Mathematical Analysis of Continuum Mechanics and Industrial Applications

This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.

Provides state-of-the-art mathematical modeling in continuum mechanics Introduces interesting mathematical applications in industry Gives readers clues to enhance competitiveness and innovation in industrial research on the strength of mathematics Includes supplementary material: sn.pub/extras

Autorentext
Masato KimuraKanazawa University
HiromichiItouTokyo University of Science
Vladimir ChalupeckýFujitsu Ltd.
KohjiOhtsukaHiroshima Kokusai Gakuin University
Daisuke TagamiInstitute of Math-for-Industry, Kyushu University
Akira Takada Asahi Glass Co., Ltd.

Inhalt
Part 1: Fracture Mechanics.- Strong but slippery adhesion of mushroom-shaped polysaccharide gels.- Bridging the scales between discrete and continuum dislocation models.- Phase field crack growth model with Hydrogen embrittlement.- On singularities in 2D linearized elasticity.- Part 2: Shape Optimization.- Two-Parameter Topological Expansion of Helmholtz Problems with Inhomogeneity.- Solution of shape optimization problem and its application to product design.- Shape optimization by GJ-integral: Localization method for composite material.- Shape optimization approach by traction method to inverse free boundary problems.- Part 3: Earthquakes and Inverse Problems.- Synthesis of seismic wave envelopes based on the Markov approximation.- Propagation velocity of pulse-like rupture along earthquake faults.- Inverse Source Problem for a Wave Equation with Final Observation Data.- Part 4: Fluid Mechanics and Interface Dynamics.- The contribution of Kawada to the analytical solution for the velocity induced by a helical vortex filament and modern applications of helical vortices.- A new model for fungal hyphae growth using the thin viscous sheet equations.- On Boundary Conditions for Hele-Shaw Problem.- Part 5: Industrial Applications.- Computer Simulation of the Phase Separation of Polymeric Materials for Industrial Applications.- Highly parallel computation of generalized eigenvalue problem in vibration for automatic transmission of vehicles using Sakurai-Sugiura method and supercomputers.- Mathematical analysis of synchronization from the perspective of network science.- Index