Potential Method in Mathematical Theories of Multi-Porosity Media

Merab Svanadze (Autor)

Buch | Softcover

XVI, 302 Seiten

2020 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-28024-6 (ISBN)

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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 conductionfor 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.

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.

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

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

Erscheinungsdatum	12.11.2020
Reihe/Serie	Interdisciplinary Applied Mathematics
Zusatzinfo	XVI, 302 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	492 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	boundary value problems • Elasticity • Galerkin-type solutions • Laplace transform space • Mathematics and Solid Mechanics • Multi-Porosity Media • Partial differential equations • Porosity materials • Porosity math • Potential Method • Potential method book • Potential method elasticity • Quadruple porosity materials • singular integral equation • Thermoelasticity theory • Thermoelastic Stress Analysis
ISBN-10	3-030-28024-1 / 3030280241
ISBN-13	978-3-030-28024-6 / 9783030280246
Zustand	Neuware