Multifield Variational Sectional Analysis for Accurate Stress Computation of Multilayered Composite Beams

Abstract

A multifield variational beam sectional analysis is proposed based on the Hellinger-Reissner principle for anisotropic beams with arbitrary cross-sectional geometries and material distributions. Both stresses and threedimensional (3D) warping deformations are treated as unknowns, which are modeled using the isoparametric finite element (FE) shape functions. The nodal stresses are solved on each material domain, resulting in the required continuity within the domain and discontinuity at the material interfaces. A generalized Timoshenko-like stiffness matrix is constituted from the 3D warping solution inherently describing Timoshenko model for transverse shear, Poisson deformations, and associated couplings. The accuracy of the present analysis is demonstrated for benchmark composite beams with elastic couplings. The computed elastostatic responses are in excellent agreement with those of 3D FE analysis and experimental data. The stress predictions from the present multifield formulation show excellent correlation with 3D FE results using fewer elements in comparison to the conventional displacement-based approach while maintaining the stress continuity requirements for multilayered composite beams.

Closed-Form Analysis of Thin-Walled Composite Beams Using Mixed Variational Approach

“…where A ij and B ij (i, j = 1, 2, 6) are the laminate stiffness components defined in Equation (9). It is noted that the above 0 ss is constructed from the constitutive relations (not from the kinematics).…”

“…Many beam theories have been devised for generic cross-section analysis methods with detailed cross-sectional warpings and elastic coupling effects of composites. These range from finite element (FE)-based cross-section analyses [5][6][7][8][9], polynomial or series expansion methods [10][11][12], closed-form elasticity solutions [13,14], contour-based analytic formulations [15][16][17][18][19], and to semi-analytic approaches [20][21][22].…”