Potential Method in Mathematical Theories of Multi-Porosity Media

ISBN-13: 9783030280215 / Angielski / Twarda / 2019 / 302 str.

Merab Svanadze

Recenzje

"This monograph is a valuable contribution to mathematical physics." (Vladimir Mityushev, zbMATH 1481.74007, 2022)

Spis treści

Preface.- Introduction.- Fundamental Solutions in Elasticity.- Galerkin-Type Solutions and Green's Formulas in Elasticity.- Problems of Steady Vibrations of Rigid Body.- Problems of Equilibrium of Rigid Body.- Problems of Steady Vibrations in Elasticity.- Problems of Quasi-Static in Elasticity.- Problems of Pseudo-Oscillations in Elasticity.- Problems of Steady Vibrations in Thermoelasticity.- Problems of Pseudo-Oscillations in Thermoelasticity.- Problems of Quasi-Static in Thermoelasticity.- Problems of Heat Conduction for Rigid Body.- Future Research Perspectives.

Blurb

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.  These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain).  

Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials.  The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models.

Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.