Abstract
This chapter discusses variational principles as an important part of elasticity theory. These theories have been extensively used in stability analysis of structures made of fiber-reinforced polymer (FRP) composites. Variational principles in buckling analysis of FRP composite structures are presented and studied. A survey of variational principles in stability analysis of composite structures is given, followed by a brief introduction of the theoretical background of variational principles in elasticity. A variational formulation of the Ritz method is used to establish an eigenvalue problem, and by using different buckling deformation functions, the solutions of buckling of FRP structures are obtained. As application examples, the local and global buckling of FRP thin-walled composite structural shapes is analyzed, using the variational principles of total potential. Solutions for local buckling of the plates with various unloaded edge-boundary conditions are developed. For the global buckling of FRP composite beams, the second variation of the total potential energy based on nonlinear plate theory is applied, and the formulation includes the shear effect and beam bending–twisting coupling.
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