Finite Rotation Shells: Basic Equations and Finite Elements for Reissner Kinematics by K. Wisniewski

Finite Rotation Shells: Basic Equations and Finite Elements for Reissner Kinematics



Download Finite Rotation Shells: Basic Equations and Finite Elements for Reissner Kinematics




Finite Rotation Shells: Basic Equations and Finite Elements for Reissner Kinematics K. Wisniewski
Language: English
Page: 494
Format: pdf
ISBN: 9048187605, 9789048187607
Publisher: Springer

This book treats the formulation and finite elements for shells, and its subject is defined by the following topics:

Computational mechanics of non-linear shells,

Shell equations: Reissner kinematics, finite rotations, finite strains,

Shell finite elements: 4-node, enhanced or mixed or mixed/enhanced,

Drilling rotation: drilling Rotation Constraint or Allman shape functions,

Normal strain: recovered or parameterized,

Constitutive equations: incremental, plane stress or 3D.

 A wide range of applications of shell elements implies that they should be versatile, i.e. account for finite rotations and strains, admit the incorporation of various constitutive laws and enable convenient linking with other elements. This is a serious challenge, which requires various aspects of the element's formulation to be very advanced.

The basic information on linear shell elements may be found in some textbooks on FEs, but this book contains several advanced topics related to non-linear shells, such as e.g. the parametrization of finite rotations, the methods of including the drilling rotation, various methods of treating the normal strain, and the enhanced as well as mixed and mixed/enhanced finite elements.

Some of these topics have been a subject of my research for years, and all the described methods have been implemented in my own elements, and tested. Therefore, I believe that my understanding of this complicated subject is correct and mature enough to be canned, and presented to others.

From the Back Cover

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements, not included in standard textbooks on finite elements, are addressed.

Key features include: several sets of 3D equations with the rotations introduced by either the polar decomposition equation or the rotation constraint equation; shell equations based on Reissner kinematics for finite rotations and strains, formulated in terms of different strains and stresses; a comprehensive account of finite rotations, including their properties and parameterization, as well as the algorithmic issues pertaining to rotation parameters; a comprehensive description and evaluation of several enhanced, mixed, and mixed/enhanced 4-node elements; a selection of useful remedies for such problems as: poor accuracy of in-plane shear strain, transverse shear locking, over-stiffening of warped elements, locking in sinusoidal bending, and deterioration of accuracy for extremely thin elements; a large set of numerical benchmarks for finite rotation shells; an extensive bibliography and comprehensive index.

Shells have been a subject of the author’s research for years, and all the methods described in the book have been implemented and tested in the field.

The book can be useful for graduate students, professional engineers, and researchers specializing in shells, Finite Elements and applied numerical methods.

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