A Hybrid of the New Conjugate Gradient Method and Galerkin Theory for Optimizing Beam Deflection under Uniformly Distributed Load

A hybrid of the new Conjugate gradient method and Galerkin theory has been used to find the maximum deflection of a beam under uniformly distributed load. Maximum deflection of a beam under a given pressure was found by solving a two-point linear, second order, boundary value problem with homogeneous boundary conditions without evaluating the inverse of a matrix. An objective function associated with a given member of this class of boundary value problems was optimized. The numerical results obtained from solving some of these problems are very close to the exact solutions. This method is easy to implement and automate computer-wise.