N. Bencharif et Sf. Ng, LINEAR AND NONLINEAR DEFLECTION ANALYSIS OF THICK RECTANGULAR-PLATES .2. NUMERICAL APPLICATIONS, Computers & structures, 50(6), 1994, pp. 763-776
Variational methods are widely used for the solution of complex differ
ential equations in mechanics for which exact solutions are not possib
le. The finite difference method, although well known as an efficient
numerical method, was applied in the past only for the analysis of lin
ear and non-linear thin plates. In this paper the suitability of the m
ethod for the analysis of non-linear deflection of thick plates is stu
died for the first time. While there are major differences between sma
ll deflection and large deflection plate theories, the former can be t
reated as a particular case of the latter, when the centre deflection
of the plate is less than or equal to 0.2-0.25 of the thickness of the
plate. The finite difference method as applied here is a modified fin
ite difference approach to the ordinary finite difference method gener
ally used for the solution of thin plate problems. In this analysis th
in plates are treated as a particular case of the corresponding thick
plate when the boundary conditions of the plates are taken into accoun
t. The method is first applied to investigate the deflection behaviour
of clamped and simply supported square isotropic thick plates. After
the validity of the method is established, it is then extended to the
solution of rectangular thick plates of various aspect ratios and thic
knesses. Generally, beginning with the use of a limited number of mesh
sizes for a given plate aspect ratio and boundary conditions, a gener
al solution of the problem including the investigation of accuracy and
convergence was extended to rectangular thick plates by providing mor
e detailed functions satisfying the rectangular mesh sizes generated a
utomatically by the program. Whenever possible results obtained by the
present method are compared with existing solutions in the technical
literature obtained by much more laborious methods and close agreement
s are found. The significant number of results presented here are not
currently available in the technical literature. The submatrices invol
ved in the formation of the finite difference equations from the gover
ning differential equations are generated directly by the computer pro
gram. The subroutine SOLINV using the change of variable technique ill
ustrated elsewhere takes care of the solution of the general system. S
implicity in formulation and quick convergence are the obvious advanta
ges of the finite difference formulation developed to compute small an
d large deflection analysis of thick plates in comparison with other n
umerical methods requiring extensive computer facilities.