While the theory and application of finite elements methods can be
extended to incompatible, hybrid, and mixed element methods,
important issues, such as determining the reliability of the
solution of incompatible multivariable elements, along with a
common perception of impracticality, have hindered the widespread
implementation of these methods. Today, however, recent
advances--many directly attributable to these authors--have allowed
the development of the stability theory and abstract mathematics to
useful tools.
Hybrid and Incompatible Finite Element Methods introduces these
advances in the theory and applications of incompatible and
multivariable finite element methods. After an overview of the
variation formulation of finite element methods in solid mechanics,
the authors discuss the fundamental theory and systematically
demonstrate the theoretical foundations of incompatible elements
and their application to different problems in the theory of
elasticity. They also introduce new ideas in the development of
hybrid finite elements, study the numerical stability of the hybrid
and mixed element, and establish the theory of zero energy
deformation modes. The final chapters, explore applications to
fracture problems, present a bound analysis for fracture
parameters, and demonstrate an implementation of a finite element
analysis program.
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