An alternative first-order shear deformation concept and its application to beam, plate and cylindrical shell models

A physical–mathematical interpretation of the alternative first-order shear deformation concept proposed by the author is first presented to get rid of an intuitive aspect of its basic premise that the total deflection w can be assumed as the sum of the bending and transverse shear deflections wb and ws. Then, on the basis of several beam and plate illustrative examples, the qualitative theoretical framework of the alternative concept is clarified by comparing with the traditional Timoshenko beam and Mindlin–Reissner plate theories. In addition, a new first-order shear deformation cylindrical shell theory is developed based on the alternative concept and Hamilton’s principle to obtain a frequency formula for in-plane vibrations of a thick ring. Finally, the physical–mathematical position of the present theory among the conventional thin-walled structure analysis models is deliberated. The result shows that the present theory is regarded as a refined mathematical generalization of the so-called corrected classical theory and it could lead to a reduction in the number of fundamental variables and governing equations in the modeling of the transverse shear deformable composite structures.