Finite Element Plate Bending Equilibrium Analysis

For the problem of elastic plate bending, a finite element procedure based on the minimum of complementary energy principle is developed. Primary variable of the problem is the distribution of the bending moments m_x, m_y and m_xy. These vary parabolically inside each triangular element and have continuous values throughout the plate. In order to satisfy the equilibrium conditions, Lagrangean multipliers are introduced as secondary variables. It is then shown that these multipliers are generalized displacement parameters. The final solution will therefore provide direct information about both the stress distribution and the displaced shape of the plate. Equilibrium conditions are satisfied exactly. A strain energy bound is found. For several cases numerical results are given and compared with known solutions.