(untitled) (Journal of Engineering, 2024)
A static analysis of cellular plate structures of linearly varying depth is presented by using the simplified grillage method. The cellular plate structure in this study consists of top and bottom flange plates (non-parallel) separated by longitudinal webs having varying depth. A variational formulation of thin-walled beam element with linearly varying depth has been carried out for the derivation of the stiffness matrix of the grillage members for various warping restraint effects. The effect of warping restraint in stiffness is included by two methods, firstly; the implicit method (through the torsional constant) and secondly; by the explicit method (as independent warping degree of freedom). Two differer,t approaches are used to derive the torsional stiffness matrix, namely:by the assumed displacement field and by the differential equation of equilibrium. The effect of secondary shear stresses from the warping restraint is also considercd. The varying cross section properties of the eguivalent grillage members are derived from the properties of the actual cellular plate structure. Several numerical examples and applications are presented . The results are compared with those obtained from the flat plate / shell elements of MSCA.ASTRAN program. Acceptable agreement is obtained.