A new approach of improved finite difference scheme on plate bending analysis


ERGÜN A., Kumbasar N.

SCIENTIFIC RESEARCH AND ESSAYS, cilt.6, ss.6-17, 2011 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 6 Konu: 1
  • Basım Tarihi: 2011
  • Dergi Adı: SCIENTIFIC RESEARCH AND ESSAYS
  • Sayfa Sayıları: ss.6-17

Özet

Improved Finite Difference Scheme (IFDS) for thin plates has been provided in a new way which differs from classical finite difference method and has been proposed to provide convergence with using fewer numbers of unknown deflections. For the determination of new finite difference operator, two different load-deflection systems have been considered. The first system consisted of the actual plate and loads on it. The deflected surface of the actual plate has expressed with Lagrange interpolation polynomial depending on unknown plate deflections. The second system consisted of the defined deflected surface on an infinite plate and loadings leading to this deflected surface. Applying Betti's reciprocal theorem on two different load-deflection systems, a new finite difference scheme has been found. The present scheme has been applied to solve rectangular plate bending problems that have various loadings and boundary conditions. The examples of applications by this method indicated that fewer unknowns can be used and the convergence to exact solution can be accurate and rapid. It has been seen that some plate bending problems which have not been solved without computer were analysed in this method by hand. The IFDS is simple and the numerical results agree well with those obtained from other methods.