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**Mathematical modelling of rods.**
*(English)*
Zbl 0873.73041

Ciarlet, P. G. (ed.) et al., Finite element methods (part 2), numerical methods for solids (part 2). Amsterdam: North-Holland (ISBN 0-444-81794-8). Handbook of Numerical Analysis 4, 487-974 (1995).

This work constitutes an up-to-date and unified account of the contributions of the authors and their collaborators to the field of asymptotic modelling of elastic rods and their relationship with other methods. It represents what we know about the mathematical derivation and justification of models describing the elastic behaviour of rod type structures via asymptotic expansion methods combined with techniques from functional analysis and numerical analysis.

The work is divided into ten chapters and fifty sections. More detailed information can be found in the introductions of each individual chapter or section. Any reader unfamiliar with the application of the asymptotic method in elasticity theory should refer to chapter I for notation and techniques. But for that the chapters are independent of one another and so it should be safe to read them separately.

Contents: Introduction. I. Asymptotic expansion method for a linearly elastic clamped rod. II. Linear asymptotic models. Comparison with classical theories. III. Asymptotic modelling in thin-walled rods - an introduction. IV. Asymptotic expansion method for nonhomogeneous anisotropic rods. V. Asymptotic modelling of rods in linearized thermoelasticity. VI. Asymptotic method for contact problems for rods and rods with a variable cross-section. VII. Rods with a multicellular cross-section. Some homogenization and asymptotic results. VIII. A Galerkin type method for linear elastic rods. IX. Asymptotic method for nonlinear elastic rods. Stationary case. X. Asymptotic method for nonlinear elastic rods. Dynamic case.

For the entire collection see [Zbl 0864.65001].

The work is divided into ten chapters and fifty sections. More detailed information can be found in the introductions of each individual chapter or section. Any reader unfamiliar with the application of the asymptotic method in elasticity theory should refer to chapter I for notation and techniques. But for that the chapters are independent of one another and so it should be safe to read them separately.

Contents: Introduction. I. Asymptotic expansion method for a linearly elastic clamped rod. II. Linear asymptotic models. Comparison with classical theories. III. Asymptotic modelling in thin-walled rods - an introduction. IV. Asymptotic expansion method for nonhomogeneous anisotropic rods. V. Asymptotic modelling of rods in linearized thermoelasticity. VI. Asymptotic method for contact problems for rods and rods with a variable cross-section. VII. Rods with a multicellular cross-section. Some homogenization and asymptotic results. VIII. A Galerkin type method for linear elastic rods. IX. Asymptotic method for nonlinear elastic rods. Stationary case. X. Asymptotic method for nonlinear elastic rods. Dynamic case.

For the entire collection see [Zbl 0864.65001].

### MSC:

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |