- Mathematical Elasticity by P.G.Ciarlet -- The notations on the website is based on this book.
- Direct Methods in the Theory of Elliptic Equations, by Necas,J.--Much written about Sobolev spaces defined in Lipschitz boundary
- Elliptic Partial Differential Equations of Second Order(1998) by Gilbarg, D. and Trudinger, N. S.-- Text book of PDEs
- Sobolev Spaces 1st ed. by Adams, R,A.-- Sobolev spaces defined on unbounded domains and iterpolations
- Inequalities in Mechanics and Physics, Duvaut, G. and Lions, J.L. --Book on continuum mechanics
- Mathematical elasticity Vol.1 -- 3D Elasticity by Ciarlet, P.G. -- My foundation on Elasticity
- Elliptic Problems in Domains with Piecewise Smooth Boundaries, by Nazarov, S.A. and Plamenevsky, B.A --Dealing with crack problems and J-integral (Cherepanov-Rice integral)
- Non-Homogeneous Boundary Value Problems and Applications, by J.L.Lions and E.Magenes -- Interpolations of Sobolev spaces
- Singularities in Boundary Value Problems by Grisvard, P. -- Introductory book on solutions of PDEs with singularity in domains with corner
- Introduction fo Shape Sensitivity by Sokolowski, J.and Zolesio, J.-P,--Introduction to shape sensitivity analysis }
- Nonlinear Functional Analysis and its Applications II/A, by Zeidler. E. -- Linear Monotone Operators Nonlinear Functional Analysis and its Applications II/B, by Zeidler. E. -- Noninear Monotone Operators}
- Nonlinear Functional Analysis and its Applications III, by Zeidler. E. -- Variational Methods and Optimization
- Nonlinear Functional Analysis and its Applications IV, , by Zeidler. E. -- Applications to Mathematical Physics
They are books that I often refer to, and many of them were read during graduate school. Most of them are purchased as electronic books or scanned and used.
- Functional Analysis, by Yoshida K. -- Basic book of functional analysis
- Solution of Variational Inequalities in Mechanics, by Hlavacek.I. and J. Haslinger, J., Necas, J. and Lovlsek, J.-- Unilateral Problems, One-sided contact, Plasticity
Continuum Mechanics and Shape Optimization
- Comception optimale de structures.pdf, by Allaire, G.-- Numerical examples I used
- Perturbation+Analysis+of+Optimization+Pr.pdf, by Bonnans, J.F. and Shapiro, A.
- Topological Derivatives in Shape Optimization, by Novotny, A.A. and Sokolowski,J.-- Textbook of topological derivatives, Eshelby's
- Topology Optimization, by M.P. Bends$\phi $e, M.P. and Sigmund, O.-- Text about "What is topology optimization"
- Shape sensitivity analysis via minmax differentiability, by Delfour.M.C.ssnf . Zoléio -- Important paper to refer to when dealing with the Lagrange multiplier method
- Homogenization and Porous Media, by Allaire, G., Arbogast, T., Auriault, J.L. and Bourgeat. A.-- I want to target Porous Media in the future
- Numerical analysis and optimization, Allaire, G.-- Textbook
- Thermal Stresses-Advanced Theory and Applications, by Hetnarski, R.B. and Eslami, M.R.-- For the future
- Topological Derivatives in Shape Optimization by A.A.Novotny and J. Sokolowski-- 2.5 Eshelby Energy-Momentum Tensor
- Elementary Differential Geometry, by Pressley, A.-- In 3-d fracture, Geodesic coordinates is used.
Numerical Analysis (FEM)
- Finite element analysis using Mathematical programming language FreeFem++ in Japanese,by Ohtsuka, K. and Takaishi, T.-- Basics of FreeFEM programming and applications to continuum mechanics, shape optimization by GJ-integral, reaction-diffusion system
- Theory and Practice of FiniteElements, Em, A. and Guermond,J.-L.-- From theory to notes on coding
- Fracture Mechanics - Inverse Problems and Solutions, by Bui, H.D. -- Short summary of cracked materials, non-homogeneous materialss, composite materials, dissimilar interface, etc.
- Mathematical and Computational Analyses of Cracking Formation. by Sumi, Y. -- Theoretical researches in Fracture mechanics
- Analysis of Cracks in Solids, by Khludnev, A.M. and Kovtuenko, V.A.-- Variational methods in Crack problems
- Multiscale modeling in continuum mechanics and structured deformations, Energy Minimization for Isotropie Nonlinear Elastic Bodies by M. Silhavy; Variational Problems of Crack Equilibrium and Crack Propagation by Le,K.G; Griffith Theory Revisited by Marigo, J.-J.; Foundations of the Theory of Structured Deformations by Piero. G.D.; Second-Order Structured Deformations: Approximation Theorems by Paroni，R.; Crystalline Plasticity and Structured Deformations by Deseri, L.; Elastieity with Disarrangements by Owen, D.R.
- Shape Optimization Problems by H.Azegami, H1-gradient method
- Introduction fo Shape Sensitivity by Sokolowski, J.and Zolesio, J.-P,--Hadamard formula
- Optimal Shape Design for Elliptic Systems by Olivier Pironneau
Information about the page: The current position is orange filled circle circle in the diagram below. Blue is the My favorite books in Library and orange is a duplicate for public use, where dashed line means the intrface to the Library in private.