A simple and efficient curved beam element for the linear and nonlinear analysis of laminated composite structures.

*(English)*Zbl 0638.73030Summary: The paper reports on the development and application of a curved, two- noded beam finite element capable of analyzing the pre- and post-buckling behavior of laminated anisotropic structures undergoing large elastic deformations (displacements and rotations). The total number of the elemental degrees-of-freedom equals six. The formulation of the geometrically nonlinear problem is performed along the lines of the ‘updated Lagrangian’ (UL) description of motion. The development of the pertinent element matrices is based on a modified version of the variational theorem due to Hellinger and Reissner which - unlike the ‘classical’ assumed displacement formulation - allows for stress resultants and displacements to be approximated independently from one another. In order to assess the performance of the element, a number of sample problems were investigated. Some of the numerical results obtained are presented and discussed in the final part of the paper.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74E30 | Composite and mixture properties |

74B20 | Nonlinear elasticity |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |