The formulation and development of methods of solving thermomechanics problems for irradiated layered solids
Date
2017-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
Запропоновано математичну модель, що описує на основi феноменологiчної теорiї ви-
промiнювання та теорiї квазiстатичної термопружностi термонапружений стан опро-
мiнюваних плоско-шаруватих тiл (пластин) зi складниками рiзної прозоростi з ураху-
ванням впливу теплового випромiнювання на поверхнях, у частково прозорих обла-
стях i на межах контакту. Записано вихiднi спiввiдношення моделi для нескiнченних
двошарових пластин за рiзних комбiнацiй радiацiйних властивостей складникiв. За-
пропоновано методи розв’язку нових нелiнiйних задач. Виявлено, на основi аналiзу
знайдених розв’язкiв, ряд нових закономiрностей у розподiлах температури та ком-
понент тензора напружень в опромiнюваних шаруватих пластинах залежно вiд умов
закрiплення, радiацiйних властивостей складникiв
A mathematical model to describe a thermoelastic state of plane-parallel plates (plate composites) subjected to a thermal radiation is developed. The model is grounded on phenomenological theory of radiation and quasistatic thermoelasticity. It takes into account an effect of radiation on plate surfaces, contact boundaries, and in semi-transparent areas. It is assumed a perfect contact between the constituents of layers that boundary contact is modeled on the plane surface defined on both sides of its radiation characteristics of the material layers and the conditions of heat and mechanical contacts are ideal. The methods to solve new nonlinear contact-boundaries problems of thermoelasticity are proposed. On analysing the posed problems solutions, the new features of temperature and stresses distributions in plates are established, dependent on radiative properties of layers, layer’s thickness and on source temperature.
A mathematical model to describe a thermoelastic state of plane-parallel plates (plate composites) subjected to a thermal radiation is developed. The model is grounded on phenomenological theory of radiation and quasistatic thermoelasticity. It takes into account an effect of radiation on plate surfaces, contact boundaries, and in semi-transparent areas. It is assumed a perfect contact between the constituents of layers that boundary contact is modeled on the plane surface defined on both sides of its radiation characteristics of the material layers and the conditions of heat and mechanical contacts are ideal. The methods to solve new nonlinear contact-boundaries problems of thermoelasticity are proposed. On analysing the posed problems solutions, the new features of temperature and stresses distributions in plates are established, dependent on radiative properties of layers, layer’s thickness and on source temperature.
Description
Keywords
моделювання, термонапружений стан, теплове опромінення, теплоперенос, багатошарові пластини, частково-прозорі та непрозорі шари, modeling, thermal and stressed states, thermal irradiation, heat transfer, multilayered plates, semi-transparent and opaque layers
Citation
Hachkevych O. The formulation and development of methods of solving thermomechanics problems for irradiated layered solids / O. Hachkevych, R. Terlets’kyi, O. Turii // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 21–36.