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Semi-inverse method in nonlinear problems of axisymmetric shells forming. (English) Zbl 1459.74001

Hackensack, NJ: World Scientific (ISBN 978-1-78634-981-1/hbk; 978-1-78634-983-5/ebook). xv, 230 p. (2021).
Publisher’s description: Currently, solving problems based on designing and calculating complex structures with significant nonlinearity usually require:
Expensive and difficult to learn software packages
High-performance computers
Spare time as calculations take a long time to complete
The book provides an alternative method for solving problems with deep geometric and physical nonlinearity. Easily implemented on normal PCs, this method is fast and creative. The reader can use integrated packages of the MathCad variety that implement “live mathematics”. Such packages give the reader the freedom to create programs for themselves.
In the proposed method, a function for molding pressure is constructed, which is output to a stationary value by varying the shape parameters and edge reactions. The final shape of the shell is given using analytical approximations. Applications of the method are applied to real shell structures. Forming spherical and ellipsoidal shells (flapping membranes), correcting the shape of the bottom of a container for liquid cargo, modeling the operation of a flat jack, and converting a cylindrical shell into a barrel-shape are also considered.

MSC:

74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74K25 Shells
74B20 Nonlinear elasticity
74Sxx Numerical and other methods in solid mechanics

Software:

Mathcad
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