An Overview of Shear Deformation Theories and Their Relationships to the Classical Theory

Abstract The paper presents a review of various shear deformation theories of beams and plates and a critical evaluation of the theories from analysis points of view. In particular post-computation of stresses in composites is revisited and alternative approaches are discussed in light of Paganos works on the subject. In addition, relationships for bending, vibration, and buckling solutions of shear deformation theories in terms of the corresponding solutions of the classical theory are discussed. These relationships may be used to determine the solutions of shear deformation theories by knowing the corresponding solutions of the classical theory. These relationships are also used to develop finite element models of the shear deformation theories of beams and plates. These finite element models, unlike the conventional finite element models, are free of so-called shear locking. Dedication: This work is dedicated to Nicholas J. Pagano, a friend and colleague, on his sixty fifth birthday.

An Overview of Shear Deformation Theories and Their Relationships to the Classical Theory Conference Paper