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Book Summary
Finite element method has been the dominant technique in computational mechanics
in the past decades, and it has made significant contributions to the
developments in engineering and science. Nevertheless, finite element method is
not well suited to problems having severe mesh distortion owing to extremely
large deformations of materials, encountering moving discontinuities such as
crack propagation along arbitrary and complex paths, involving considerable
meshing and re-meshing in structural optimization problems, or having
multidomain of influence in multi-phenomenon physical problems. It is impossible
to completely overcome those mesh-related difficulties by a mesh-based method.
The highly structured nature of finite element approximations imposes severe
penalties in the solutions of those problems.
Finite element method has been the dominant technique in computational mechanics
in the past decades, and it has made significant contributions to the
developments in engineering and science. Nevertheless, finite element method is
not well suited to problems having severe mesh distortion owing to extremely
large deformations of materials, encountering moving discontinuities such as
crack propagation along arbitrary and complex paths, involving considerable
meshing and re-meshing in structural optimization problems, or having
multidomain of influence in multi-phenomenon physical problems. It is impossible
to completely overcome those mesh-related difficulties by a mesh-based method.
The highly structured nature of finite element approximations imposes severe
penalties in the solutions of those problems.