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1.

図書

図書
Philippe G. Ciarlet
出版情報: Amsterdam ; Tokyo : North-Holland, 2000  lx, 599 p. ; 24 cm
シリーズ名: Studies in mathematics and its applications ; v. 29 . Mathematical elasticity ; v. 3
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Linear Shell Theory / Part A:
Three-dimensional linearized elasticity and Korn's inequalities in curvilinear coordinates / 1:
Inequalities of Korn's type on surfaces / 2:
Asymptotic analysis of linearly elastic shells: Preliminaries and outline / 3:
Linearly elastic elliptic membrane shells / 4:
Linearly elastic generalized membrane shells / 5:
Linearly elastic flexural shells / 6:
Koiter's equations and other linear shell theories / 7:
Nonlinear Shell Theory / Part B:
Asymptotic analysis of nonlinearly elastic shells: Preliminaries / 8:
Nonlinearly elastic membrane shells / 9:
Nonlinearly elastic flexural shells / 10:
Koiter's equations and other nonlinear shell theories / 11:
Linear Shell Theory / Part A:
Three-dimensional linearized elasticity and Korn's inequalities in curvilinear coordinates / 1:
Inequalities of Korn's type on surfaces / 2:
2.

図書

図書
Philippe G. Ciarlet
出版情報: Amsterdam ; Tokyo : North-Holland, 1988  xl, 451 p. ; 23 cm
シリーズ名: Studies in mathematics and its applications ; v. 20 . Mathematical elasticity ; v. 1
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Description of Three-Dimensional Elasticity / Part A:
Geometrical and other preliminaries / 1:
The equations of equilibrium and the principle of virtual work / 2:
Elastic materials and their constitutive equations / 3:
Hyperelasticity / 4:
The boundary value problems of three-dimensional elasticity / 5:
Mathematical Methods in Three-Dimensional Elasticity / Part B:
Existence theory based on the implicit function theorem / 6:
Existence theory based on the minimization of the Energy / 7:
Bibliography
Index
Description of Three-Dimensional Elasticity / Part A:
Geometrical and other preliminaries / 1:
The equations of equilibrium and the principle of virtual work / 2:
3.

