Plate and beam moment-field formulation

Governing equations of the linear elastic Euler–Bernoulli beam and pure bending Kirchhoff–Love plate are developed in a pure stress form with the evolution of the bending moments fields. In the case of elastodynamics, the governing equations are used to find mode restrictions of vibration within both structures. These vibration restrictions are then compared with the solutions found through the displacement formulation finding both forms to give the same solution under the same boundary conditions. The waves are assumed to be harmonic with only spatial contributions being examined, validating the stress approach. More advanced cases involving anisotropic and non-classical boundary conditions are also explored to demonstrate further implications of following the stress evolution. Elastostatic plates are examined under the compatibility conditions to be met for moment fields to possess uniqueness and to show the CLM (Cherkaev–Lurie–Milton) invariance of the inhomogeneous plane-stress problem.