The paper established the displacemental dynamical equations of the middle-thick shells by transverse shearing deformation,based on the geometric equations,physical equations,and middle surface equilibrium equations,concerning five independent variables,i.

The displacement fundamental equations of the thick shallow shells and thick cylindrical shallow shells concerning five independent variables,ie five middle surface displacements were established based on the displacement fundamental equations of the thick shells by transverse shearing deformation and basic hypothesis on shallow shells.

The paper establishs the displacemental fundamental equations of the vibration with middle-thick plates by transvers shearing deformation,based on the geometric equations,inner fundamental relations and mechanical relations,concerning three independent variables,i.

At first, a rotational displacement equation for geometrically nonlinear structures is derived; and then the inner forces and lateral displacements of a sway frame are calculated by the displacement equation; an example has been given for comparing the inner forces and displacements between the second-order and firs.

This paper present the accurate displacement equation of beam subject to bending distortion, the error between accurate solution and approximation solution is analyzed.