Abstract
This chapter is dedicated to theories for the mechanical analysis of structures. An overview of the literature is given based on classical and advanced theories. A general classification is first introduced concerning displacement or mixed models, asymptotic or axiomatic approaches, and equivalent single-layer or layerwise modeling techniques. The proposed classification pertains to beam, plate, and shell models. Classical theories and advanced ones are subsequently presented with precise description of the underlying hypotheses. For the sake of conciseness, the mathematical description is limited to plate structures and beam theories are briefly discussed in the Appendix. Some numerical results are given for layered and sandwich structures with respect to linear bending, free vibration, and buckling analyses. The model assessment allows to define applicability ranges and limitations of these theories.
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