Finite Rotation Shells ― Basic Equations and Finite Elements for Reissner Kinematics
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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.
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