An Intuitive Derivation of Beam Models of Arbitrary Order

This article presents a new beam model that employs recursive derivation procedure enables the user to set order of governing differential equations as an input parameter, without need for ad hoc assumptions or methodologies. novel system kinematic variables, section constants, and functions facilitate development higher-order models retain clear philosophical link classical such Euler–Bernoulli theory Timoshenko theory. The present is type equivalent single layer model, wherein constants are used global stiffness characteristics beam, recover sectional fields displacements, strains, stresses. solved several example beams, results compared finite element analyses. It shown can accurately predict deformed shapes stress each beams. also reveals interesting peculiarity elastic potential energy pertains any unidimensional governed by order.