図書

図書
Philippe G. Ciarlet
出版情報: Amsterdam ; New York : North-Holland , New York : Sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1978  xvii, 530 p. ; 23 cm
シリーズ名: Studies in mathematics and its applications ; v. 4
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Preface to the Classics Edition
Preface
General plan and interdependence table
Elliptic boundary value problems / 1.:
Introduction
Abstract problems / 1.1.:
The symmetric case. Variational inequalities
The nonsymmetric case. The Lax-Milgram lemma
Exercises
Examples of elliptic boundary value problems / 1.2.:
The Sobolev spaces H[superscript m] ([Omega]). Green's formulas
First examples of second-order boundary value problems
The elasticity problem
Examples of fourth-order problems: The biharmonic problem, the plate problem
Bibliography and Comments
Introduction to the finite element method / 2.:
Basic aspects of the finite element method / 2.1.:
The Galerkin and Ritz methods
The three basic aspects of the finite element method. Conforming finite element methods
Examples of finite elements and finite element spaces / 2.2.:
Requirements for finite element spaces
First examples of finite elements for second order problems: n-Simplices of type (k), (3')
Assembly in triangulations. The associated finite element spaces
n-Rectangles of type (k). Rectangles of type (2'), (3'). Assembly in triangulations
First examples of finite elements with derivatives as degrees of freedom: Hermite n-simplices of type (3), (3'). Assembly in triangulations
First examples of finite elements for fourth-order problems: the Argyris and Bell triangles, the Bogner-Fox-Schmit rectangle. Assembly in triangulations
General properties of finite elements and finite element spaces / 2.3.:
Finite elements as triples (K, P, [Sigma]). Basic definitions. The P-interpolation operator
Affine families of finite elements
Construction of finite element spaces X[subscript h]. Basic definitions. The X[subscript h]-interpolation operator
Finite elements of class l[superscript 0] and l[superscript 1]
Taking into account boundary conditions. The spaces X[subscript 0h] and X[subscript 00h]
Final comments
General considerations on convergence / 2.4.:
Convergent family of discrete problems
Cea's lemma. First consequences. Orders of convergence
Bibliography and comments
Conforming finite element methods for second order problems / 3.:
Interpolation theory in Sobolev spaces / 3.1.:
The Sobolev spaces W[superscript m,p]([Omega]). The quotient space W[superscript k+1,p]([Omega])/P[subscript k]([Omega])
Error estimates for polynomial preserving operators
Estimates of the interpolation errors |v - [Pi subscript K]v|[subscript m,q,K] for affine families of finite elements
Application to second-order problems over polygonal domains / 3.2.:
Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 1,[Omega]
Sufficient conditions for lim[subscript h[right arrow]0 double vertical line]u - u[subscript h double vertical line subscript 1,[Omega] = 0
Estimate of the error
Concluding remarks. Inverse inequalities
Uniform convergence / 3.3.:
A model problem. Weighted semi-norms |.|[subscript [phi],m,[Omega]
Uniform boundedness of the mapping u [right arrow] u[subscript h] with respect to appropriate weighted norms
Estimates of the errors
Other finite element methods for second-order problems / 4.:
The effect of numerical integration / 4.1.:
Taking into account numerical integration. Description of the resulting discrete problem
Abstract error estimate: The first Strang lemma
Sufficient conditions for uniform V[subscript h]-ellipticity
Consistency error estimates. The Bramble-Hilbert lemma
A nonconforming method / 4.2.:
Nonconforming methods for second-order problems. Description of the resulting discrete problem
Abstract error estimate: The second Strang lemma
An example of a nonconforming finite element: Wilson's brick
Consistency error estimate. The bilinear lemma
Estimate of the error ([Sigma subscript K[set membership]t subscript h]
Isoparametric finite elements / 4.3.:
Isoparametric families of finite elements
Examples of isoparametric finite elements
Estimates of the interpolation errors |v - [Pi subscript K]v|[subscript m,q,K]
Application to second order problems over curved domains / 4.4.:
Approximation of a curved boundary with isoparametric finite elements
Taking into account isoparametric numerical integration. Description of the resulting discrete problem
Abstract error estimate
Interpolation error and consistency error estimates
Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 1,[Omega]h]
Additional bibliography and comments
Problems on unbounded domains
The Stokes problem
Eigenvalue problems
Application of the finite element method to some nonlinear problems / 5.:
The obstacle problem / 5.1.:
Variational formulation of the obstacle problem
An abstract error estimate for variational inequalities
Finite element approximation with triangles of type (1). Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 1,[Omega]
The minimal surface problem / 5.2.:
A formulation of the minimal surface problem
Finite element approximation with triangles of type (1). Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 1,[Omega]h]
Nonlinear problems of monotone type / 5.3.:
A minimization problem over the space W[superscript 1,p subscript 0]([Omega]), 2 [less than or equal] p, and its finite element approximation with n-simplices of type (1)
Sufficient condition for lim[subscript h[right arrow]0 double vertical line]u - u[subscript h double vertical line subscript 1,p,[Omega] = 0
The equivalent problem Au = f. Two properties of the operator A
Strongly monotone operators. Abstract error estimate
Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 1,p,[Omega]
Other nonlinear problems
The Navier-Stokes problem
Finite element methods for the plate problem / 6.:
Conforming methods / 6.1.:
Conforming methods for fourth-order problems
Almost-affine families of finite elements
A "polynomial" finite element of class l[superscript 1]: The Argyris triangle
A composite finite element of class l[superscript 1]: The Hsieh-Clough-Tocher triangle
A singular finite element of class l[superscript 1]: The singular Zienkiewicz triangle
Estimate of the error [double vertical line]u - u[subscript h double vertical line subscript 2,[Omega]
Sufficient conditions for lim[subscript h[right arrow]0 double vertical line]u - u[subscript h double vertical line subscript 2,[Omega] = 0
Conclusions
Nonconforming methods / 6.2.:
Nonconforming methods for the plate problem
An example of a nonconforming finite element: Adini's rectangle
Consistency error estimate. Estimate of the error ([Sigma subscript K[set membership]t subscript h]
Further results
A mixed finite element method / 7.:
A mixed finite element method for the biharmonic problem / 7.1.:
Another variational formuiation of the biharmonic problem
The corresponding discrete problem. Abstract error estimate
Estimate of the error (
Concluding remarks
Exercise
Solution of the discrete problem by duality techniques / 7.2.:
Replacement of the constrained minimization problem by a saddlepoint problem
Use of Uzawa's method. Reduction to a sequence of discrete Dirichlet problems for the operator - [Delta]
Convergence of Uzawa's method
Primal, dual and primal-dual formulations
Displacement and equilibrium methods
Mixed methods
Hybrid methods
An attempt of general classification of finite element methods
Finite element methods for shells / 8.:
The shell problem / 8.1.:
Geometrical preliminaries. Koiter's model
Existence of a solution. Proof for the arch problem
The discrete problem. Approximation of the geometry. Approximation of the displacement / 8.2.:
Finite element methods conforming for the displacements
Consistency error estimates
Estimate of the error ([Sigma superscript 2 subscript [alpha] = 1] [double vertical line]u[subscript [alpha] - u[subscript [alpha]h double vertical line superscript 2 subscript 1,[Omega] + [double vertical line]u[subscript 3] - u[subscript 3h double vertical line superscript 2 subscript 2,[Omega])[superscript 1/2]
Finite element methods conforming for the geometry
Conforming finite element methods for shells
A nonconforming method for the arch problem / 8.3.:
The circular arch problem
A natural finite element approximation
A finite element method which is not conforming for the geometry. Definition of the discrete problem
Epilogue: Some "real-life" finite element model examples
Bibliography
Glossary of symbols
Index
Preface to the Classics Edition
Preface
General plan and interdependence table
4.

