Study on an alternative deformation concept for the Timoshenko beam and Mindlin plate models

An overall historical survey on the bending and shearing deformation concepts in first-order shear deformation theories is carried out in relation to the corrected classical models from the viewpoint of distinguishability of both the deflections in beams and plates, including the alternative deformation concept for the Timoshenko beam and Mindlin plate models proposed by the author and his co-worker. The survey shows that in the corrected classical models, the bending and shearing deflections are recognized as distinguishable physical entities, and which has gained widespread acceptance in the various fields of continuum and structure mechanics, though both deflections cannot be obtained concurrently using a deductive approach. With regard to the conventional first-order shear deformation theory, both deflections are not to be recognized as distinguishable physical entities, and it is shown that these two deflections cannot be uniquely determined for a beam and cannot be specifically defined for a plate. In contrast to this, the alternative deformation concept is shown to be effective in resolving all the above inconsistencies. To demonstrate its effectiveness and practical advantages, both static and dynamic analyses are carried out. The static analysis involves a simply supported beam subjected to a uniform or concentrated static load, for which both the bending and shearing deflections are obtained concurrently and uniquely in addition to the total deflection using a deductive approach, and a thought experiment that distinguishes both deflections as physical entities is also presented. The dynamic analysis involves the application of an extension of the Southwell–Dunkerley methods for synthesizing frequencies. Based on a series-type synthetic-frequency method established by the author and his co-worker, a frequency analysis with two deflections coupled in series is carried out for isotropic plates and carbon fiber reinforced plastic laminated composite beams. It is also shown that the alternative deformation concept is a model that can contribute to the development of a practical finite element formulation that is free from shear locking.