Potential Method in Mathematical Theories of Multi-Porosity Media

Description

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. Front Matter ....Pages i-xvi Introduction (Merab Svanadze)....Pages 1-23 Fundamental Solutions in Elasticity (Merab Svanadze)....Pages 25-56 Galerkin-Type Solutions and Green’s Formulas in Elasticity (Merab Svanadze)....Pages 57-82 Problems of Steady Vibrations of Rigid Body (Merab Svanadze)....Pages 83-96 Problems of Equilibrium of Rigid Body (Merab Svanadze)....Pages 97-112 Problems of Steady Vibrations in Elasticity (Merab Svanadze)....Pages 113-130 Problems of Quasi-Static in Elasticity (Merab Svanadze)....Pages 131-156 Problems of Pseudo-Oscillations in Elasticity (Merab Svanadze)....Pages 157-166 Problems of Steady Vibrations in Thermoelasticity (Merab Svanadze)....Pages 167-198 Problems of Pseudo-Oscillations in Thermoelasticity (Merab Svanadze)....Pages 199-208 Problems of Quasi-Static in Thermoelasticity (Merab Svanadze)....Pages 209-245 Problems of Heat Conduction for Rigid Body (Merab Svanadze)....Pages 247-271 Future Research Perspectives (Merab Svanadze)....Pages 273-282 Back Matter ....Pages 283-302