A new generalized approach for implementing any homogeneous and non-homogeneous boundary conditions in the generalized di erential quadrature analysis of beams

In this paper, a new way of implementing any homogeneous and nonhomogeneousboundary conditions in the generalized dierential quadrature (gdq)analysis of beams is presented. like analytical methods in the solution of a dierentialequation, this approach governs the general solution of gdq discrete equations for thedierential equation of beams by assuming some unknown constants, and satises theboundary conditions in the general solution. then, unknown constants are evaluated bysolving the resultant algebraic equation system. thus, the particular solution for thebeam equilibrium dierential equation is obtained by the gdq method. as described,this approach satises the boundary conditions in the general solution, so, it is referredto as sbcgs (satisfying the boundary conditions in the general solution). the sbcgsapproach can satisfy any type of boundary condition exactly at boundary points with highaccuracy and can easily be implemented for each type of boundary condition. so, thisapproach overcomes the drawbacks of previous approaches by its generality and simplicity.at the end of this paper, a comparison of the sbcgs approach, using the method ofsubstitution of boundary conditions into governing equations (the sbcge approach), ismade by their accuracy with the analysis of beam equilibrium under lateral loading withcombinations of simply supported and clamped boundary conditions. other boundaryconditions and dierent numbers of mesh point results are also discussed for the sbcgsapproach only. the results indicate that although the sbcgs approach is essentially verysimilar to some other approaches, like sbcge, it is an easy and powerful method forimplementation of any boundary condition to the gdq governing equations, and provideshighly accurate results.