A Higher Order Shear Deformation Approach to the Local Buckling Behavior of Moderately Thick Composite Laminated Beams

Abstract

This paper presents a novel closed-form analytical approximate solution for the local buckling behavior of composite laminated beams under uniform axial compression. The laminates that constitute the segments of the beam cross-sections (i.e. webs and flanges) are assumed to be moderately thick so that the current analysis approach is based on Reddy’s third-order shear deformation theory? (TSDT). The idealization relies on the discrete plate approach, meaning that the individual segments are separated from the beam cross-section, and the local buckling behavior is analyzed by performing a TSDT-based plate buckling analysis by assuming adequate boundary conditions for webs and flanges. At those edges where the segment under consideration has been separated from the cross-section, elastic restraints are applied to the stiffness values of which depend on the geometric and material properties of the adjacent segments. The analysis approach uses the principle of minimum elastic potential of the considered discrete plate in the buckled state and relies on rather simple shape functions for the buckling modes, thus eventually enabling a closed-form analytical approximate solution that does not necessitate any numerical means of evaluation. Results are generated for a number of I-beam configurations and are compared to results generated in the framework of classical laminated plate theory (CLPT) and first-order shear deformation theory (FSDT). It is shown that the present new approach delivers reliable results without any significant computational effort and thus can be recommended for all engineering analysis tasks where computational time and effort are deciding factors in day-to-day engineering work, such as systematic optimizations or extensive parametric studies.