Before revision: The Euler–Bernoulli hypotheses that plane sections remain plane and normal to the axis of the beam lead to displacements of the form Using the definition of the Lagrangian Green strain from finite strain theory, we can find the von Kármán strain for the beam that are valid for large rotations but small strains by discarding all the higher-order terms (which contain more than two fields) except From the principle of virtual work, the balance of forces and moments in the beams gives us the equilibrium equations where is the axial load, is the transverse load, and To close the system of equations we need the constitutive equations that relate stresses to strains (and hence stresses to displacements).
After revision: The Euler–Bernoulli hypotheses that plane sections remain plane and normal to the axis of the beam lead to displacements of the form Using the definition of the Lagrangian Green strainsThe resulting strains take the form: from finite strain theory, we can find the von Kármán strain for the beam that are valid for large rotations but small strains by discarding all the higher-order terms (which contain more than two fields) except From the principle of virtual work, the balance of forces and moments in the beams gives us the equilibrium equations where is the axial load, is the transverse load, and To close the system of equations we need the constitutive equations that relate stresses to strains (and hence stresses to displacements).