the theory of elasticity and Reissner's variational principle. The main dependencies are obtained. Derived systems of high-order differential equations of equilibrium with partial derivatives and boundary conditions containing nonlinear terms from the SSS. The conjugation conditions at the boundary of adjacent layers (rigid connection) are exactly fulfilled for displacements, transverse tangential and normal stresses. The boundary conditions for stresses on the horizontal faces of the plate are also exactly fulfilled. The system of high-order differential equations of equilibrium is transformed into two systems that independently describe skew-symmetric and symmetric deformation relative to the median plane of the plate. In turn, each of these systems is transformed into differential equations that describe vortex boundary effects and equations that describe an internal SSS with a potential boundary layer-type boundary effect. The solution of systems of high-order equations by the developed method is reduced to the solution of second-order differential equations (Poisson and Helmholtz equations). General solutions of the system of differential equilibrium equations are obtained. The validity and accuracy of the variant of the mathematical theory is confirmed by comparisons with exact solutions of bending problems for linearly elastic plates with different mechanical and geometrical parameters. The newly constructed variant of the theory and the developed method provide a real opportunity to solve boundary problems in a spatial formulation with high accuracy for multilayer platens under various loads and boundary conditions on the lateral surface.

Abstract: The principal coke modification possibility with butyl potassium xanthate was revealed. It was shown that the modified coke exhibits sorption properties with respect to nickel ions compared to untreated coke, traditionally used for melting. The influence degree of various factors on the sorption capacity of the modified coke was established.

Abstract: Thanks to the industrial and technological development, man has managed to travel fast, to take advantage of artificial light in the absence of natural light, to enjoy the air-conditioned rooms in case of discomfort and much more. The engine of these processes is energy, which needs to be considered the production phases. The world's energization began mainly through fossil sources, but due to the thinning of the atmospheric ozone layer and the overall increase in the concentration of CO₂over the years, due to anthropogenic and non-human causes, which led to overheating global, global decarbonisation has become necessary. It is essential to encourage the development of low-carbon and energy-efficient technologies. This document shows the current problems, in terms of environmental impact, and the possible solutions applied and applicable in the future to counteract the increase in average temperature of 2 degrees by 2050. The main point is to make buildings less energetic with technological devices, addressing their honors and obligations.

Abstract: In order to deal with the collapse of soil in pile bore holes due to construction wastes, this essay discusses four possible solutions. By comparing the advantages and disadvantages of these solutions, the method of Manual boring + Machinery boring is finally chosen. This provides a reference to other similar construction projects.

Abstract: A class of shallow water waves equations are studied in this paper. Using Kato's existence theorem, we mainly study the initial and bounded value problem for the quasi-linear evolution equations. Meanwhile, we prove the existence of local and global existence of solutions to the equations.

Abstract: Through the No. 5 boiler of a power plant in Jilin lower abrasion of economizer and air preheater of the inspection, find out the causes of air preheater of clogging, and conducted a detailed analysis of the low temperature corrosion of air preheater, puts forward relevant suggestions for improvement.

Abstract: On 21 July 2012, a huge thunderstorm hit Beijing, prompting the city government to act immediately to deal with the emergency. Yet great losses were caused, exposing problems about urban flood control and drainage, and making people take a new look at them. It is not uncommon for a rainfall of such a degree to happen in Asia. Comparatively speaking, however, unlike in Beijing, fewer damages are caused in Taiwan, Japan and the Philippines given the same situation. In this article, therefore, the problems arising after a heavy rainfall and their solutions will be discussed.