図書

図書
Philippe G. Ciarlet, Patrick Rabier
出版情報: Berlin ; New York : Springer-Verlag, 1980  vi, 181 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 826
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5.

図書

図書
Philippe G. Ciarlet
出版情報: Amsterdam ; Tokyo : North-Holland, 1997  lxi, 497 p. ; 24 cm
シリーズ名: Studies in mathematics and its applications ; v. 27 . Mathematical elasticity ; v. 2
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Linear Plate Theory / Part A:
Linearly elastic plates / 1:
Junctions in linearly elastic multi-structures / 2:
Linearly elastic shallow shells in Cartesian coordinates / 3:
Nonlinear Plate Theory / Part B:
Nonlinearly elastic plates / 4:
The von Karman equations / 5:
Linear Plate Theory / Part A:
Linearly elastic plates / 1:
Junctions in linearly elastic multi-structures / 2:
6.

図書

図書
Ciarlet, Philippe G. ; Lions, Jacques Louis, 1928-2001
出版情報: Amsterdam ; Tokyo : North-Holl , New York, NY : Elsevier, 1991  ix, 928 p. ; 25 cm
シリーズ名: Handbook of numerical analysis / general editors, P.G. Ciarlet, J.L. Lions ; v. 2
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7.

図書

図書
Ciarlet, Philippe G. ; Lions, Jacques Louis, 1928-2001
出版情報: Amsterdam : North-Holland , New York : Elsevier, 1990  vii, 652 p. ; 25 cm
シリーズ名: Handbook of numerical analysis / general editors, P.G. Ciarlet, J.L. Lions ; v. 1
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8.

図書

図書
general editors, P.G. Ciarlet, J.L. Lions
出版情報: Amsterdam : North-Holland , New York ; Tokyo : Elsevier, 1990-  v. ; 25 cm
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9.

図書

図書
P.G. Ciarlet
出版情報: Paris : Masson , Berlin : Springer-Verlag, 1990  vi, 215 p. ; 24 cm
シリーズ名: Collection recherches en mathématiques appliquées ; 14
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10.

電子ブック

EB
Philippe G. Ciarlet, Patrick Rabier
出版情報: SpringerLink Books Lecture Notes In Mathematics Archive , Springer Berlin Heidelberg, 1980
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