Some comments on the status of shell theory at the end of the 20th century - Complaints and correctives

摘要

This review is divided into complaints and correctives. ^Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the misnaming or miscrediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory is fundamentally different from 3D elasticity; and the irrelevance of Cosserat-type theories. ^Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because in the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally; (5) all equations may be expressed in coordinate-free form. ^(Author)