BENDING OF BEAMS, PLATES AND LAMINATES: REFINED THEORIES AND COMPARATIVE STUDIES.

摘要

Bernoulli-Euler beam theory, Kirchhoff's plate theory and classical laminated plate theory are the principal tools for the analysis of slender beams, thin plates and laminates. Theories which account for transverse shear deformations are extensions of these engineering theories. There are, however, additional factors that influence bending-related behavior. They include the consequences of section warping and its concomitant nonclassical surface-parallel stress contributions and transverse normal strain. For materials that are characterized by relatively low elastic modulli in the lateral and transverse directions, these influences are much more pronounced than for conventional isotropic materials. Modern graphite/epoxy composites belong to this class. As these materials are increasingly favored for application, it is imperative that adequate analytical prediction capability be available. It is also desired for the improved theories to retain simplicity consistent with the needed refinements. This facilitates understanding, ease of application and maximum use of existing computational resources. This has provided the motivation for this work. New, comprehensive theories are developed for homogeneous plates, beams of circular cross-section and laminates.;The homogeneous plate theory is also used as a layer model in a ply-level analysis of composite laminates. This firmly establishes the capability of the new theory to model transverse normal strain and cross-section warping-related effects.;Several clamping models are formulated to demonstrate the flexibility available with the new displacement distributions in the idealization of kinematic boundary conditions. An ideal clamping model is identified through an edge-zone analysis.;Applications of practical interest are provided through the study of hygrothermal (related to high temperature and humidity) effects on the response of a cross-ply laminate and a quasi-isotropic laminate under static loading.;Several applications are provided to demonstrate the predictive capability of the new theories. Special emphasis is placed on applications in stress analysis. A qualitative validation is provided for the homogeneous plate equations through a consistent order of magnitude analysis.;This work demonstrates the significance of the nonclassical effects in describing bending related behavior and the exceptional predictive capability of the theories that are developed.