STABILITY ANALYSIS OF SSSS THIN RECTANGULAR PLATE USING MULTI – DEGREES OF FREEDOM TAYLOR MACLAURIN’S SERIES IN GALERKIN’S VARIATIONAL METHOD
The stability analysis of all four edges simply supported (SSSS) thin rectangular plate using multi-degrees of freedom (MDOF) Taylor Maclaurin’s series polynomial function in Galerkin’s variational method has been investigated. This was achieved by truncating the two domain Taylor Maclaurin’s series at the seventh term to evolve the general deflection polynomial function for thin rectangular plate continuum. Consequently, the SSSS plate boundary conditions were applied, reducing the polynomial function to four degrees of freedom function. Thereafter, Galerkin’s model was applied to the classical governing differential equation of uniaxial plate buckling with the improved function to obtain the auxiliary equation, whose lowest eigenvalue corresponds to the SSSS plate buckling load coefficient, K. However, this process was facilitated using the commands in the Mathematica. The average percentage difference of K – values from two previous works and the present study when compared with the exact solution stood at 0.066%, 0.011% and 0.002%respectively.This shows that MDOF function converges better than SDOF function. Among other revelations by the study is that Galerkin’s variational methods remains a veritable tool for MDOF continuum problems.