A Method for Exact Series Solutions in Structural Mechanics

A systematic analysis method for solving boundary value problems in structural mechanics is presented. Euler-Lagrange differential equations are transformed into integral form with respect to sinusoidal weighting functions. General solutions are represented by complete sets of functions without being concerned with boundary conditions in advance while all boundary conditions are satisfied in the process. The convergence of results is assured, and the procedure leads to pointwise exact solutions. A number of simple structural mechanics problems of stress, buckling, and vibration analyses are presented for illustrative purposes. All results have verified the exactness of solutions, and indicate that this unified method is simple to use and effective.