Semi-inverse Method in Nonlinear Problems of Axisymmetric Shells Forming

Semi-inverse Method in Nonlinear Problems of Axisymmetric Shells Forming

Anatoly S Yudin, Dmitry V Shchitov


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Currently, solving problems based on designing and calculating complex structures with significant nonlinearity usually require:Semi-inverse Method in Nonlinear Problems of Axisymmetric Shells Forming 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.Contents:

  • About This Book
  • Preface
  • About the Authors
  • Introduction
  • Generalization of E Reissner's Equations for the Problem of Shells of Rotation Deformation
  • Large Plastic Deformation of Shells of Rotation
  • Membranes in Systems for the Protection of Equipment from Destruction by Excessive Pressure
  • Stretching of Dome Shell From a Circular Plate
  • Solving Problems of Changing the Form of Some Shells of Rotation
  • About Containers for Liquid Cargo Transportation
  • Jack Systems in Construction
  • Equations for Axisymmetric Shells Calculating within the Elasticity Limits
  • Conclusion
  • References
  • Index

Readership: Recommended for researchers, graduate students and advanced undergraduates studying physical and mathematical engineering as well as scientific and technical workers dealing with thin-walled structures.Mathematical Modeling;Shell Shapes;Adequate Equations;Large Deformations;Large Displacements and Rotation Angles;Material Loading Diagrams;Power Approximation;Building Physical Relations;Davis–Nadai Materials;Equipment Protection from Destruction by Excessive Pressure;Safety Membranes;Membranes;Popping Membranes;Bursting Discs;Experiments and Manufacturing Technologies;Semi-inverse Method;Spherical and Spheroidal Domes;Inflating a Cylindrical Shell;Tank Strength Problems;Bottom-Weak Link;Destruction;Mathematical Modeling of Shape Changes by the Semi-Inverse Method;Flat Jacks;Piston Jacks;Geometry Variations;Elastic State;Flat Jack Operation by Semi-inverse Method;Elasticity Equations;Sealing Shells of Hydraulic Connections0Key Features:
  • Provides a mathematical model adequate to the problem of complex shape of shells, taking into account the new metric and the physics of plastic behavior of the material
  • Gives an original semi-analytical method that allows the user to effectively solve essentially nonlinear problems
  • Application of real-life engineering problems are included in the book


Anatoly S Yudin: