To Solution of Contact Problem for Elastic Half-Strip

Contact problems for elastic stripes have been well studied and published in domestic scientific literature. This is partly due to the fact that normative documents on the foundation structure it is recommended to use this elastic foundation model for simulation of a “structure – foundation – soil foundation” system. Two variants of boundary conditions at the contact between a half-strip and a rigid non-deformable base are usually considered. The first boundary condition nullifies the vertical displacements and tangential stresses, the second one nullifies vertical and horizontal displacements. Contact problems for an elastic half-strip are much less investigated. The paper considers this contact problem when the first boundary condition for zeroing of vertical displacements and tangential stresses at the contact of a half-strip with a rigid, nondeformable base. When performing calculations in the traditional formulation without taking into account tangential stresses in the contact zone, the Zhemochkin method has been used, which reduces the solution of the contact problem of solid mechanics to the solution of a statically indeterminate problem by the mixed method of structural mechanics. Therefore, at first, we have found the displacements of the upper edge of the half-strip from the unit load uniformly distributed over the edge section. The resulting expression is used to compose a system of equations for the Zhemochkin method. The case of translational displacement of the die has been considered, and the graph of contact stress distribution under the die's sole has been given in the paper.

Solvability Criterion for Convolution Equations on a Half-Strip

We obtain the criterion of solvability of homogeneous convolution equation in a half-strip. Proof is based on a new decomposition property of the weighted Hardy space. This result has relations to the spectral analysis-synthesis problem, cyclicity problem, information theory. All data generated or analysed during this study are included in this published article.

Structural Analysis of Bamboo Wall Framed Structure – An Approach

Structural applications of indigenous materials such as bamboo are considered as an integral part of the sustainable development. In the study, the author has tried to analyze bamboo wall framed structure using half strip bamboo anchored to a sheathing material. It has been modeled in STAAD Pro software and different load as- Dead Load, Live Load, Seismic Load, Wind load were applied on the frame. The material properties of bamboo were defined using the value of modulus of elasticity, Poisson’s Ratio, density, and shear modulus obtained from the tests conducted here in laboratory.

An inhomogeneous problem for an elastic half-strip: An exact solution

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

On a boundary value problem in a half-strip for a fourth-order parabolic equation with a Riemann-Liouville operator in a time variable

In this work a fourth-order inhomogeneous parabolic equation with time fractional derivative is considered. The boundary-value problem in the half-strip for equation under consideration is studied. In this paper a fundamental solution for fourth-order parabolic equation with time fractional derivative in terms of the Wright function is presented, а representation of the solution of the problem is constructed and uniqueness of the solution in the class of fast growth functions is proved.

The second boundary value problem in a half-strip for a B-parabolic equation with the Gerasimov–Caputo time derivative

В работе исследуется вторая краевая задача в полуполосе для параболического уравнения с оператором Бесселя, действующим по пространственной переменной, и частной производной Герасимова–Капуто по времени. Доказаны теоремы существования и единственности решения рассматриваемой задачи. Представление решения найдено в терминах интегрального преобразования с функцией Райта в ядре. Единственность решения доказана в классе функций быстрого роста. При частных значениях параметров, содержащихся в рассматриваемом уравнении, последнее совпадает с классическим уравнением диффузии. In the present paper, we investigate the second boundary value problem in a half-strip for a parabolic equation with the Bessel operator acting with respect to the spatial variable and the Gerasimov–Caputo partial time derivative. Theorems of existence and uniqueness of the solution of the problem under consideration are proved.The solution representation is found in terms of an integral transform with the Wright function in the kernel. The uniqueness of the solution is proved in the class of functions of rapid growth. The considered equation for particular values of the parameters coincides with the classical diffusion equation.