An asymptotic analysis of composite beams with kinematically corrected end effects

Abstract

A finite element-based beam analysis for anisotropic beams with arbitrary-shaped cross-sections is developed with the aid of a formal asymptotic expansion method. From the equilibrium equations of the linear three-dimensional (3D) elasticity, a set of the microscopic 2D and macroscopic 1D equations are systematically derived by introducing the virtual work concept. Displacements at each order are split into two parts, such as fundamental and warping solutions. First we seek the warping solutions via the microscopic 2D cross-sectional analyses that will be smeared into the macroscopic 1D beam equations. The variations of fundamental solutions enable us to formulate the macroscopic 1D beam problems. By introducing the orthogonality of asymptotic displacements to six beam fundamental solutions, the end effects of a clamped boundary are kinematically corrected without applying the sophisticated decay analysis method. The boundary conditions obtained herein are applied to composite beams with solid and thin-walled cross-sections in order to demonstrate the efficiency and accuracy of the formal asymptotic method-based beam analysis (FAMBA) presented in this paper. The numerical results are compared to those reported in literature as well as 3D FEM solutions.