Explicit Buckling Analysis of Fiber-reinforced Plastic Structural Shapes
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In this dissertation, the comprehensive explicit local, distortional, and global (flexural-torsional) buckling analyses of fiber-reinforced plastic (FRP) structural shapes are presented. Based on the energy method, the explicit formulas for local, distortional, and flexural-torsional buckling of thin-walled FRP beams under transverse loading are derived. The eigenvalue problems are established based on the total potential energy function and considering the boundary and loading conditions, of which the buckled shape functions are treated as admissible shape functions for either intended rectangular plates or FRP beams. The buckling analysis of both rotationally- and vertically-restrained orthotropic composite plates subjected to uniform compression is first conducted to obtain the explicit solutions. The explicit formulas for the local buckling loads of rotationally-restrained orthotropic plates subjected to various in-plane loads under generic boundary conditions are also obtained. Using the discrete plate analysis technique, the closed-form explicit solution for the critical buckling of restrained plate components under the combined in-plane shear and in-plane bending is applied to the web local buckling analysis of several common FRP structural shapes (i.e., Box-, I-, C-, Z-, T-, and L-section beams) under transverse loading. Based on the energy method and generic displacement shape function, the closed-form explicit solution for the flexural-torsional buckling of thin-walled open section beams is proposed, and it is applicable to eight different beam end boundary conditions by adjusting the spring stiffness. The explicit method is also capable of dealing with different loading cases by calculating the corresponding stress resultants acting on the plate components of the beams. Simple procedures to construct the displacement field of the I-section beams in distortional buckling mode are proposed. Taking advantage of the kinematic assumptions of each plate component, the order of the eigenvalue problem is significantly reduced. The explicit formulas for distortional buckling of double symmetric and monosymmetric FRP I-section beams are developed. To verify the explicit solutions for the stability of FRP structural shapes, the numerical finite element analyses are conducted, and reasonable agreements between the explicit and numerical solutions are obtained, thus validating the accuracy of the proposed approximate explicitness of formulas for buckling analyses of composite structures. The theoretical methods and admissible shape functions presented are useful for deriving effective explicit solutions for relatively complex problem of structural stability; while the explicit solutions proposed in this study for local, distortional, and flexural-torsional buckling analysis of thin-walled FRP structures can facilitate design, analysis and optimization of existing and new composite structures and assist the preliminary design in practical analysis.