Papers by Abdall Khatir Ibrahim
Structural Engineering and Mechanics, 2007
ABSTRACT
In recent years there are many plate bending elements that emerged for solving both thin and
thic... more In recent years there are many plate bending elements that emerged for solving both thin and
thick plates. The main features of these elements are that they are based on mix formulation interpolation
with discrete collocation constraints. These elements passed the patch test for mix formulation and
performed well for linear analysis of thin and thick plates. In this paper a member of this family of
elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both
thin and thick plates with geometric nonlinearity. The Von Kármán’s large displacement plate theory based
on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate
the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterativeincremental
procedure is implemented to solve the nonlinear equations. The element is then tested for
plates with simply supported and clamped edges under uniformly distributed transverse loads. The results
obtained using the geometrically NDRM element is then compared with the results of available analytical
solutions. It has been observed that the NDRM results agreed well with the analytical solutions results.
Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and
thick plates with geometric non-linearity
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Papers by Abdall Khatir Ibrahim
thick plates. The main features of these elements are that they are based on mix formulation interpolation
with discrete collocation constraints. These elements passed the patch test for mix formulation and
performed well for linear analysis of thin and thick plates. In this paper a member of this family of
elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both
thin and thick plates with geometric nonlinearity. The Von Kármán’s large displacement plate theory based
on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate
the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterativeincremental
procedure is implemented to solve the nonlinear equations. The element is then tested for
plates with simply supported and clamped edges under uniformly distributed transverse loads. The results
obtained using the geometrically NDRM element is then compared with the results of available analytical
solutions. It has been observed that the NDRM results agreed well with the analytical solutions results.
Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and
thick plates with geometric non-linearity
thick plates. The main features of these elements are that they are based on mix formulation interpolation
with discrete collocation constraints. These elements passed the patch test for mix formulation and
performed well for linear analysis of thin and thick plates. In this paper a member of this family of
elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both
thin and thick plates with geometric nonlinearity. The Von Kármán’s large displacement plate theory based
on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate
the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterativeincremental
procedure is implemented to solve the nonlinear equations. The element is then tested for
plates with simply supported and clamped edges under uniformly distributed transverse loads. The results
obtained using the geometrically NDRM element is then compared with the results of available analytical
solutions. It has been observed that the NDRM results agreed well with the analytical solutions results.
Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and
thick plates with geometric non-linearity