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

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